Statistical Quality Control Methods in Infection Control and Hospital Epidemiology, Part I: Introduction and Basic Theory Author(s): James C. Benneyan Source: Infection Control and Hospital Epidemiology, Vol. 19, No. 3 (Mar., 1998), pp. 194-214 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/30143442 Accessed: 25/06/2010 18:26

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http://www.jstor.org 194 INFECTONCONROL AD0EIDEM00LGYMarch1998

Statistics for Hospital Epidemiology EDITEDBY DAVID BIRNBAUM, PHD, MPH

Statistical Quality Control Methods in Infection Control and Hospital Epidemiology, Part I: Introduction and Basic Theory

James C. Benneyan,PhD

ABSTRACT This articleis the firstin a two-partseries discussing ences for furtherinformation or statisticalformulae. Part II and illustratingthe applicationof statisticalprocess control discusses statisticalproperties of control charts, issues of (SPC)to processes often examinedby hospitalepidemiolo- chart design and optimalcontrol limit widths, alternate pos- gists. The basic philosophicaland theoreticalfoundations of sible SPC approachesto infectioncontrol, some common statisticalquality control and their relationto epidemiology misunderstandings,and more advancedissues. The focus of are emphasizedin order to expand mutualunderstanding both articles is mostly non-mathematical,emphasizing and cross-fertilizationbetween these two disciplines.Part I importantconcepts and practical examples rather than acad- providesan overviewof qualityengineering and SPC,illus- emic theoryand exhaustive calculations (Infect Control Hosp trates commontypes of controlcharts, and providesrefer- Epidemiol1998;19:194-214).

At its most basic level, statisticalquality control is controlcharts to such epidemiologicalconcerns as surgical- rooted in the graphicaland statisticalanalysis of process site infections,bacteremia, Clostridium difficile toxin-positive data for the purposes of understanding,monitoring, and stool assays, medicalintensive-care-unit (ICU) nosocomial improvingprocess performance-general objectives that infections, and needlestick injuries. Additionally,several in essence are quite similar to those of epidemiology. other authors17-26have discussed surveillanceand related Particularadvantages of qualitycontrol charts over other epidemiologytopics that in essence are quite similarto the analysis methods are that they offer a simple graphical philosophyand methods of SPC. manner by which to display process behavior and out- For example,Birnbaum18 recently stated that a "sta- comes, they examine these data chronologicallyas a time tisticallyvalid, systems approachto surveillanceanalysis is series, and, althoughbased in valid statisticaltheory, they the key to determiningwhether occurrenceof unexpected are easy to constructand use. Moreover,once constructed, events is generic ... or an exception"and discussed some even the more complexmethods discussed in partII of this approaches-dependentupon whetherthe underlyingrate series' remainrelatively easy to interpret. is constant,very rare,and so on-for determiningwarning Severalprevious articles that have appearedin this2-5 and thresholdlimits for sentinel events that would signal- and otherjournals' 16discuss healthcare applications of sta- such exceptions.More recently,in a reviewof surveillance tistical quality control charts and other tools generally methodsfor detectingdisease clusters,Jacquez et a124sug- associatedwith statisticalprocess control(SPC), total qual- gested examiningthe time between successive infectious ity management(TQM), and continuousquality improve- diseases with respect to an appropriatenull reference dis- ment (CQI).(Many of these applicationsare describedfur- tribution(assumed by the aboveauthors to be exponential) ther in the "SuggestedReferences" section later in this for non-randombehavior. That is, a deviationfrom the theo- article.)As one recent example,Sellick2 and a subsequent retical exponentialmodel-and in particularan excess of letter by Lee3discussed the basic applicationof statistical several consecutiveshort waitingtimes-would be a low-

From NortheasternUniversity, Boston, Massachusetts. Address reprint requests to James C. Benneyan, PhD, Mechanical, Industrial, and ManufacturingDepartment, 334 Snell EngineeringCenter, Northeastern University, Boston, MA 02115. 96-SX-198.Benneyan JC. Statistical qualitycontrol methods in infectioncontrol and hospital epidemiology,part I: introduction and basic theory.Infect Control Hosp Epidemiol 1998;19:194-214. Vol. 19 No. 3 STATISTICSFOR HOSPITAL EPIDEMIOLOGY 195

probabilityevent if no clusterswere occurringand infec- neering andthe closely relatedfield of operationsresearch tiousdiseases were assumed to occurotherwise over time spanmany industries and utilize a host of methods,increas- accordingto a Poissonprocess. Such deviant observations ing their widespreadgeneral value but makingexplaining thuswould be takenas signalsof the presenceof one or their specificssomewhat of a difficulttask. Nonetheless,to moreinfectious disease clusters. establish some context for later discussion,the remainder As the aboveand other authors indicate, these con- of this section provides a basic overview of some typical cernsare quitesimilar to thosein SPCand therefore also skills and methods used by industrialengineers and com- couldbe handledwith "industrial" statistical quality control mon applicationsof these tools in health care, manufactur- charts.The intent of the current series, therefore, is to relate ing, and other settings. the use of controlcharts to thesegeneral types of epidemio- Most generally,industrial engineers and operations logicalissues and to expandon muchof what has been writ- researcherscan be describedas being concernedwith the ten aboutSPC in the healthcareliterature to dateby clini- scientificstudy, improvement, and optimizationof processes cians, consultants,and other healthcarepractitioners. It and process outcomes of any type and in any industry. shouldbe emphasized,however, that, much like epidemiolo- Clearly,this quite broad definitionmight describe many gy,statistical quality control is a broadfield, and not all tech- types of individualsin a varietyof industries,perhaps includ- nicalissues can possiblybe coveredin satisfactorydepth ing epidemiologistsand health care. Of interestto the pre- here.The currentseries instead aims to providea broad sent article,TQM and SPC fit within the abovedefinition and overviewof subjectsat the foundationof SPC,so thatepi- are an integralpart of most industrialengineers' training. In demiologistsand other clinical researchers, based on their additionto these areas, industrialengineers engage in sev- healthcareexpertise, can consider if andhow to bestincor- eral other activitiesthat can range considerablyfrom basic porateSPC into their other methodologies. Particular atten- managementsupport services through advanced mathemat- tion,for example,is givento providinga broaderunder- icaland optimization techniques. For example, a "traditional" standingof industrialand quality engineering, the general industrialengineer might use tools such as process flow theoreticalbasis of SPC, various approaches to applyingSPC analyses,time and motionstudies, hypothesis tests, design to infectioncontrol data, and the role of controlcharts in of experiments,reliability methods, networktheory, com- establishingand improving consistent processes. For addi- putersimulation, queueing analysis, Markov chain analysis, tionalbackground information, Benneyan6 recently provided game theory, decision analysis,economic analysis,linear a thoroughgeneral introduction tothe use and interpretation and nonlinearprogramming, mathematical modeling and of statisticalprocess control charts in a wide varietyof optimization,and regressionand other statisticalanalyses to healthcareapplications, and several references are provided studyand improveissues relatedto inventorymanagement, herefor readers wishing to pursueany of the discussedtop- productionscheduling, facility and location, scheduling, and ics in greaterdepth. capacityand throughputanalysis."7 Note that many of the A moregeneral objective is to stimulateincreased dia- same mathematicalmodeling and optimization methods also logue,collaboration, and cross-fertilization between industri- frequentlyare used in epidemiology,disease control, and al statisticians,quality engineers, epidemiologists, clinicians, publichealth research.2130 andother healthcare practitioners. By developing a common Althoughthe title of industrialengineering is an arti- understandingof each discipline,similarities between epi- fact of the field'sorigins, it is in manyways todayan unfor- demiologyand quality control, and their potential to comple- tunateand misleadinglabel, perhapsimplying a scope that menteach other, their various methods may be integrated primarilyis limited to industrial or manufacturingcon- betterwhen and where they might be broughtmutually to cerns. An industrialengineer's multidisciplinary nature, in bear on importanthealthcare issues. Finally,this series fact, increasinglyfinds such a person workingin business, hopesto clearup some confusionthat appears to exist in health care, finance, portfolio management,banks, fast- manyrecent healthcare publications, seminars, and training food restaurants,distribution, telecommunications, airline materials,including the role(s)and use(s) of statisticalcon- management,and various other service industries,to name trol charts,selection of an appropriatecontrol chart(s), but a few.This broadscope also is reflectedby the variety underlyingdistributional assumptions, optimal control limit of academic departmentsin which the above topics are widths,various fundamental statistical and technical issues, taught, including management, industrial engineering, and severalother points of concern. mathematics,statistics, computer science, economics,pub- lic policy,electrical engineering, and others. SOME BACKGROUND ON INDUSTRIAL To complicatematters further, within some of these ENGINEERING AND QUALITY ENGINEERING specific industries, an industrialengineer or operations researchermight be knownby some otherlabel. For exam- Overviewof Industrial Engineering ple, within the business community,these disciplinestypi- Due largelyto its historicorigins in the earlypart of cally are referredto as operationsmanagement or manage- this century, the fields of statisticalprocess control and mentscience, here focusingmostly on the applicationof sci- qualityengineering typically are associatedwith industrial entific, quantitative,and optimizationmethods to such engineers and statisticians,often in, but certainly by no areas as employee and product scheduling, pricing and means limited to, manufacturingsettings. Industrialengi- market strategies, service delays, process efficiencies, 196 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

demandforecasting, financial and investment planning, and mon enough that several organizationsand journalsexist basic statisticaland exploratory data analysis. Although the specificallyfor such applicationsand practitioners, including more mathematicalmethods often are categorizedas oper- the healthcare divisions of the Institute for Operations ations researchor managementscience and the less theo- Research and ManagementScience and of the Decision retical methods as industrial engineeringor operations Sciences Institute, the Healthcare Information and management,distinctions between all of the above subspe- ManagementSystems Society, and others. Additionally, the cialties can be quite gray. Instituteof IndustrialEngineers has a healthcare-specific organizationcalled the Society of Health Systems, which Healthcare Applications publishes the Journal of the Society of Health Systems. These same methods also have long been used in Studiesbased more in mathematicaloptimization or opera- health care at operational,clinical, strategic, and public pol- tions research often appear in journals such as Medical icy levels. For example, at least as early as 1916, Frank DecisionMaking, Health Services Research, and others. Gilberth suggested the use of process flow analysis and time and motion studies of hospital systems31to improve Quality Engineering, TQM,and SPC surgery outcomes and to reduce cycle times, delays, and Withinthe broadrange of analysisand optimization waittimes, with a steadygrowth in applicationsthroughout methods discussed above,quality engineers and industrial the 8 decades since these origins. Over 50 years later,for statisticiansfocus on technicaland implementationaspects example, during the period from 1967 to 1982, a team of of qualitycontrol, process improvement,variance reduc- industrialengineers, healthcare researchers, and others tion, and the like. The terms statisticalprocess control, sta- developed the now-familiarconcept of diagnosis-related tisticalquality control, and qualityengineering typically are groups32to serve as a set of precise productor service- used somewhat interchangeably,broadly defined as the familydefinitions, much as those used in industryfor more generaluse of probabilitytheory andvarious graphical and effective management,analysis, budgeting, and cost and statistical methods, including quality control charts and qualitycontrol.33 In manyhospitals and healthmaintenance other tools, to study and improveprocesses, process quali- organizations(HMOs) today, individuals trained in industri- ty, andthus process outcomes.Fundamental concepts with- al engineeringskills generallyexist withinsystems engineer- in this quality-focusedorientation is that almost all health- ing, managementengineering, information systems, or CQIor care systems can be consideredas processes, that all out- TQM departments.For the most partand with some excep- comes are the result of internal and external processes, tions, these functions tend mostly to be oriented more and that these processes exist across time with inherent toward basic industrialengineering projects, rather than variability.That is, when viewed longitudinally(ie, over advancedmathematical optimization research. See Sahney,34 time), these processes exhibit various amountsof consis- Freis,35 Flagle and Young,36and Smalley37for good tent and inconsistenttemporal variability. overviewsof the history of industrialengineering and oper- Objectivesof qualitymanagement are to study,con- ationsresearch in healthcare. trol, and reduce this variationand to improveprocess per- Just a few typicalexamples38,39 of the types of opera- formance otherwise. The concepts and methods of SPC, tional problems in which industrialengineers have been more specifically,are based largelyon the valueof reducing involvedwithin health care includeprocess flow analysis,39 variabilityand on achieving and maintainingconsistent patient routing,40,41space planning,42information systems processes (ie, being in a stable state of statisticalcontrol), planning,43inventory control of hospitalsupplies,44,45 time thereforeplaying an integralrole within the process man- studies of patientor staff activities,46,47queueing analysis of agement philosophyadvocated by the late qualitypioneer appointment access and delays,42,48forecasting bed Dr. W. Edwards Deming and his contemporaries.This needs,49and computer simulationto optimize resources, approachemphasizes a continualfocus on process and qual- staff,panel sizes, and so on.41,42,48,50Some examplesof more ity improvementvia, among other things, the use of statis- operationsresearch and mathematical-optimization-oriented tics and qualitymanagement in orderto developan under- problems in health care include resource scheduling,51 standing-physically, statistically,and otherwise-of the patient admission scheduling,52nurse scheduling,53,54uti- performanceof criticalprocesses. In some cases, this also lization and scheduling of operatingrooms and recovery may meantransitioning from a traditionalquality-assurance rooms,50,55facility design,56 and bed capacity planning.57 orientationfocused largely on inspection,reporting, and reg- Examples of strategic, clinical, and public policy uses of ulatory adherence to a quality-improvementorientation operationsresearch include Markoviananalysis of patient focusedprimarily on process study,continual improvement, care and recovery,56 regional healthcare planning,61-63 and designing better systems. While full discussionis not time and motion surgery standardizationstudies,31,64-66 possiblehere, additionalinformation on Deming'sapproach blood banking,67-69optimization of cancer screening pro- to managingfor qualityin health care and other industries grams,70',71optimal policies for when to accept a not per- can be found in some of the listed references.7"76 fectly compatibleorgan transplant,72optimal time between It is importantto emphasizethat, beyond specificsta- bladdercancer follow-ups," and manyothers. tisticaland graphical methods, the use of SPCis partof this While perhapsnot widespread,the use of industrial larger quality-management-philosophicalapproach to engineeringor operationsresearch in health care is com- understanding,managing, and improvingprocesses, and Vol. 19 No. 3 STATISTICSFOR HOSPITAL EPIDEMIOLOGY 197

that this approachis equallyapplicable to health care, ser- For example, later discussion will suggest several to-date vice, manufacturing,or any other type of process. For unansweredquestions, some of potentiallyhigh interestto example, in their well-knownpapers, Drs. Berwick77and epidemiologists,for which furtherresearch is warranted.A Laffel and Blumenthal22suggested the potentialvalue of few examples include the best approachto low-frequency several aspects of the Deming philosophyto viewing and data;the optimalcontrol limit width in varioushealthcare improvinghealthcare processes. These include, among scenarios;the impact on sensitivityand specificityof the many other importanttopics, the applicationof industrial "within-limitcontrol rules" described in partII; the effect of qualitycontrol methodologies and, most generally,a con- using standardapproaches when assumptionsare not rea- stant and almost obsessive focus on processes and on the sonablymet; the effect of variousproposed short-cuts and study,control, and reductionof poorprocess performance. simplifications;possible ways to handle highly skewed As these physiciansargue, these conceptsand meth- data;SPC approaches to mixed or nonhomogenouspopula- ods are as applicableto health care as they are to more tra- tions;the effect on varioustypes of controlcharts when the ditionalindustries. In 1987, Dr. Deming wrote about the exact time of an infectionis not known,and the best chart need to view health care as a collectionof processes,78and to use under such conditions;and when (andwhen not) to the applicationof qualitycontrol charts to epidemiology updatethe center line and controllimits. and infectioncontrol had been suggested at least as early as 198417and more recently2,18,19,24as previously noted. ROLE OF STATISTICAL CONTROL CHARTS Moreover,various regulatory and accreditationbodies are Basic Definitions and Meaning of a State of expressing a growing interest in the concept of variation Statistical Control reductionand the use of controlcharts. For example,the As discussed above,all healthcareprocesses exhibit Joint Commission on Accreditation of Health Care some amountof randomvariability. For example,although Organizations, the National Committee for Quality the rate of surgical-siteinfections may be somewhat con- Assurance,and others requirethat hospitalsand HMOsbe sistent month to month, the exact numberof infectionsis engaged in CQIactivities, including the applicationof sta- not expectedto be identicalevery monthbut ratherto vary tistical methods such as SPC to critical clinical and non- a certain amountabove and below its long-termaverage. clinicalprocesses. A paper79by several authors from the Furthermore,all such process variabilitycan be classified Centersfor Disease Controlrecently stated that as either "natural"or "unnatural."The naturalvariability of Manyof theleading approaches to directingquality a process is definedas the systemicvariation inherent as a improvementin hospitalsare basedon the principlesof regularpart of the process. Conversely,observations that W.E.Deming. These principles include the use of statistical have very small probabilitiesof occurrence based on the measuresdesigned to determinewhether improvement in regularprocess usuallyare presumedto representspecial qualityhas been achieved. Thesemeasures should include events and deviations from the regular process. Such nosocomialinfection rates. events suggest that the process or environmentfundamen- Finally,it is importantto note that the field of quality tallyhas changed and are consideredto be occurrencesof engineeringis considerablybroader than simplyusing con- nonsystemicunnatural variability. The occurrenceof these trol chartsto monitorand detect specialevents in an other- events is the result of one or more uniqueroot causes that wise statisticallyconsistent process (the "holdingthe gains" are not a part of the regularprocess, if it still was behaving third phase of Juran'squality trilogy80). Some other key in a random but consistent manner and thus exhibiting objectivesof SPC,for example,include achieving a consis- only naturalvariability. tent process, identifyingways to improvethis process, and, The term statisticalcontrol most generallyrefers to as the above quotationindicates, verifying these improve- the stabilityand predictabilityof a process over time. A ments are achieved.In additionto the use of statisticalcon- process that is completelystable and predictableover time trolcharts in these activities(which will be discussedfurther exhibits only naturalvariability, as the regularbehavior of in part II), SPC and qualityengineering also involvetradi- the underlyingprocess remainsunchanged. Such a process tional methods such as hypothesistests, exploratorydata is referred to as being in a state of statistical control. analysis,histograms, scatterplots, correlation and regression Conversely,if the processbehavior changes from its regular analysis,analysis of variance(ANOVA), statistically designed performance, it will exhibit unnatural variability, and the experiments,computer simulation modeling, and others to process is referredto as being out of statisticalcontrol. It is developa statisticalunderstanding of a process.As discussed importantto note thateither the existenceor the lack of sta- subsequently,many of these tools areeither identical or quite tisticalcontrol indicates what type of actionis appropriateto similar to those used in health care by epidemiologists. improvethe process.That is, a key conceptwithin the phi- While the presentarticles focus primarilyon the use of sta- losophy of SPC is that unnaturalprocess variationcan be tisticalcontrol charts in epidemiology,overviews of the gen- reducedor eliminatedonly by identifyingand removingits eralrole of these othervarious quality engineering tools with- nonsystemiccauses fromthe regularprocess (or otherwise in healthcare are discussedfurther elsewhere.81,82 suppressingtheir effect). To improvea processthat exhibits Just as in epidemiology,many quality engineers (the only naturalvariation, however, by definitionit is necessary present authorincluded) also engage in methodsresearch, to change fundamentallythe regularunderlying "common- both of a general theoreticalnature and situation-specific. cause"process. 198 INFECTIONCONTROL AND HOSPrrALEPIDEMIOLOGY March 1998

As a simpleexample, new staffwho followa different groupvalues shouldbe addedonto an establishedchart as clinical procedure might be a source of atypicalprocess soon as possible aftereach becomes available. performance.If a change (forbetter or worse) in the rate of Three horizontallines also are plotted on the chart, surgical-siteinfections was identifiedand tracedto such a referred to as the centerline (CL),the uppercontrol limit cause, then processes and proceduresmight be standard- (UCL),and the lowercontrol limit (LCL).The CLand con- ized to eliminatethis cause andto preventits occurrencein trol limits respectively help define the central tendency the future (or to ensure its occurrence, if the assignable and amountof naturalvariability in the process (eitherhis- cause resulted in a process improvement-a lower infec- torical or hypothesized)and thus are used to detect if the tion rate, for example).If the same proceduresalways are underlyingprocess performancehas changed statistically followed by all staff, conversely,then-all else remaining (ie, whether unnaturalvariation exists). The CL almost unchanged-the monthlynumber of infectionsmost likely always is set equal to the arithmeticmean or expected will exhibit only naturalvariation, and it thereforewill be value of the plotted statistic,so that approximatelyhalf of necessary to study and change these standardprocedures the process data will exist on each side. (The theoretic in order to reduce the infectionrate. Of course, this is an median alternativelymight be used in cases of highly oversimplifiedexample to illustratethe above concepts. In skewed data.69,85)The control limits then usually are set manymore realisticscenarios, without the use of statistical equal to the CL plus and minus three standarddeviations methods, it often is difficultto determineintuitively which of the plottedstatistic (the issue of using some other num- type of variation(natural versus unnatural)is present and, ber of standarddeviations or probability-basedlimits will therefore,which type of process intervention(ie, unique be discussed furtherin part II). identificationor systemwide experimentation)is in order. Furthermore,once an unnaturalevent has been detected, Control Chart Interpretation such as via controlcharts as discussed subsequently,more By observingthe behaviorof an infectionrate or other advancedepidemiological methods may be requiredin the process overtime with respectto a controlchart, a determi- search for its assignablecause(s). nationcan be made aboutthe stability(the "stateof statisti- cal control")of thatprocess. With process datacollected and Statistical Quality Control Charts plottedfrequently and close to the continuousmanner in Qualitycontrol charts are graphicalstatistical tools which they are produced, near-immediateaction can be specificallydesigned to help in the difficulttask of distin- taken to initiateinvestigation and either to correct process guishing between process data that exhibit "common- deteriorationsor to standardizeimprovements. Most gener- cause" naturalvariation and those that exhibit "special- ally,a process is considered(with high probability)to be in cause"unnatural variation, indicating the presence of one statisticalcontrol if all of the plottedsubgroup values exhibit or more special assignable causes. The statisticalcontrol only expected randombehavior over a sufficient span of chart was developed at Bell Laboratoriesby Dr. Walter time. The most familiarindication that a process is out of Shewhartin 1924and has become one of the primarytools controlis if valuesexist outsidethe controllimits. Such out- of modernquality improvement and SPC.While based in a comes exceed their specifiedprobabilistic range and there- bit more statistical theory than meets the eye, control fore are indicationsthat nonsystemic (atypical) causes likely charts also are intendedto be relativelyeasy for nonstatis- exist thatshould be investigatedand, if possible,removed in ticiansand practitionersto use and interpret.Although the orderto achievea single, stable,and predictableprocess. basic format and interpretationof control charts are There also shouldbe no evidenceof non-randomvari- described in greater detail elsewhere,2,6,11,83,84a brief ationbetween the limits,such as trends,cycles, shifts above descriptionfollows. or beneaththe CL,and other forms of non-randomor low- A set of observations(called a subgroupin SPCtermi- probabilitybehavior. Several of these within-limittests willbe nology) periodicallyis sampledfrom the process, and some discussedfurther in part II of this series. Conversely,if no parameteror value of particularinterest, such as the week- signals of specialcauses exist, then no outcomesshould be ly number of patient falls, the weekly proportion of consideredas deviationsfrom the regularprocess, regard- Cesarean-sectionbirths, or the monthly rate of a certain less of any standardsor thresholdsimposed by management type of infection,is estimatedfrom each such subgroupand or some external body. Note that, although unequal sub- plotted on an appropriatecontrol chart, in the manner group sizes, such as a varying number of surgicalproce- shown in later examples.The number of observationsin dureseach week, result in varyingcontrol limits (see below), each subgroupis calledthe subgroupsize andusually denot- their interpretationbasically is the same. Note also that a ed as n. Note that, in some cases, all datafrom each time minimumof at least25 subgroupsof dataare recommended periodare includedin the correspondingsubgroups, and, in in orderto concludethat a process is in statisticalcontrol, a other cases, only a portionof these are sampled (basically requirementthat will be discussedfurther in partII. for economicand logistic reasons,as discussedlater in this series). When first constructinga control chart based on Relation Between Quality Engineering and historicaldata, all past subgroupvalues are calculatedand Hospital Epidemiology plottedat once, in their chronologicalorder, whereas, when As the previous discussions have suggested, many later monitoringa process in relativelyreal time, new sub- similaritiesexist between the general objectivesand meth- Vol. 19 No. 3 STATISTICSFOR HosPITAL EPIDEMIOLOGY 199

TABLE 1 RELATIONBETWEEN STATISTICAL PROCESS CONTROL AND EPIDEMIOLOGY TERMINOLOGY ANDCONCEPTS Statistical Process Control EpidemIology Naturalvariation Generic Common-causeevents Endemic Stateof statisticalcontrol Constantinfection rate Unnaturalvariation Nonendemic Special-causeevents Adverseevents Outof statisticalcontrol Processmonitoring Infectionsurveillance Increasein processrate Epidemic Outof controlpoints Sentinelevents Controllimits Thresholdor actionlimits Supplementaryrun rules Diseasetrends or clusters Confidence Specificity Falsealarm rate, type I error Positivepredictive value* Powerto detectprocess changes Sensitivity TypeII error Negativepredictive value* Reductionof bothunnatural (uncommon) Reductionof bothepidemic and endemic events andnatural (common) cause variation Optimaleconomic design of controlcharts Use of 3-sigmaversus 2-sigma or otherthreshold limits Reliabilityand queueing methods Incidence,prevalence, duration analysis * Not precisely identicalconcepts. ods of industrialquality engineering and those of epidemi- Table 1 summarizesseveral similarities between the ology. In fact, if the languageand terminologywere modi- concepts and terminologyof epidemiologyand statistical fied slightlyin severalarticles authored by epidemiologists, process control. For example, hospital epidemiologypro- many of their statementseasily could read as if they were grams tend to be concerned with both epidemic (nonsys- writtenabout SPC by a qualityengineer or industrialstatis- temic) and endemic (systemic) infections,8swhich in SPC tician. For example, Birnbaum19distinguished between terminologyequate to unnatural(special-cause) and natur- generic process events "requiringsystematic correction" al (common-cause)variability, respectively. While surveil- and exceptionsthat represent"a new class of generic prob- lance programsfocus on the detectionof sentinel and epi- lems (specialcause eventsin CQIjargon)." In a 1979paper, demic events (ie, monitoringfor unnaturalprocess varia- McGuckinand Abrutyn20 described a surveillancemethod tion), the often greater epidemiologyconcern of reducing quite similarto qualitycontrol charts for detectingpotential endemic occurrences equates to the often greater quality- epidemicsand triggeringinvestigative action. control concern of improvinga process whose defect rate Additionally,several other epidemiologists2,17,19have is in a state of statisticalcontrol but still is unacceptably proposedmonitoring infection rates over time in manners high. Additionally,the quality-controlactivity of bringinga that are either identical or quite similar to SPC. Other process into a state of statisticalcontrol (to be discussed authors13,86and a recent series of articles in Quality furtherin part II) basicallyis the same as the infectioncon- Progress8,9also discussed similarities and differences trol activityof removingpreexisting chaos suggested in the between epidemiologyand statisticalquality control meth- recent letter by Lee.3 ods, as well as some possibledifficulties related to the appli- Based on these discussions and similarities, it cationof basic controlcharts to infectioncontrol. Although seems clear that SPC can make several potentialcontribu- a few authors87to some extent have suggested an tions to healthcareepidemiology. For example, aftervari- "either/or"viewpoint, this perspectiveposes the dangerof ous epidemiologymethods first discoverthe risk factorsor drawingattention away from the mutualobjective of analyz- predictorsthat are importantto monitorand control,SPC ing datacreated by a processover time in orderto studyand charts can help monitorthese factors. (Similarto epidemi- improvethat process. It is encouragingthat, despite some ology, a qualityengineer also might use hypothesis tests, concerns aboutthe use of controlcharts in epidemiology, experimental design, ANOVA,regression, truth tables, most healthcarepractitioners appear to view SPCas an addi- time-seriesanalysis, and exploratorydata analysisfor the tionalset of tools for epidemiologiststo use when andwhere investigativeand identificationpurpose, although general- appropriate,rather than as a differentor competingfield. ly not getting into more advancedstatistical methods that 200 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

epidemiologistsor biostatisticiansmight use.) Once iden- companycan influencedriver education programs in order tified, other epidemiologicalor SPC methods also might to reduce claims and premiums."93 be used to analyze these factors, develop a better under- It also is importantto emphasizethat controlcharts standingof their effect, reduce their influenceon the clin- are by no meansjust a "manufacturing"tool but rathercan ical outcomes of concern, and so on. be used to examine outcomes and other dataproduced by Statisticalprocess control also can complementepi- any process, be it manufacturing,healthcare, or other- demiology in the reverse order.That is, SPC charts can wise. For example, it is noteworthy that Dr. Shewhart's identify special-cause (atypical,nonendemic) events that classic 1939 text, StatisticalMethod from the Viewpointof then could be examined in greater detail via classic epi- QualityControl,94 was not writtenfor a manufacturingaudi- demiology,such as in order to identifyexplanatory factors ence (note Shewhart's industry-nonspecific title) but or underlying root causes. As another example of this ratherwas developedfrom a series of lecturesinvited by the potential interaction, several epidemiologists79recently US Departmentof Agriculture,which wished to consider reportedimportant distinctions in infectionrates (such as how these concepts and methods could be appliedto agri- for adult and pediatricICUs, surgical patients, and high- culturalresearch. In this text, Shewhartsuggested that con- risk nursing patients) and recommended that infection trolcharts were applicableto a wide rangeof scientificor sta- rates be based on the numberor durationat-risk (such as tisticalstudies and that non-engineering"data are not to be the number of patient days, surgeries, and device-use regardeddifferently with respect to the assumptionof statis- days), rather than being based simply on the number of tical control"(p 65). Other early uses of controlcharts by admissionsor discharges.A later SPC paper89by a quality Deming and Shewhartincluded their applicationto mea- engineer discussed some approaches to applying SPC surements of the velocity of light, census data, financial charts to any of these specific recommendedcalculation processes, and other nonmanufacturingconcerns. Also see methods and (fairly)homogeneous patientcategories. Latzko,95,6Rosander,97 Deming,98 Philpot,99 Benneyan,10t In additionto controlcharts andthe othertools men- Bicking,o10Mandel,102 Selover,103 Anderson and Diaz,104and tioned previously,many qualityengineers also work with Ramseyand Cantrell105for discussionsof qualityand control stochasticprocesses and reliabilitymethods that are quite charts in the boardroom,service, administration,banking, similarto other epidemiologytools. For example,the equa- accounting,finance, insurance, mail distribution,clerical tion discussedby Birnbaum18relating the prevalenceof the work, government,transportation, freight administration, total numberof cases (P), the incidence of the numberof accountsreceivable, retail trade, national census, criminolo- new cases (I), and the mean durationof disease (D) gy, and publicutilities. Finally,it is interestingthat several metaphorsoften P=(I) (D) used when trainingSPC in other industriesutilize medical concepts, such as monitoringa "patient"(eg, a manufac- is the sameformula that industrial engineers refer to as turing process) for early indicationsthat its conditionhas Little'slaw27,90 and use to investigatethe averageduration deteriorated,so that an interventioncould be takenbefore and averagenumber of people or items in a particularstate deteriorating further. Using such metaphors, factory at any given time (typicaluses are to study queueing,wait- workers and managementoften get beyond their resis- ing, capacity, and throughput). Quality engineers also tance to the applicationof SPC in their workplace(where study system and productreliability with various survival things surely must be different)and are shownthat, just as analysis and special-purposecontrol charts based on the taking a patient'svital signs at the end of every month same cumulativeinfection incidence formulas used by epi- might indicateonly that the patienthad died or survived, demiologists.8 manufacturingshould use real-timeinformation to inter- Finally,very similarto the analyticmaps andlocation vene when a change first occurs. plots recentlydescribed by Jacquezet a124for cancer cases As another example of a "problem-diagnosis- and bone-fractureincidences, industrialand qualityengi- prescription"type of metaphor,consider the language of neers sometimesuse defect locationor concentrationplots Dr. Juran's80"Diagnostic Journey" of discovery, in which to analyzeproblems and inform process improvement.83,91-93one seeks to understandthe possible cause(s) of deteriora- Some representativeexamples of the range of applications tion, and subsequent"Remedial Journey," in which process include the locationof scratches on refrigerators,the type interventionsare made to remedy this condition.Having and location of defects and contaminationparticles on establishedthe above philosophicalfoundation, the follow- printedcircuit boards and semiconductorwafers, the loca- ing section brieflyreviews the theoreticalbasis of standard tion of automobile paint blemishes and manufacturing types of controlcharts and illustratespossible epidemiolo- defects in engine blocks, and the locationof bulletholes in gy applicationsof each type. military airplanesthat returned from battle (in order to resistant of nonmanufac- COMMON PROBABILITY DISTRIBUTIONS design more aircraft).Examples AND CONTROL CHARTS turing applicationsinclude concentrationplots of the loca- tions where postal mail is lost or misplaced,in order to Control Chart Selection improvemail delivery;traffic accidents, to reducethe num- Controlcharts are statisticaltools and, as such, are ber of fatalities;and automobiledents, so that an insurance based on probabilitytheory. Several different types of con- Vol. 19 No. 3 STATISTICSFOR HOSPITAL EPIDEMIOLOGY 201

trol charts exist (customarilydenoted by various letters greaterdetail subsequently in orderto demonstratethe rela- such as np,p, c, u,X, and S), each being appropriatein dif- tion betweenprobability distributions and control charts. As ferent situations.Because there appearsto be some confu- with any statisticalmethodology, there are exceptionsfor sion regarding when each chart is appropriateand the which some other,and perhapsmore complex,distribution- charts' underlyingassumptions, this section clarifies the al phenomenonis at play.In such situations,an alternatesta- relation between probability distributions and control tisticalapproach should be taken to developingappropriate charts. Severalcommon types of process data and proba- controlcharts based on some alternateprobability model. bilitydistributions exist, such as measuredvalues, counts, fractions,and rates, and specific control charts have been Bernoulli Trials and Binomial Distributions: developedfor each of these situations.Just as there are dif- np and p Control Charts ferent types of hypothesis tests for means, variances,pro- A basic buildingblock of the binomial-basednp and portions, and counts, each control chart is based mathe- p control charts (and of many other parametricand non- maticallyon a particularunderlying statistical distribution parametricstatistical methods) is a dichotomous event that is appropriatefor its correspondingtype of empirical called a Bernoullitrial, which basicallyis any situationthat process data. results in one of two outcomes,each with some probability. The selectionof an appropriatecontrol chart for any Examplesinclude a coin toss resultingin eithera "head"or given situation,therefore, is based directlyon identifying "tail,"a birth being via either a vaginal or Cesareandeliv- whichtype of processdata is being investigated.Although it ery, a surgical site developingor not developingan infec- is somewhatpopular in introductorySPC articles to provide tion, a dischargedpatient having had no or some variances diagramsor tables to aid in controlchart selection,most of fromthe appropriateclinical pathway, a maternitylength of these can be problematicand somewhatmisleading. The stay exceeding or not exceeding 48 hours, a particularpro- most straightforwardand accurateapproach, instead, is to cedure resultingin mortalityor survival,and multiple diag- recognizewhat type of process data (eg, discreteor continu- noses or repeatedlaboratory results agreeing or disagree- ous) is being analyzedand to identifyan appropriateproba- ing with each other,to namejust a few. bility distributionthat reasonablydescribes these data. In When more than one of the same type of Bernoulli manycommon applications, this is not nearlyas difficultas it trial are considered together (eg, several surgeries of a mayseem, especiallyas just a few distributionsand their cor- particulartype performed in a given month), each pre- respondingcontrol charts can be applicableto a wide range sumably independentfrom the others and with the same of situations.For example, (or reasonablythe same) probabilityp of resultingin a par- * when analyzingdiscrete data from binomialdis- ticular outcome (eg, a surgical-siteinfection), the total tributions,either an np or a p controlchart should number and the fractionof such outcomes from all these be used; cases are binomial random variables. Note that many * for countdata generated by Poisson distributions, processes either are described directlyby such indepen- either a c or u chart shouldbe used; and dent and identicallydistributed (ie, "i.i.d.")Bernoulli trials * for normallydistributed continuous data, both an and binomialdistributions or can be framedto be viewed X (pronounced"x-bar") and an S chart should be in such a manner.For example, in the above maternity used together. example, althoughlength of stay is a continuousvariable, These three probability distributions-binomial, this durationalso can be considered simply as exceeding Poisson, and normal-will be familiarto many readers as or not exceeding a recommended48 hours (althoughsee being among the most commonfor many practicalempiri- later comment regarding reduction in statisticalpower). cal situations,and the six charts listed abovetherefore are The np and p control charts (and any other statistical appropriatefor most (but not all69)basic applicationsof methodsbased on binomialdistributions) therefore can be SPC. For example, many types of continuous measure- widely applicablein health care or any other environments ments can be expected to be distributedaccording to the interestedin the totalnumber or fractionof all (reasonably well-knownnormal (Gaussian) bell-shaped distribution, similar)cases that result in a particularoutcome. andX and S charts would be applicablein such situations. The distinctionbetween these two control charts is Examples might include patient waits, procedure dura- thatan np chartis used for the totalnumber of a certainout- tions, the timing of preoperativeantibiotics, other time come per subgroup,whereas ap chart is used for the frac- intervals,various physical measurements, and other phys- tion (proportion)of cases per subgroupthat result in this iologicalvariables. outcome.Other np andp chart examplesmight includethe Alternatively,many types of discrete counts are total numberof cathetersand other devices that result in assumed to occur accordingto Poisson distributions,for associatedinfections, the fractionof complication-freecoro- which c and u controlcharts are appropriate,such as the nary arterybypass graft surgeries, and the numberor frac- numberof patientfalls per month,arrivals to an emergency tion of handlingsof needles and other sharp objects that room,maternity cases per week, andinfectious diseases per resultin inadvertentsticks. (Ofcourse, detailed data such as time period.A second very commondiscrete distribution is for the latterexample may be less likelyto be easilyaccessi- the binomial,for which np andp controlcharts are appropri- ble;see laterdiscussion about the use of Poisson-basedc and ate. Binomialand Poisson distributionsare discussed in u controlcharts in such cases). An implicitassumption in 202 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

any exampleis thateach case has reasonablythe same prob- tion p estimatedfrom the historicaldata, viathe method of abilityof the given outcome occurring(eg, reasonablythe maximumlikelihood as shownin Table 2, asps.084. As can same infectionrate). If this assumptionis not thoughtto be be seen by simplevisual comparison, with the exceptionof met fairlywell, then the data should be adjustedappropri- the high numberof infectionsduring months 28 and 29, the atelyor stratifiedinto morehomogeneous subsets"79 and sep- empiricaldata appearto fit the theoreticalbinomial model aratecontrol charts applied to each of these. fairlywell. More rigorously,a chi-squaredgoodness-of-fit Beforeproceeding, note that Bernoullitrials also can test (excludingmonths 28 and 29, as it will be shown later be combinedin several other manners,resulting in other that something atypical likely occurred during these probabilitydistributions, although the binomialdistribution months), results in a significanceP value of .73, indicating by far is the most common.For example,hypergeometric thatthe datastatistically fit a binomialdistribution very well distributionsresult if sampling(without replacement) from a (generally,we wouldreject the nullhypothesis of a good fit finitepopulation, and any of severaltypes of pooledor mixed if P<.05 or P<.01).While several other more sophisticated binomial distributionsresult if considering nonhomoge- goodness-of-fitmethods exist,106the histogram and chi- neous eventstogether for which the probabilityof a particu- squared test suit the present purposes of demonstrating laroutcome is not reasonablythe same.69A simplerexample the usefulnessof theoreticalprobability models, describing that will be discussed further in part II is the geometric empiricalprocess data,and graphically illustrating the high probabilitydistribution, which, like the binomial,assumes level of agreementbetween the two. (Note that some sta- that such an outcome is equallyprobable case-to-case but tisticiansprefer more powerfuldistribution-checking meth- nowresults from counting the numberof cases (ie, Bernoulli ods, although these tend to be more complicatedto use, trials)between particular outcomes (ratherthan the number less intuitivefrom a lay perspective,and beyond the scope of such outcomeswithin a given numberof cases or trials). of the currentdiscussion.) Additionally, as more data (sub- Note that any Bernoulliprocess that could be viewed via a groups) become available,the binomial fit visually will binomialdistribution also could be tabulatedslightly differ- improveeven more (if the process is, and remains, in a ently in orderto form a geometricdistribution, such as now state of statisticalcontrol). by countingthe numberof coin tosses between"heads," the Giventhat these data are binomial,they also can be numberof surgeriesbetween infections, the numberof nee- examinedvia an np or p controlchart for departuresfrom dle handlingsbetween sticks, and, in nonparametrictests, this underlyingprobability distribution. The formulasand the numberof consecutivevalues abovea medianvalue. As mechanics for constructing all common control charts willbe shownin partII, this transformationmay be advanta- tend to be fairly easy to use and are detailed in several geous in certainsituations. qualitycontrol texts.83,84,91,107 For the present example,the CLand k-sigmacontrol limits for binomial-basednp charts Example of Relation Between Probability are calculatedas follows: Distributions and Control Charts As an example of the relation between np and p Center Line (CL) = n x p = np charts and binomial distributions,Table 2 contains two hypotheticalsets of monthlycatheter-associated-infection Upper Control Limit (UCL) = np + k ( np (1 - p) data,each spanning36 consecutivemonths. For simplicity of illustration,the first example assumes that a constant Lower Control Limit (LCL) = np - k V( np (1 - p) number of patient records, n=50, are sampled from all patientswho receiveda urinarycatheter at some pointdur- ing each month and that these patientsrepresent a fairly with p often (but not always) estimated from the data as similargroup with respect to their durationof catheteriza- discussed above and shown in Table 1, kF:3standard devi- tion, age, and other attributes(so that each had reasonably ationstypically (but not always)used in the controllimits, the same Bernoulliprobability, p, of developinga catheter- and a LCL< 0 by conventionset equal to 0. In this case, associatedurinary tract infection).Then, assuming these substitutingp forp (note that some texts alternativelyuse datacame froma stableprocess, the theoreticalprobability the notationP) yields: A A of numberof catheter-associatedinfections, any particular Center Line (CL) = n x p = np x, out of the total numberof patientsconsidered, n, can be .084 4.22 obtained using the familiarbinomial probability distribu- k50 x p tion function: UpperControl =np+k (np(1-p) Prob.{ X= x } = p(1 - p)" Limit(UCL) + 3 50 (.084).916) -10.084 x! (n -x)! z4.22

Lower Control Limit (LCL) = - k ( n p (1 - p) Figure 1 comparesa relativefrequency histogram of np - 5.884 ~ (-1.884)-+ 0 the example 1 datawith this theoreticalbinomial distribu- a4.22 tion, with the parametern=50 and the probabilityof infec- The trialnp controlchart correspondingto example Vol. 19 No. 3 STATISTICSFOR HOSPITAL EPIDEMIOLOGY 203

TABLE2 NUMBER OF CATHETER-ASSOCIATEDURINARY TRACT INFECTIONSPER MONTH Example1 Example2 TotalNo. TotalNo. Patients TotalNo. That No. of Patients That Resulted In Who Received Resulted in Catheter- Sampled Catheter-Associated Catheters Associated MonthNo. (SubgroupSize n) Nosocomial Infections (SubgroupSize n) Nosocomial Infections 1 50 8 213 15 2 50 4 212 12 3 50 5 182 15 4 50 3 286 21 5 50 3 248 23 6 50 1 228 19 7 50 6 258 15 8 50 4 340 13 9 50 5 68 9 10 50 5 201 12 11 50 2 290 20 12 50 3 229 19 13 50 6 271 22 14 50 1 226 13 15 50 2 213 17 16 50 6 268 19 17 50 2 311 25 18 50 8 251 29 19 50 5 211 20 20 50 4 290 31 21 50 0 232 28 22 50 2 273 30 23 50 7 246 26 24 50 2 321 39 25 50 1 167 9 26 50 5 190 7 27 50 0 255 11 28 50 11 302 16 29 50 12 268 4 30 50 3 369 14 31 50 4 240 13 32 50 6 267 18 33 50 3 246 11 34 50 7 255 21 35 50 4 199 18 36 50 2 362 25

Totals: 36x50=1,800 152 8,986 659 Averagenumber of catheter-associatedinfections per month: 152/36-4.22 8,986/659-13.64 Estimatedper-patient probability of a catheter-associatedinfection ():152/(36x50)n-0.084 659/8,986-0.073

1 (with k=3) for the total number of catheter-associated this meansthat these dataprobably were producedby some- infectionsper month is shown in Figure 2. Alternatively,a thing other than the standardand consistentprocess that p control chart could be constructed using the formulas existed duringthe rest of the examinedtime period, sug- shown below for the fractionof catheters that developed gesting an epidemiologicalor other investigationmay be infections per month (this p chart would be identical in appropriateto identifyand remove, if possible,any causal fac- appearanceand statisticalproperties to the above np chart, tors.Under the philosophyof SPC,a firststep in reducingthe with the CL,control limits, plotted values, and verticalaxis infectionrate is to bringthe process into a state of statistical all reducedby a functionof 1 ). control,so thatit is operatingwith only natural variability (ie, Note that in Figure 2 the subgroupvalues corre- no indicationsexist of a lack of statisticalcontrol) and thus spondingto months28 and 29 are outsidethe controllimits can be studiedmore methodicallyas a definablesystem. and thereforeshould be consideredas probabledeviations from the norm,whereas all othermonths appear to be part Relation of Control Charts to Hypothesis Tests, of the same catheter-associatedinfection process. That is, Goodness-of-FitTests, and Other Statistical Concepts with high probability,the observationsfrom months 28 and The previousexample illustrates several similarities 29 werenot generated by the sameunderlying distribution as and differencesbetween controlcharts and related statis- those from all other months examined.In practicalterms, tical methods. For example, using X control charts is 204 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

FIGURE1. Relativefrequency his- (Mean 4.22) 0.25 togram of catheter-associated infections per month data from example1 in Table2 and compar- ison to theoreticalbinomial proba- distribution. 0.20 bility EmpiricalCatheter-Associated Infection Data

Theoretical BinomialProbability ) 0.15 (pn.084, n=50) :Distribution :

U-.

(Mean+ 3 standard deviations 10.08) Non-Systemic = Events? 0.05 li\1/ 0.00 :

0 1 2 3 4 5 6 7 8 9 10 11 12 13 Numberof Catheter-AssociatedInfections per Month

FIGURE2. Trial controlchart of np Non-Systemic catheter-associatedinfections per Events month for example 1 in Table 2. 12 Abbreviations:CL, center line; LCL, con- lowercontrol limit; UCL, upper 0 limit. UCL trol 10 -

0

SI I 4 ';I CCL 0 ; 'i I, ,I "I , , 0 CL i I S, , I'.1 \ 1 I, I o,,, ,I I; 0/ .,

4 6S2 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

directlyanalogous to using hypothesis tests or ANOVAto furtherin part II, that traditionaltests might not detect. As test whether all means likely came from the same distrib- a recent example,8"an ANOVA(which ignores chronolog- ution,but now also examiningthe time-orderof the datain ical order) resulted in a conclusionthat no significantdif- order to assess this equality and stabilitylongitudinally. ference existed in cervical-smeardata, whereas control That is, manytraditional tests do not considerdata in their chart within-limittests revealed that a significantchange naturaltime order nor in small quantities,often aggregat- had occurredover time. In this application,the use of SPC ing datainto a few largertime-independent quantities; this also helped to identifyquickly when particularindividuals aggregation can pool natural and unnatural variation were in need of retraining. together, thereby losing some ability to detect process As the previoussection suggests, controlcharts also irregularities.94Although the examplein the previoussec- are related to tests for distributionalfit, here augmenting tion was fairly simple, control charts also can identify traditional(time-independent) tests with an examinationof trends and cycles in the time-ordereddata, as discussed the goodness-of-fitover time. While histogramsand classic Vol. 19 No. 3 STATISTICSFOR HOSPITrrAL EPIDEMIOLOGY 205

FIGURE3. Trialp controlchart of rate of catheter-associatedinfec- 0.18 tions per month for example 2 in Table basedon C 0.16 2, unequalsubgroup 0 sizes (unequalnumber of monthly Abbreviations: catheterizations). CL, 0.14 centerline; LCL, lower control limit; a UCL,upper control limit. 0.12 -UCL - 0.1 1 ' /

o 0.0 I

004 - , cc0.04 , L 0.02 ,CL LCLLL

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 Subgroup(Month) Number goodness-of-fitanalysis examine the distributionalform, hypothesis tests can be used either to test whether all en masse, of all data aggregated together (thus ignoring means are equal to each other or to test whether one or their time order), a controlchart essentiallytests whether more means all equal a specifiedvalue (such as a clinical- process data consistently occur individuallyacross time ly or epidemiologicallyrelevant value). This use often is accordingto the same particulardistribution. (This con- referredto as a standards-givencontrol chart, in contrastto cept is related very closely to Shewhart's objective to the more common parameters-estimatedcontrol chart. examine the stabilityof a distributionover time.) Again, Possible and perfectly valid uses of standards-givencon- while histograms and classic goodness-of-fittests ignore trol charts might (and arguably should) include testing trends, process shifts, cycles, and other non-random whether a given institutionis in a state of statisticalcontrol behaviorwithin an unordereddata set, control charts will with respect to some nationalstandard or with respect to flag these distributionaldepartures. Conversely, if the the performanceof anotherfacility.108,109 process were more dramaticallyout of statisticalcontrol Finally,much like the powerand significancelevel of than in the previoussection, histogramsand goodness-of- simplehypothesis tests, controlcharts occasionallywill sig- fit tests would not produce such good results and even nal erroneously that a significantly atypical outcome could (and in practice often do) suggest an incorrect occurredwhen in factthe process remainedin a state of sta- process distribution.While this sometimes is a different tistical control or, conversely,will fail to detect a true way of thinking,the importanceof using both goodness-of- process change. The general topics of power (sensitivity) fit tests and controlcharts to test the "dualhypothesis" of and confidence(specificity) will be takenup furtherin part distributionalform and process stability simultaneously II. Of course,all of the abovediscussion and analogiescon- has been discussed elsewhere.69 cerning np, p, andX charts applyto all othertypes of statis- Additionally,while (most) control charts are based tical controlcharts as well. on the assumption that data come from a reasonably homogeneous group, in the reverse sense, they also test Handling Unequal Subgroup Sizes whether this assumption is reasonable. For example, Note that, in some cases, particularlywhen all sub- muchlike a hypothesistest for equalproportions, ap or np groups are of equal size, the choice between whether to controlchart tests whether all datawere generatedfrom a use an np or a p controlchart (andlikewise whether to use binomialprocess with the same probabilityof resulting in a c or u controlchart) can be largelypreferential (total vs a certain outcome. It also should be emphasizedstrongly fraction or rate), be based on established reporting con- that, while this is the most commonuse, it is not true that ventions, and so on. Equal subgroup sizes occur when a control charts can not nor should not be based on any- specified constant number of cases are sampled from all thing but historical process data (contrary to frequent cases in each time period (even if more dataexist), such as statements).That is, although control charts usually are due to the economics or work load of data collection and used to test whether a process is in a state of statistical analysis. In many practicalcases, however,the total num- control with respect to itself (and thus are developed ber of cases per time period may vary from periodto peri- based on its own data), they also can be developedbased od, with unequalsubgroup sizes being especiallycommon on some internal or external specified values, much like when all historical data are readily availablefor analysis. 206 INFECTIONCONTROL AND HOSPITrrAL EPIDEMIOLOGY March1998

FIGURE4. Trialc control chart of "Non-Systemic numberof needlesticksper week. Event"

UCL

4 i *

' * I,

i / I / \ \ , I I L

T TlLCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Week(Subgroup) Number

Examples might include differing total numbers of plotted the total number of infected patients.The control patientsreceiving catheters or differingnumbers of surg- limits vary because each subgroupnow represents a dif- eries being performed each month. Contrary to some ferentbinomial distribution, each with the same parameter statementsin the healthcareliterature, unequal subgroups p (eg, the same per-catheterizationprobability of an infec- also are very common in industrialuses of SPC, such as tion) but a differentparameter ni (eg, a differentdenomi- when differingnumbers of items are manufacturedor dif- natornumber of catheterizationsper month).The sampling fering volumes of paperworkare processed each month. distributionscorresponding to each subgroupi therefore To illustrate,the second examplein Table 2 contains have the same mean or expected value (p) but different a data set for all patientswho received catheters in each variances (p(1-p)/ni), and thus each subgroup is inter- monthand the numberof these catheterizationsthat result- preted with respect to a constant CL but varying control ed in infections.(If easily accessible,it generallyis betterto limits. In Figure 3, note that the catheter-associatedinfec- use all availabledata ratherthan to sample partiallyfrom tion rate is out of control,with the fractionof infectionsin these datato obtaina constantsubgroup size.) In such sit- month 24 being above the upper control limit and that in uations,p (and u) controlcharts have the advantageover month 29 being beneaththe lower controllimit. np (andc) charts of being adaptedmore easily to unequal This chartalso illustratesthe importanceof adjusting samples, still directly based on exact probabilitytheory control limits for materiallydifferent subgroup sizes. For (adaptingstandardX and S charts is a bit trickier,but pos- example,if "average"straight control limits were used, then sible nonetheless1O).In the case of p charts, for example, the subgroupvalues corresponding to months9, 21, 24, and the CL and k-sigmacontrol limits now are calculated(for 29 mightfall on the other side of the limits as they do here equal or unequalsubgroups) as follows: and thus lead one to an incorrectconclusion. (To help see this, visualizestraight lines drawnhorizontally through the Center Line (CL) = p middle of each controllimit.) Finally,although any control limitscan be made more UpperControl Limit (UCL) = p + k - chartwith varying control visually (1 p) / n varioustransforms and other statistical LowerControl Limit (LCL) = p - k (1 - p) / appealingby using /p n methods83,84,110to produce straight limits, these tendto make where the parameterp is estimated much as before as the plottedvalue lose physicalmeaning. (Technically, none of these methods are necessary or add statisticalvalue. A Totalnumber of cases that yield the outcome Moreover,simply averaging the subgroupsizes introduces P = Total numberof cases examinedin all subgroups unknownapproximations and, unless they vary only slightly, is not recommendedin orderto maintainstatistical integri- and and ni denotes the size of each subgroupi, where i=1, 2, ty-that is, roughlythe desiredsensitivity specificity). ..., 25, ... (eg, month 1, month 2, etc). Using these formulas, the trialp controlchart correspondingto the datain exam- ple 2 (withk=3) is shown in Figure 3. Poisson Distributions: c and u Control Charts Note that this p chart plots the fraction of patients While much of the above discussion was motivated with an infection,whereas the earliernp chart in Figure 2 fromthe perspectiveof binomialdistributions and np andp Vol. 19 No. 3 STATISTICSFOR HosPrrAL EPIDEMIOLOGY 207

FIGURE5a. TrialS controlchart. Abbreviations:CL, center line; LCL, lower control limit; UCL, uppercontrol limit. 250

200

i: , . . 0 150 'h "E~ e I a 'i ,! I , 1 0. , " 100 I I SI I; i " I CL4

50 4 II So ( S tut uti C.

cnco M M M M n It V, Itv(M It LIt VVvVn LSubrou Ionth)Numbe

Subgroup (Month) Number

FIGURE5b. TrialX control chart of the time (numberof minutes)pro- phylacticantibiotic is administered S300 before first surgical incision. a Abbreviations:CL, center line; LCL, lower control limit; UCL, E uppercontrol limit. 200 200 /UCL c .E 100 , c o o " :" 4-', .

So 4- 0 -1oCL F~CE %.Win 0 -100 LCL 4)

-200 v I wv L L L LML N N N N N LnNwN m N Nw NN MNNN NN Subgroupr' pM (Month)oLN Number mLILO control charts, the same basic concepts regarding chart In such cases, either a c or u controlchart shouldbe selection, interpretation,and relation to other statistical used to monitorthe total numberor the averagenumber, methods applyto all other charts as well. For example,as respectively,of occurrences per subgroupor time period. one commonalternative to the binomial,Poisson distribu- Note that these two types of control charts are directly tions generally (but not always) apply to the number of analogousto the np and p charts illustratedpreviously for events that occur where an event is equally likely at any the totalnumber and fractionper subgroup,but now math- time or location,no clear Bernoullitrials exist, and no clear ematicallybased on a Poisson distributionrather than a maximumexists. Poisson distributionsalso often provide binomial distributionand thus calculated slightly differ- good models for the number of events that occur-and ently.83,84,91,107Figure 4 illustratesa recent c controlchart of especiallythe numberof rare events that occur infrequent- the total number of needlesticks reported per week in a ly-in any given unit of time, space, volume, or other small 75-bedrural hospital,here assuming relativelycon- dimension.For example, in an earliercolumn on disease stant opportunitiesfor exposures week-to-week(eg, rela- clusteringmethods, Jacquez et a124discussed infectious dis- tively constant census and amount of needle handlings). eases in a given populationas occurring according to a As can be seen, this chart suggests that something atypi- Poisson process. cal occurredin week 4. 208 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

Contraryto some statements,it should be empha- falls per patient day, where a patient day here represents sized that c charts,like np charts, assume that the denomi- the equal "areaof opportunity." natorpopulation, even if unknown,must be of identicalsize In other cases for which it is difficultto obtain the for each subgroup (what statisticiansoften refer to as the data detailnecessary for np and p charts, a Poisson distri- equal "areaof opportunity").If the opportunityfor sticks bution sometimes can be used to approximatethe under- were thoughtto differconsiderably each month,then, anal- lying binomialvery accurately.For example,in Figure 4, it ogous to the previoususe of p charts, a u chart should be would be infeasibleto record every time a needle was han- used with the controllimits properly adjusted (to reflectdif- dled by any personnel (which would more closely fit the feringamounts of relativerisk) by plottingthe averagenum- binomial description),whereas one of the above surro- ber of sticks per some specifiedbase amountof potential gates for relative risk (eg, patient days, needles used) is exposures,such as averagesticks per 1,000"units" of some collected more easily. In such situations, the Poisson- type. (As the dataand effort to adjusteach month'sfigures based c and u charts often can be used as good approxi- exactlymight be impractical,such as per every 1,000han- mationsto the binomial-basednp andp charts, respective- dlings of needles or per 1,000 opportunitiesto transmitan ly. Mathematically,as the binomial subgroup size n con- infection,some more convenientrepresentation of approxi- verges to infinity,any binomialdistribution converges to a mate relativerisk typicallymight be used, such as the num- Poisson distributionwith rate parameterX-np. For practi- ber of needles used or, more practically,patient days.) cal purposes, this means that, for sufficientlysmall p and Anothercommon application of a u chart might be for the large n, such as oftenmight be encounteredwith low infec- monthlynumber of bloodstreaminfections per 1,000patient tion rates, the difference will be negligible. (Althougha days,where the totalnumber of patientdays (ie, the "areaof few ballparkrules-of-thumb exist for when a binomialdis- opportunity")per month varies. Also see Sellick2for an tributionmight be reasonablyapproximated by a Poisson exampleof a u controlchart with varyingcontrol limits for distribution,it always is better to use the correct chart if the averagenumber of medical ICU nosocomialinfections the necessary dataare availablerather than introducepos- per 1,000ICU patient days each month. sible error.) Note that,while the Poisson andbinomial are distinct As anotherexample, Burnett and Chesher4recently distributionsapplicable in distinctsituations, in some cases described their applicationof CQI tools to laboratory they can appearonly subtly different.Determining which needlestickscaused by arterialblood-gas syringes arriving chart is appropriatecan be dependenton specificallyhow with needles still attached,which is a binomial (and not datawere collected,on what collectionmethod is most fea- Poisson) randomvariable. If the numberof syringessent to sible, or on whatreporting method is preferable.In the ear- the laboratoryis not reasonablyconstant each month,then lier catheterscenario, for example,any given patienttheo- a p chart with varyingcontrol limits would be most appro- reticallymight developmore than one catheter-associated priate and exact. Alternatively,if the number of syringes infectionduring the course of hospitalization.Although a per month is assumed to be fairly constant, then an np binomialdistribution would be appropriatefor the number chart also could be used, which, given the above condi- of like patients who develop one or more infections, a tions, could be further approximated,as in the authors' Poisson distributionwould be more appropriatefor the example,with a c chart. (Again,if the denominatoris likely total number of such infections (including any multiple to vary,a u chart could be used to approximatethe p chart, cases per same patients,assuming these occur at the same adjustedas in Figure 3, in order to account for differing rate; see later section on "OtherProbability Distributions samplingvariances, such as per 1,000patient days.) As any and ControlCharts"). approximationintroduces error6985 and as the calculations Similarly,the numberof like patientswho fall (one or are not much simpler,these approximationsare recom- more times) is a binomialrandom variable, although these mended only in cases for which the subgroupdenomina- data are likely to be less accessible than simply the total tors are not knownprecisely but eithercan be relatedclose- numberof falls (not trackedat the patient-specificlevel of ly to some other measure (such as patientdays) or can be detailand includingany multiplefalls per patient),which is assumedto be relativelyconstant. When dealingwith small a Poisson random variable (again assuming that subse- subgroupsand in other situationswhen these approxima- quent falls occur at the same rate). In such cases, defining tions are not appropriate,however, clearly distinguishing subgroupsslightly differentlyas above and using a c or u which distributionand chart is most appropriateremains chart can be more convenientand in some cases even pre- an importantendeavor. ferred statistically.That is, "reducing"Poisson counts into binomialrandom variables of the "one-or-more"type indi- Normal Distributions: X and S Control Charts rectlyignores some of the process data,thereby sacrificing While the above discrete control charts are appro- statisticalpower, although insignificantlyso for low rates. priatefor many situationsinvolving counted data,X and S (This reductionin power tends to be much larger when charts83,84,91,07now should be used when dealing with con- transformingcontinuous data into dichotomousevents and tinuous normally distributed data. However, unlike the then using np or p charts instead ofX and S charts.) cases for binomial and Poisson data, in which only one Additionally,patients with significantlydifferent lengths of control chart is used, these charts now are used simulta- stay might be accommodatedby trackingthe number of neously as a pair.Somewhat analogous to hypothesistests Vol. 19 No. 3 STATISTICSFOR HOSPTrAL EPIDEMIOLOGY 209

for equal means and equal variances,an X chart monitors limits on both charts being too wide); nonetheless, note the process mean, and an S chart monitors the process that the X chart still indicatesthat the process mean is not standarddeviation. These two charts are used together in control (with the average times in October 1993 being because either the process mean or standarddeviation of abovethe UCLand in July 1994being below the LCLof the a normaldistribution can change while the other remains X chart).This lack of statisticalcontrol potentially is of clin- in control;thus, both charts must be in control for the ical concern, as by definition no consistent preventive overall process to be in a state of statistical control. process exists patient-to-patient. (Technically,this is because the normalprobability densi- Of furtherpractical interest, note that, even if these ty function is completely specified by two parameters,p1 out-of-controlconditions did not exist, the antibioticcurrent- and(r, andthe arithmeticmean and the empiricalstandard ly is administeredan averageof 61.15 minutesbefore the deviation of data generated from a normal universe are first incision,which may or may not be acceptable,but the independentrandom variables. As a statisticalaside, and to amountof variabilityis very large and probablyof greater address a point of confusion,it is importantto comment concern, with a standarddeviation of 89.61 minutes. For that control charts do more than control only a process example,based on normalprobability, 99.73% of cases from mean, variance,or rate, in fact controllingestimates of all an in-controlprocess will receive an antibioticanywhere parametersthat define the entire shape of any given prob- withinapproximately 1 hour c4.5 hours beforethe surgery abilityfunction and thus controllingall percentile points (assumingthe processwas broughtinto control;more prob- and all propertiesof that distributioncompletely. This rea- ably will be outsidethis interval,given the process is out of soning also helps to explainwhy only one chart--and not control).Additionally, again assuming an in-controlprocess one for the mean and one for the variance,for example-- with this mean and varianceand using standardnormal is used to control data generated by binomialor Poisson probability,the portion of surgery patients who receive distributions,whose mathematicalfunctions each contain antibioticprophylaxis within a recommendedwindow of 0 to only one parameter.) 2 hours beforethe firstincision7,113,114 is less than49.7%. A few healthcare examples of X and S charts Again, while varying subgroup sizes result in non- described in other papers6,11,12,111include laboratoryturn- constantcontrol limits (in most X and S cases it is easier to aroundtimes, blood-sugarlevels, laboratorysupply costs, sample a constantnumber of patientrecords), alternative- peak expiratoryflow rates, blood pressures, heart rates, ly, if the averagesubgroup size was used in the limitcalcu- blood clottingtimes, andothers. As a more recent example, lationsas an approximation,then severalpoints (eg, March the X and S controlcharts in Figure 5 examinethe month- 1993, May 1994,_andSeptember 1995 on the S chart and ly average and standard deviation, respectively, of the July 1994on theX chart) wouldbe on the opposite (thatis, elapsed times before incision of perioperativeantibiotic incorrect)side of the controllimits. Finally, note that a nor- administrationin a midsize,public, urban hospital. Because mal distributionsometimes is used to approximatebinomi- it has been linked to postsurgicalinfections,112-114 the tim- al and Poisson distributionsthat have large averages;while ing of presurgeryprophylactic antibiotics has been identi- this simplifies probability calculations that otherwise fied as an importantkey "upstream"surgical process mea- involve the difficultyof computing large factorials,it is sure to control.7As Figure 5 illustrates, however, this much less useful in setting k-sigmacontrol limits (which process is not in a state of statisticalcontrol (in fact, both are fairlyeasy to calculateexactly), can introducesome sta- the S andX charts are out of control).A negativetime indi- tistical problems, and thus is not recommendedin most cates thatthe antibioticwas given either duringor afterthe control chart situations.(Also note that S charts for sub- surgery. No subgroup values exist for the months of group standarddeviations always technically are preferred Januaryand February1994 due to missing data. for severalstatistical reasons overthe alternateR chartsfor Note that,while severalauthors place the X chart on subgroupranges.) top, the S chart typicallyshould be examinedfirst (the rea- soning is analogous to first testing for homoscedasticity Other Probability Distributions and Control Charts priorto conductingan ANOVAor other hypothesistest for Althoughnot the primaryfocus here, it is important equal means). That is, the process mean can not be deter- to comment that, while binomial, Poisson, and normal mined to be in controlunless the process standarddevia- probabilitydistributions are perhaps the most common tion also is in control (conversely,however, the S chart (and their correspondingcontrol charts therefore are the does not necessarilyhave to be in control in order some- most commonlyused), they are by no means the only pos- times to be able to determinethat an X chart is out of con- sibilities.15Process data periodicallycan occur according trol). In the presentexample, the S chart indicatesthat the to several other types of continuousand discrete distribu- process standarddeviation is not in a state of statisticalcon- tions, and to minimizethe risk of using incorrect control trol (the subgroup standarddeviations corresponding to charts in any given situation,one should confirmwhether April 1994, September1994, May 1995, and June 1995 are the general assumptionsof a chart's underlyingdistribu- above the UCL,and that in May 1993 is below the LCLof tion are reasonablysatisfied. If not, differentcontrol charts the S chart).The excess of values above the UCLof the S based on a more appropriateunderlying statistical model chart causes the overall process standarddeviation, if it should be constructed.Contrary to some statements,fail- were in control,to be overestimated(resulting in all control ure to identifyan appropriatedistribution and then to select 210 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

or design control charts based on this distributioncan can be significantlynon-Poisson and asymmetrical,often result in erroneousconclusions about the statisticalcontrol more closely followinga negativebinomial distribution."n of a process, a situationthat will be illustratedin partII and Negative binomial,Neyman, and related-countdis- that has been illustratedelsewhere.69'85,92 tributionsalso can be particularlyappropriate in situations While a complete review is beyond the present that exhibit a naturalclustering or lack of independence scope, furtherdiscussion and examplesof severalalternate between events, such as the geographicdistribution of dis- possible distributionscan be foundin manygood statistics ease (for this reason these distributionstend to be used publications.11-d19As quick examples of alternatecontinu- more in biological sciences than in manufacturing).92,120 ous distributions,waiting times and lengths of stay, when From a practical viewpoint, more importantly,because consideredas continuousrandom variables, are unlikelyto they are more flexiblein shape than the Poisson (basically have normal distributions,"10but rather are likely to be due to being 2-parameterrather than 1-parameterdistribu- skewed positively (with a longer tail stretching to the tions), these can be useful alternategeneral-purpose count right). In such cases, lognormal, gamma, exponential, distributionsin cases for which neither a Poisson nor a Rayleigh, Weibull, or Gumbel distributions-to name a binomial distributionseems to fit reasonably (although few-may be more appropriate,as they are commonlyused their mathematics and parameter estimation are some- to describe event durations and in other life analysis. what more involved).For example,negative binomial mod- Fortunately,from a practicalstandpoint, X and S charts can els can be fit to datawith various amounts of positive skew be moderatelyrobust to slight departuresfrom their under- (such as the discrete length-of-stayexample), and Neyman lying theoreticaldistributions, with only slight degradation and other compounddistributions can be fit to naturally in statisticalpower and confidence.If the departureis sub- multimodaldata. stantial(such as if very significantskewness is suggested As an exampleof these more complex distributions, by simplehistograms or more advancedmethods), howev- the proportionof patientdays spentin the ICU2,12typically is er, their use can result in greater error.For example,sur- not a binomialrandom variable (even if stratifiedinto homo- veillanceof the time between disease detectionshas been geneous patient groups). The complexityof this random discussed by Jacquezet a124as an exponentialdistribution variableand the lack of a binomial,in particular,can be seen (if no clusteringoccurs). Because exponentialdistributions by recognizingthat, whether any given patientday is spent are highly skewed, decaying left-to-rightand not at all in the ICUis dependentlargely on where that patientspent approximatelynormal, a specialcontrol chart based on this the previousday (ie, in the ICUor not).The probabilityof an distributionshould be used for examiningthis randomvari- ICUday therefore is neitherindependent nor identicallydis- able, as will be illustratedin part II. tributedfor each patientday. (Moreprecisely, this is a cer- A discreteanalog to this highly skewed and decaying tain type of compoundrandom variable15",n6,120 for which shapeis the geometricdistribution, which can ariseeither as each patientfirst either does or does not end up in the ICU, the number of discrete i.i.d. (ie, similar) Bernoullitrials withsome probability,and then the numberof daysthat each betweencertain outcomes as describedearlier (as opposed ICUpatient spends in the unitis describedby anotherdistri- to the continuousexponential inter-occurrence length of bution.As alternativemotivations, a zero-inflatedcount dis- time) or simplyas a shapethat occursas a "stateof nature." tribution69,n5also couldbe used to modelthe totalnumber of Because none of the standard control charts are even days each patient spends in the ICU, and a Neyman, remotely appropriatefor geometric data, differentcontrol Thomas,Short, or some other compoundor clusterdistrib- charts, calledg and h charts,have been developedfor such ution92,115,116,120could be used for the totalnumber of ICU situations.120,121Recent papers69'85 illustrated several applica- days summedacross all patients.) tions of g and h controlcharts to certainlength-of-stay data In either case and contraryto some advice,np andp and several other processes where geometricdistributions control charts would be inappropriatefor these random were foundto be appropriate.Infection control examples of variablesand could result in substantialerror, and there- geometricand exponential distributions, histograms of their fore a correctcontrol chart or charts insteadbased on one "shapes,"and uses of the correspondingalternate control of the above mentionedrandom variables should be used. chartswill be illustratedin partII. Anothercommon example of a similartype of compound Among other discrete probabilitydistributions that randomvariable, where an occurrenceof one event leads in periodicallyarise69,n5 are negativebinomial, Neyman, and some way to the possibility of one or more additional varioustypes of mixed, compound,and truncateddistribu- events, is the numberof babies deliveredper time period, tions. As one exampleof truncateddistributions, Newell'22 where there are a randomnumber of maternitycases in applieda certain type of right-truncatedPoisson distribu- each period,each of which couldresult in one or more new- tion to the number of occupied hospital beds, given that borns. Similarly,if the risk of acquiringsubsequent infec- there is some maximumnumber available. Negative bino- tions is significantlygreater than that of acquiringone's mial distributionscan arise either as the sum of indepen- first such infection,'23then control charts based on alter- dent and identically distributedgeometric random vari- nate probabilitymodels for the number of infections per ables, due to various types of mixtures of populations,or patientor the totalnumber across all patientsper time peri- again simply as a state of nature. For example, when od should be developed. (In practice, however, using a recordedas an integer numberof days, length-of-staydata Poisson distributionwith the rate parameter estimated Vol. 19 No. 3 STATISTICSFOR HOSPITAL EPIDEMIOLOGY 211

from the empiricaltotal numberof infectionsor falls often The current trend in high-level aggregate metrics, still maybe appropriatehere for severalstatistical reasons.) "reportcards," and "dashboardindicators" also has been discussed and criticizedfrom a statisticalquality-manage- SUGGESTED REFERENCES ment perspective,8,9,108,134including the applicationof con- Good standardSPC texts used by qualityengineers trol charts to these process data. As part of an effort to include those by Montgomery,83Duncan," Banks,107and manage costs, Ramsey and Cantrell105applied SPC to Grantand Leavenworth,91all of which are excellent tech- healthcarecost variances.Finally, as mentionedpreviously, nical sources for further details on statisticalquality con- several epidemiologistshave discussed (and debated)the trol methods, calculations,and underlyingtheory. While relationof controlcharts and other CQI and SPC tools to Duncan'sbook is somewhatof a comprehensivedesk ref- epidemiologyl3,85,86or illustrated specific uses.2-5,7For erence, readersmight find the other three to be a bit more example, IntermountainHealth Care reports using CQI approachablebut still to containvery thoroughtreatments techniques to reduce its postsurgicalinfection rate from of the fundamentaland intermediateaspects of statistical 1.8%to 0.4%.7A recent slightly more technical paper"8 qualitycontrol, well beyond those of several recent popu- reviewedand examinedalternative SPC approaches to low- lar publications.(A slight drawbackof the above books, frequency infection control and needlestick data (as dis- from a practitioner'sviewpoint, is that they tend to read cussed furtherin part II). like the textbooksthey are. However,while a considerable In terms of journalsand organizations,the American numberof more practitioner-focusedbooks have appeared Society for Quality(ASQ) is the primaryinterindustry US in the past severalyears, manyof these tend to be less rig- organizationfor qualitypractitioners, currently with approx- orous and exact, often losing important informationin imately 140,000members. While ASQ recently formed a their efforts to oversimplifystatistical methods.) healthcaredivision, it still is maturing.Several other more Within health care, Drs. Berwick2' and established healthcare-specificquality organizations exist, Blumenthal23each followedup on their earlierpapers22,77 including the InternationalSociety for Qualityin Health with general discussions of the utility of SPC to control Care, the NationalAssociation for HealthcareQuality, the healthcare process variationand to inform medical deci- Institute for Healthcare Improvement,and others. The sion making. Both also suggested that statisticalprocess Journalof QualityTechnology is one of the primarytechnical control charts might be used to verify whether clinical journalsfor statisticalquality control and relatedresearch, interventions,in fact, resulted in an intended benefit or with QualityEngineering being slightly more applications- unintended consequence. Later papers by the present oriented.Technometrics is publishedjointly by ASQ and the author and others provide more specific overviews and AmericanStatistical Association and, along with the Journal illustrate the use and interpretationof control charts in of theAmerican Statistical Association, tends to be the most health care,6,9,10,81,82,124,125as well as some common pitfalls mathematicallyadvanced. Quality Progress, ASQ's monthly to avoid. Some empirical applicationsin these papers tradejournal, has the highest circulationand tends to be the include patient falls, prescriptionerrors, infection rates, most readableby nontechnicalpractitioners, containing arti- needlesticks, cesarean-section births, clinical pathway cles andcase studieson a widerange of quality-management variances,lengths of stay, admissionrates, billing errors, topics,often less quantitativethan SPC (eg, qualityplanning, HMO disenrollment, blood counts, emergency room team building,benchmarking, customer satisfaction, cost of arrivals,mortality, and others. poorquality, basic dataanalysis, etc). In more clinicalapplications, in 1990,Zimmerman et all" explored the utility of control charts to monitorthe CONCLUSION OF PART I heart rate,systolic blood pressure, and diastolicblood pres- Statisticalprocess controland controlcharts provide sure of surgerypatients; Schnelle et all4illustrated the use of another,and in manyways quite similar,effective statistical controlcharts for managingnursing home patientswith uri- and graphicalmanner for viewingand analyzingprocesses nary incontinence;and Liu et a1126proposed a crude SPC and outcomes.The identificationof what processes, vari- type of graphicalapproach to evaluatingcarpal tunnel syn- ables, and outcomes (whetherin-process or end-process)to dromerisk. Blumenthal, Laffel, and others22,23,108,127 also sug- study and monitoris anothersubject and one beyond the gested using controlcharts to examinemortality rates, and currentintended scope. Once the appropriateprocess para- several other authors"-16,128have discussed healthcare meters or outcomeshave been identified,through epidemi- applicationsof SPC, althoughsome of these tend to range ologicalor other methods, statisticalcontrol charts can be considerablyin terms of technicalaccuracy and detail.The appliedeffectively to any of these. Whilethe issue of process use of controlcharts in chemistryand clinicallaboratories versus outcomemeasures has been discussedby others,8135 also was suggested at least as early as 1946 by it should be emphasizedthat actualphysical application of Wernimontl29and later by Levey and Jennings,130with controlcharts is equallyapplicable to eithermanner of data. some more recent applications'1-133including radiology, In fact, some of the SPC emphasison a "processori- mammographyimaging, repeated chest radiographs,pro- entation"as opposed to an "outcomeorientation" is con- cessing times for beta human-chorionicgonadotrophin cerned with how any data, whether in-process or end- laboratorytests, and the accuracy of Pap smear, human process, are considered-that is, frequently via control immunodeficiencyvirus assay, and hepatitisresults. charts for the purpose of understanding,improving, and 212 INFECTIONCONTROL AND HOSPITALEPIDEMIOLOGY March 1998

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Control of Legionellapneumophila in Hospital Hot-Water Supply

Gina Pugliese, RN, MS return lines immediately upstream ples obtained from hot-watertanks, Martin S. Favero, PhD from hot-watertanks. Recoveryrates 42%and 50%exceeded the silver and of L pneumophilawere monitoredby copperstandards, respectively. Heattreatment and application of culturingswab samples from faucets. The authorsconcluded that cop- copper-silverionization often are used Concentrationsof copperand silverin per-silver ionization effectively con- for controllingLegionella pneumophila water samples were determined by trols L pneumophilain high-volume in high-volumehospital plumbing sys- atomicabsorption spectrophotometry. plumbingsystems and is superiorto tems. However,the comparativeeffica- Four heat-flushtreatments failed to thermal treatment. However, high cies of these measuresin high-volume providelong-term control of L pneu- concentrationsof copper and silver systems are unknown. mophila.In contrast,ionization treat- can accumulateat the bottom of hot- Investigators from Children's ment reduced the rate of recovery of water tanks. Hospitalof Pittsburghhave reported L pneumophilafrom 108 faucets from From:Miuetzner S, SchwilleRC, on studies that show differences in 72%to 2%within 1 month and main- FarleyA, WaldER, Ge JH, States SJ. efficacy.Thermal treatment of a hot- tained effective controlfor at least 22 Efficacy of thermal treatment and water circuit was accomplished by months. Onlythree samples (1.9%)of copper-silverionization for control- flushing hot water (>60'C) through hot water from faucets exceeded ling Legionellapneumophila in high- distalfixtures for 10 minutes.Copper- Environmental Protection Agency volume hot water plumbingsystems silver ionization was conducted in standardsfor silver,and none exceed- in hospitals. Am J Infect Control three circuits by installingunits into ed the standardsfor copper. Of 24 sam- 1997;25:452-457.