Confounding: What Is It and How Do We Deal with It?

CONTINUING MEDICAL EDUCATION FORMATION MÉDICALE CONTINUE

PRACTICAL TIPS FOR SURGICAL RESEARCH Confounding: What is it and how do we deal with it?

Luis Henrique P. Braga, MD, urgical treatments are half as likely as medical therapies to be based on MSc, PhD *† randomized controlled trial (RCT) evidence. 1 The paucity of random - Forough Farrokhyar, MPhil, S ized surgical trials may reflect ethical challenges to randomization, insufficient funding and insufficient knowledge and infrastructure in surgery PhD *‡ *‡§ to conduct large, full-scale and definitive trials. Many surgical events, such as Mohit Bhandari, MD, PhD scapholunate dissociation as compared with hypertension, are relatively rare; this undoubtedly accounts for part of the discrepancy. As a result, most surgic- From the *Department of Surgery, the 1 †Division of Urology, the ‡Department of al research uses retrospective designs, often with a small number of patients. Clinical Epidemiology and Biostatistics Despite efforts to design a methodologically sound surgical technique study and the §Division of Orthopaedic and perform proper statistical analyses, the results may not accurately reflect Surgery, McMaster University, the true situation. This is a major concern in observational studies of surgical Hamilton, Ont. interventions. Whenever one observes an association between an exposure, Accepted for publication such as a surgical intervention, and an outcome measure, one is tempted to Dec. 21, 2011 derive a causal inference when, in fact, the relation may not be causal. The exposure could be a risk factor causing harm or a protective factor preventing Correspondence to: harm. For example, one may detect an increased rate of postoperative wound L.H.P. Braga infection in patients who undergo open appendectomy compared with those Division of Urology Department of Surgery who have a laparoscopic procedure and presume that the type of approach McMaster University (open surgery in this case) is a risk factor for the increased postoperative 1280 Main St. W wound infections. However, this association may simply be owing to the pres - Hamilton ON L8S 4K1 ence of a third factor or a confounding factor, such as obesity (as shown fur - [email protected] ther on), which ought to be controlled for at the stages of design or analysis. 2 DOI: 10.1503/cjs.036311 Failure to control for confounders in a study undermines its credibility and internal validity.

ObjeCtiveS Of thiS artiCle

This article will discuss the importance of confounding factors and the meth - ods of detecting and dealing with these factors in surgical research. By the end of this article, the reader will be able to understand the methods available to deal with confounding factors at the stages of design and analysis of any given study. The subject matter is divided into 2 sections: 1. What is a confounding factor? 2. How do we deal with a confounding factor?

What iS a COnfOunding faCtOr ?

To understand the phenomenon of “confounding,” one needs to consider the potential relation between an exposure (e.g., novel surgical technique) and an outcome (e.g., revision surgery or postoperative infection). The term “con - founding” refers to a situation when one finds a spurious association or misses a true association between an exposure variable and an outcome variable as a result of a third factor or group of factors referred to as confounding vari - able(s). A confounding variable is a factor associated with both the exposure

variable and the outcome variable. 3 For example, delay to wound infection. However, we know that postoperative surgery has been shown to increase the risk of mortality in wound infection and obesity are related because obese patients with hip fractures in a number of observational patients usually have a higher rate of postoperative wound cohort studies. It is presumed, therefore, that the delay to infection than nonobese patients. 6 Let us also assume that surgery (risk factor) increases mortality (outcome). How - obese patients are more likely than nonobese patients to ever, critical evaluation of the literature suggests that this undergo open appendectomy. In this hypothetical exam - effect is confounded by other patient characteristics, such ple, if an association is observed between open appendec - as age and American Society of Anaesthesiologists (ASA) tomy and postoperative wound infection, it may be, first, score. 4 Surgery is often delayed for sicker patients to seek that open appendectomy leads to increased postoperative medical optimization before surgery, and sicker patients wound infection ( Fig. 1A ) or, second, that the observed are generally at greater risk for mortality. association is confounded by the factor of obesity (Fig 1B). For a variable to be considered a true confounder, it When examining the effect of a risk factor (factor A: open cannot lie in the causal pathway of association between appendectomy) on the outcome (condition B: postopera - the exposure variable and the outcome variable. Bio- tive wound infection) without taking into account the logic al and clinical knowledge are usually used to judge effect of the confounder (factor X: obesity), one may mis - whether a potential confounder is in the causal pathway represent the true effect of open appendectomy in increas - of an association. 2 ing postoperative wound infection ( Fig. 1A ). Thus, in this Confounding is essentially an intrinsic limitation of hypothetical study, obesity may confound the relation observational studies (e.g., cohort studies, case–control between surgical approach (open or laparoscopic appen - studies) but is usually well addressed by large and well- dectomy) and wound infection unless the results are designed RCTs. 5 However, small RCTs can occasionally adjusted for obesity ( Fig. 1B ). run into problems with confounding simply owing to How do we identify a confounder? A convenient meth - chance if their treatment groups are unbalanced with od to check for a potential confounding factor is, first, to respect to participants’ baseline characteristics. Not recog - find out if the assumed confounding factor is associated nizing confounding factors certainly increases the chance with both outcome variable and exposure variable and, sec - of this happening — particularly in smaller studies. ond, to compare the associations before and after adjusting What do we mean by confounding? In an observational for that confounding factor. Table 1 displays data from our study, for example, if factor A is associated with condition hypothetical example of an unmatched case–control study B, we might conclude that a third factor, X, is a confounder of open and laparoscopic appendectomy. Let us assume for if both of the following are true: 5 simplicity that 100 cases (patients with wound infection) 1. Factor X is a known risk factor for condition B. and 100 controls (patients without wound infection) were 2. Factor X is associated with factor A, but it is not a result studied. The unadjusted odds ratio (OR) of postoperative of factor A. wound infection in open appendectomy versus laparo - Whenever we observe an association between a poten - scopic appendectomy was calculated to be 1.95. The OR is tial risk factor and an outcome, we have to question defined as the odds of the outcome occurring in exposed whether this association is true or whether it is a result of individuals divided by the odds of the outcome occurring confounding by a third factor. Let us look at a hypothetic - in unexposed individuals. If the outcome is not related to al example of open versus laparoscopic appendectomy. We the exposure, the OR will be equal to 1. The OR will be have conducted an unmatched case–control study to see if, greater than 1 for a positive association and less than 1 for compared with laparoscopic appendectomy, open appen - a negative association. The unadjusted OR of 1.95 suggests dectomy is associated with a higher rate of postoperative that the postoperative wound infection is almost 2 times higher for open appendectomy than laparoscopic appen - A) Caus al B) Due to co nfound in g dectomy. In the next step, we must examine whether the observed relation between open appendectomy (exposure

↑ ↑

Open appendecto my Open appendecto my O n

b Table 1. Number of la parosc op ic and ope n appende ctom ie s o i s t e a i

r ac cording to po st operative wound infe ct io n rate v c e o d s

s a

a Po st oper ativ e wo und in fe cti on, no. (% ) s Obesity s d o e c v r i

a Appe nd ec to my Ye s No Total e t s i o b n O Postoperat iv e wound Postoperat iv e wound Op en 30 ( 63) 18 ( 37) 48 infection ↑ infection ↑ Lapa rosc opi c 70 ( 46) 82 ( 54) 152 Total 100 100 200 20 × 82 Unad ju st ed od ds ra ti o = = 1.95 fig. 1. The association between open appendectomy and wound 70 × 18 infection.

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variable) and postoperative wound infection (outcome vari - to be dealt with when planning a research study. 7 Con - able) is confounded by obesity (confounding variable). founding can be dealt with at the stage of study design First, we need to find out whether obesity is related to (before collecting the data) or at the stage of data analysis postoperative wound infection and to open appendectomy. (after collecting the data). The commonly used methods By looking at Table 2, we see that 50% of the patients to control for confounding factors and improve internal with postoperative wound infections and 20% of the validity are randomization, restriction, matching, stratifi - patients without postoperative wound infections are obese. cation, multivariable regression analysis and propensity It seems that, with a ratio of 2.5, obesity is related to score analysis. 3 A brief explanation of controlling for con - increased risk for postoperative wound infection. We then founders at each stage is subsequently described. Note need to assess whether obesity is related to open appen - that the use of these methods should be justified, prede - dectomy. Table 3 shows the relation between obesity and fined, specified and taken into account in a power calcula - type of appendectomy for 200 patients. Of 70 obese tion a priori, at the stage of study design. patients, 35 (50%) underwent open appendectomy and of 130 nonobese patients, 13 (10%) underwent open appen - Dealing with confounding at the design stage dectomy. Thus, with a ratio of 5.0, we clearly observe that obese patients were more likely than nonobese patients to randomization (rCt) have an open appendectomy. At this point, obesity seems Randomization is the most optimal method of controlling to be related to both postoperative wound infection and for confounders. It has the advantage of balancing both open appendectomy. measured and unmeasured confounders between study Second, we need to calculate the adjusted OR and com - groups, which reduces the uncertainty as to whether the pare it with the unadjusted OR of 1.95. We first stratify observed associations might be confounded by prognostic study population to obese and nonobese patients. Within factors in the study. In our previous example, a well- each stratum, a contingency (2 × 2) table is created and the designed and powered RCT to study the effect of surgical OR is calculated (Table 4). When we calculate the OR sep - approach (open v. laparoscopic appendectomy) on postop - arately for obese and nonobese patients, we find that the erative wound infection would more likely provide a bal - OR is 1 in each stratum, indicating the lack of association anced number of obese and nonobese patients between between postoperative wound infection and type of sur- the open and laparoscopic groups. Since the method of gical approach. We could conclude that the unadjusted OR randomization is based on probability, it is unlikely that of 1.95 in Table 1 was owing to the unbalanced distribution this balance will be achieved for all patient characteristics, of obesity between cases and controls. Thus, in this exam - even with a large number of observations. However, ran - ple, obesity was a confounder, and the association between domization does guarantee that any differences between open appendectomy and postoperative wound infection the 2 groups (open and laparoscopic appendectomy) are was spurious. owing to chance, 7,8 rather than the choice of the surgeon. Thus, although differences between patient characteristics hOW dO We deal With a COnfOunding faCtOr ? may still exist after randomization, their confounding effects are likely minimized. 7 The chances of achieving As confounders influence the real treatment effect (ob - balanced groups with respect to prognostic factors will scure the etiological importance of a variable), they need increase if larger numbers of patients are studied. 1,8 Ran - domization may be insufficient to achieve balanced groups Table 2. Di stribut io n of wo und infe ctio n case s with small sample sizes (i.e., fewer than 200 patients) 8 The and cont ro ls by obe sity status larger the sample size, the more confidence one may have Po st oper ativ e wo und in fe ct io n

Obes it y Ye s No Table 4. Calc ul ation of odd s ra ti o after stratifying by ob esity No 50 80 st atus Ye s 50 20 Wound in fe cti on, no. (% ) Total 100 100 Obes it y; appe nd ec to my Ye s No Total Adjusted odds rati o No Table 3. Relation be tw een surg ical appr oach (ope n v. Op en 5 (3 8) 8 (6 2) 13 5 × 72 360 laparo sc opic) an d ob esity st atus = = 1.0 Lapa rosc opi c 45 ( 38) 72 ( 62) 117 45 × 8 360 Appe nd ec to my, no . (% ) Total 50 80 130 Ye s Obes it y Total Op en Lapa rosc opi c Op en 25 ( 71) 10 ( 29) 35 25 × 10 250 No 130 13 ( 10) 117 (9 0) = = 1.0 Lapa rosc opi c 25 ( 71) 10 ( 29) 35 25 × 10 250 Ye s 70 35 ( 50) 35 ( 50) Total 50 20 70

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that balance of prognostic factors in an RCT has been have no interest in investigating. Matching on variables achieved. The methods of optimizing the chances of other than those is called overmatching and should be achieving balanced groups in RCTs of surgical interven - avoided. Third, the design is prone to loss of data; if tions are explained elsewhere. 8 1 member of a matched pair does not provide adequate data, the pair has to be excluded from the analysis. A fur - restriction (observational study) ther disadvantage of matching is the complexity of the Restriction is simple and easy to understand and can at data analysis if unmatched variables need to be adjusted or least partially eliminate the influence of a confounding if the matching ratio varies. 5,11 In our example, patients factor. We restrict our study population to individuals with would be matched by obesity status. Obese patients under - certain characteristics by tightening the eligibility criteria. going open appendectomy would be matched to obese For example, we could include nonsmokers younger than patients undergoing laparoscopic appendectomy, and 60 years of age to remove the effect of smoking and older nonobese patients undergoing open appendectomy would age. Restriction can be used to address a limited number be matched to nonobese patients undergoing laparoscopic of confounders. This usually involves selecting patients appendectomy, thus eliminating the confounding effect of with specific characteristics to have a more homogeneous obesity. study population, but this comes at the expense of external validity and loss of generalizability. 2 Because of the selec - Dealing with confounding at the data analysis stage tion process, the number of eligible participants is usually reduced; consequently, achieving the required sample size Stratification becomes more difficult. Another disadvantage of restric - Stratification divides data as strata or layers based on a tion is that once we restrict our study population on cer - suspected confounding variable. Data are stratified and tain variables, we can no longer investigate those variables. analyzed for each stratum. Indeed, we have already used Therefore, we should only use restriction on variables that the stratification method of analysis for our clinical exam - we are convinced are confounders. In our example, the ple. In our clinical scenario, patients with and without investigator would only select nonobese patients to con - postoperative wound infections were divided into 2 strata trol for the factor of obesity. Note that there are more based on obesity status, and then stratum-specific ORs for likely other patient characteristics that need to be consid - open versus laparoscopic appendectomy were calculated ered for adjustment at the stage of data analysis. for obese and nonobese patients separately. With respect to a confounding factor, the OR of 1.0 for each stratum Matching (observational study) makes the interpretation of data self-explanatory and sim - Matching involves pairing the study groups for potential ple. However, in most situations, treatment effect is differ - confounding factors, such as smoking, age, tumour size or ent between strata (Table 5). In these situations, statistical sex. Matching could be used in case–control studies (e.g., methods, such as the Mantel–Haenszel test, are used to patients with postoperative wound infection are matched produce a single estimate of treatment effect, which is to patients without wound infection for 1 or more con - adjusted for the effects of the confounding factor. 5,7 This is founders) and cohort studies (e.g., patients who have open called the adjusted treatment effect, which is then com - appendectomy are matched to patients who have laparo - pared with the unadjusted treatment effect to determine scopic appendectomy for 1 or more confounders). Match - the effect of the confounding factor. There is no general ing permits the adjustment for multiple confounding fac - agreement as to how much change is required in the tors, provided that appropriate control patients can be identified. It also improves between-group comparability. Table 5. Calc ul ation of odd s ra ti o st ratifying by obe sity st atus Matching is useful when there is a limited number of cases using th e Mant el –H aensz el met hod or a limited number of exposed persons. Furthermore, Wound in fe cti on, no. (% ) matching each case to more than 1 control maintains the Obes it y; function of matching and increases study power. 9 The appe nd ec to my Ye s No Total Adjusted odds rati o method of matching must be specified a priori at the stage No of study design. There are certain disadvantages to match - Op en 6 (4 6) 7 (5 4) 13 6 × 73 438 = = 1.42 ing that one should consider. First, it can be difficult to Lapa rosc opi c 44 ( 37) 73 ( 63) 117 44 × 7 308 find suitable matched pairs for multiple confounding fac - Total 50 80 130 tors. Second, variables selected for matching can no longer Ye s Op en 25 ( 71) 10 ( 29) 35 25 × 10 250 = = 1.0 be evaluated as risk factors for the outcome or disease Lapa rosc opi c 25 ( 71) 10 ( 29) 35 × 10 25 10 250 under investigation. Also, matching is very difficult to Total 50 20 70 perform in surgical studies. In carrying out a matched (6 × 73 ) / 130 + (25 × 10 ) / 35 Adjusted odds rati o = = 1.11 cohort study or a matched case–control study, we should (44 × 7) / 130 + (25 × 10 ) / 35 match variables that have confounding effects and that we

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strength of an association after adjustment for a factor to ables (potential risk factors) and 1 dependent variable be considered a confounder; some experts have argued (outcome). This method uses all the study data and exam - that at least 10% change in the strength of any association ines many variables, either continuous or dichotomous, is acceptable. 2,12 To estimate the pooled adjusted treatment simultaneously, including the comparison variable (sur - effect, the treatment effect (i.e., OR) should be homogen - gical technique). 14 Multivariable regression analysis allows eous across strata, and we need to test for heterogeneity to the estimation of the effect of an exposure variable (open ensure this assumption. If the treatment was heterogen- appendectomy) on a given outcome variable (postopera - eous across strata, the pooled estimate of treatment effect tive wound infection) after controlling for the cofounding should be avoided because this situation might reflect pos - effect of other included variables (e.g., obesity, age). 15,16 sibilities of effect modification — the effect of an interac - Multivariable regression analysis is regarded as the most tion between exposure variable and confounding variable powerful but complex type of analysis to deal with con - on the outcome. In our example, assuming that the treat - founders. 3 It is the most commonly used method to deal ment effect is homogeneous across strata, the adjusted OR with confounding factors in the medical literature because is 1.11 (Table 5). The change from the unadjusted OR of of its flexibility. 3 When we use regression models to assess 1.95 is more than 10%, suggesting that obesity was a con - the change in the association between outcome and ex- founder. We should therefore report the adjusted OR of posure, it is the extent of change, not the statistical signifi - 1.11 and suggest that the risk of postoperative wound cance, that is considered important. One limitation of infection is increased by about 1.1 times in open appen - regression analysis is that it can deal with only a limited dectomy compared with laparoscopic appendectomy. number of factors when there is a small number of obser - Note that the use of the test of statistical significance to vations (e.g., a small study sample size with few outcome detect a confounding effect should be avoided because we events). 3 The acceptable number of covariates (i.e., poten - are interested in the strength of the association between tial risk factors, confounding or interacting variables) the confounder, the exposure and the disease; p values will depends on the number of observations or sample size. It not provide the information on the magnitude of associa - is recommended to have 10 or more observations (postop - tion if a particular variable is a confounder. 7 erative wound infection) per variable. 15,17 We suggest in - Stratification is effective when dealing with dichotomous clud ing only variables that are likely risk factors for the confounding variables because the data can be separated outcome of interest. A literature review might provide the into 2 or more distinct strata. Stratification is more difficult most relevant variables. Other disadvantages of regression for continuous variables, such as age and tumour size, analysis are that the interpretation of output from regres - because arbitrary strata must be created. 3 Such adjustment sion models can be challenging for researchers with lim - for confounding does not always remove the confounding ited statistical knowledge and that the results may be inac - effect of that variable. There may be residual confounding curate if assumptions of the mathematical models are not when there are relatively few strata of continuous variables satisfied and if sample size is insufficient. 3 In our example, (e.g., age is in only 2 strata: ≤ 50 yr and > 50 yr). 7 The a multivariable regression model would include postoper - adjustment for the confounding factor can be improved by ative wound infection as a dependent (outcome) variable increasing the number of strata; however, this requires and surgical approach (open v. laparoscopic appendec - inflating the number of observations in each stratum. The tomy), obesity and other patient characteristics as in - main disadvantage of stratification is the inability to deal depend ent variables (covariates). with multiple confounding factors simultaneously. If multi - ple confounders are considered, each stratum may become Propensity scores very small or disappear (i.e., no patients in the stratum). 3 Propensity score analysis, defined as the conditional prob - Similar principles apply to relative risk (RR) as another ability of being treated given the patients’ risk factors measure of treatment effect applicable to prospective (covariates), can be used to balance the between-group designs. Relative risk is defined as the ratio of the event rate differences and, therefore, reduce bias. 16 Binary regression (postoperative wound infection) in the exposed group (open analysis provides an estimate of the propensity toward appendectomy) divided by the event rate in the unexposed (probability of) belonging to one group versus another. 16 group (laparoscopic appendectomy). The interpretation of Once the propensity score is calculated for each patient, RR is similar to the interpretation of OR. Detailed informa - this score can be used through matching, stratification and tion on calculating adjusted ORs or adjusted RRs using the regression to estimate the adjusted treatment effect. Mantel–Haenszel test 12 and the standardization method 13 Propensity scores are applicable when dealing with for matched data is available elsewhere. dichotomous variables and can reduce the number of covariates in a multivariable regression model. 18 The main Multivariable regression analysis disadvantage of this method is that, like any other meth - Regression analysis is a mathematical model that estimates odological or statistical method, the propensity score does the association between a number of independent vari - not account for unknown and unmeasured covariates.

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Another limitation is its lack of familiarity among phys - be less robust than those generated from an RCT because icians. Other limitations applied to multivariable regres - one cannot eliminate the effect of all known confounders, sion analysis are also applied to propensity score analysis. and because there is no way of incorporating the effect of The advantages and disadvantages of the main methods potential unknown confounders. Therefore, the conclu - for adjusting for confounders in a study are summarized in sions drawn from observational studies must be inter - Table 6. Some practical tips on dealing with confounders at preted with caution. the stage of planning a research project are provided in Box 1. Box 1. Ti ps fo r dealin g with confounders wh en pla nning research stud ie s COnCluSiOn 1. Fo rm a clea r a nd well- de fin ed re se ar ch ques ti on . Fo r mo re de tail ed info rm ati on on ho w to de ve lo p a re se ar ch ques ti on , hy po th esis a nd 19 Confounding occurs when a risk factor is associated with objec tive s, re fe r to th e a rticl e by Fa rr ugi a and coll eag ues . 2. Revi ew th e liter at ur e an d id en ti fy th e re leva nt risk fact or s an d both the comparison variable and the outcome of interest. conf ou nd ers. The most optimal method for controlling confounders 3. Sele ct th e mo st op ti mal desi gn to an sw er t he re se ar ch qu esti on. is randomization. When randomization is not feasible, 4. Ch oos e t he op ti mal me th od of deali ng with t he co nf ound er s at th e stag e of st ud y de si gn be fo re coll ecti ng data . Consider the effe ct of th e observational studies are conducted. The findings from sele ct ed study de sign on t he in te rnal a nd ex te rn al valid it y studies using observational designs are subject to bias if (ge ner alizabilit y) of t he st ud y. the researchers do not adjust for the effect of confounding 5. Co nsid er th e fu rt he r ad ju st me nt s ne ede d at t he st ag e of data analysis variables. In observational studies, confounding variables afte r co lle ct in g da ta . 6. Co nsid er th e me th od c hos en to dea l wi th conf ou nde rs in sample si ze should be predefined and measured, and the method of calculati on. No te th at t he same me th od us ed fo r sam pl e si ze adjustment should be specified and taken into account in calculati on sh oul d be also consid er ed fo r data analys is . the power analysis a priori at the stage of study design. 7. T hes e c onsi der atio ns sh ou ld be pr ed efin ed an d ju st ifie d a pr io ri at th e stag e of de si gn a nd be fo re th e pr oc es s of data coll ecti on. Even then, the conclusions drawn from these studies will

Table 6. Advantage s and di sa dv antages of method s to deal wi th c onfou nding

Method Sta ge of th e st ud y Advantage s Disadva nta ges Randomiz at ion Desi gn • Balances and ad ju st fo r bot h measu re d • May no t be feasi ble fo r so me su rgi cal re se ar ch qu esti ons ow in g to and unm easure d co nf oun de rs ethi ca l issu es or im prac ticalit y • More ex pen sive Restri ct ion Desi gn • Si mp le to implem en t • Loss of da ta: pati ent s wi th res pec t to the res tri ct ed varia bl e ar e • Remove s, at leas t pa rti ally, th e infl ue nc e exclu ded of th e re stri ct ed me asure d co nf oun de r • Loss of ge ne ralizabili ty • Pr olon ge d re cr uitm en t ti me • Cannot as sess th e ef fe ct of th e res tri ct ed va riab le on th e ou tcom e • Can only ad ju st fo r kn ow n co nf ou nd er s and th os e fo r whic h da ta are a vailabl e Matchi ng Desi gn • Can deal with more than 1 me asu re d • Pr one to loss of da ta: th e pa ir is excl ud ed if t he data ar e lacki ng fo r conf ou nd er 1 me mb er of a matc he d pa ir • Useful wh en th er e ar e a limit ed num ber of • Cannot estimate the effects of the matched var ia bl es on t he cases or ex po se d per so ns out co me • Difficu lt to ma tch pati en ts if t her e ar e ma ny co nf ou nde rs • Can only ad ju st fo r kn ow n co nf ou nd er s and th os e fo r whic h da ta are a vailabl e • More comp le x st at is tical analysi s St ra tifi catio n Analysi s • All data ar e us ed • Suit able to ap ply fo r 1– 2 me as ur ed co nf ou nd er s • Si mp le r to in te rp re t re sult s • May re sult in ve ry small s tra ta with lo w po we r if st ra tifi ca ti on is applie d fo r fe w co nf oundi ng fa ct or s • Can only ad ju st fo r kn ow n co nf ou nd er s and th os e fo r whic h da ta are a vailabl e Multiv ar iabl e Analysi s • Suit able to adju st fo r many me as ur ed • Requi res la rg er sampl e size wh en th er e is la rg e num be r of re gr ession conf ou nd er s covaria te s model • Can es ti mate t he ef fe ct s of all me asu red • Can only ad ju st fo r kn ow n co nf ou nd er s and th os e fo r whic h da ta conf ou nd ers on th e ou tc om e are a vailabl e • Complex st at istical anal ys is Pr ope nsit y Analysi s • Easier to impl em en t wh en ex po su re • Difficu lt to cal cula te wi th co nt in uous ex pos ur e varia bl e score analysis variabl e is dich ot om ous • Only su it ab le wh en ex po su re varia bl e does no t ch an ge ov er time • Pr ovid es 1 risk score fo r ea ch pati en t in • Requi res la rg er sampl e size wi th la rg e num be r of co va riat es th e st udy th at is us ed fo r ad ju stme nt • Can only ad ju st fo r kn ow n co nf ou nd er s and th os e fo r whic h da ta • Can es ti mate t he ef fe ct s of all me asu red are a vailabl e conf ou nd ers on th e ou tc om e • Complex st at istical anal ys is

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Competing interests: M. Bhandari was funded, in part, by a Canada 10. Brookhart MA, Sturmer T, Glynn RJ, et al. Confounding control in Research Chair, McMaster University. None declared for L.H.P. Braga healthcare database research: challenges and potential approaches. and F. Farrokhyar. Med Care 2010;48(Suppl):S114-20. 11. van Stralen KJ, Dekker FW, Zoccali C, et al. Confounding. Nephron references Clin Pract 2010;116:c143-7. 12. Tripepi G, Jager KJ, Dekker FW, et al. Stratification for confound - 1. Farrokhyar F, Karanicolas PJ, Thoma A, et al. Randomized controlled ing — part 1: the Mantel-Haenszel formula. Nephron Clin Pract trials of surgical interventions. Ann Surg 2010;251:409-16. 2010;116:c317-21. 2. Kestenbaum B. Methods to control for confounding. In: Epidemiology 13. Tripepi G, Jager KJ, Dekker FW, et al. Stratification for confound - and biostatistics. An introduction to clinical research . 1st ed. New York: ing — part 2: direct and indirect standardization. Nephron Clin Pract Springer; 2009. 2010;116:c322-5. 3. Petrie A, Sabin C. Bias and counfounding. Medical statistics at a glance . 14. Morshed S, Tornetta P III, Bhandari M. Analysis of observational 3rd ed. Oxford: Wiley-Blackwell; 2009. studies: a guide to understanding statistical methods. J Bone Joint 4. Franzo A, Francescutti C, Simon G. Risk factors correlated with Surg Am 2009;91(Suppl 3):50-60. post-operative mortality for hip fracture surgery in the elderly: a 15. Tripepi G, Jager KJ, Dekker FW, et al. Linear and logistic regression population-based approach. Eur J Epidemiol 2005;20:985-91. analysis. Kidney Int 2008;73:806-10. 5. Gordis L. More on causal inferences: bias, confounding and interaction. 16. Blackstone EH. Comparing apples and oranges. J Thorac Cardiovasc In: Epidemiology . 4th ed. Philadelphia: Saunders Elsevier; 2009. p. 247-65. Surg 2002;123:8-15. 6. Giles KA, Wyers MC, Pomposelli FB, et al. The impact of body mass 17. Peduzzi P, Concato J, Kemper E, et al. A simulation study of the index on perioperative outcomes of open and endovascular abdom - number of events per variable in logistic regression analysis. J Clin inal aortic aneurysm repair from the National Surgical Quality Epidemiol 1996;49:1373-9. Improvement Program, 20052007. J Vasc Surg 2010 ;52 :1471 -7. 18. Sturmer T, Joshi M, Glynn RJ, et al. A review of the application of 7. Jager KJ , Zoccali C, Macleod A, et al. Confounding: what it is and propensity score methods yielded increasing use, advantages in spe - how to deal with it. Kidney Int 2008;73:256-60. cific settings, but not substantially different estimates compared 8. Farrokhyar F, Bajammal S, Kahnamoui K, et al. Practical tips for sur - with conventional multivariable methods. J Clin Epidemiol 2006;59: gical research. Ensuring balanced groups in surgical trials. Can J Surg 437-47. 2010;53:418-23. 19. Farrugia P, Petrisor BA, Farrokhyar F, et al. Practical tips for surgical 9. Jaeschke R, Sackett DL. Research methods for obtaining primary evi - research: Research questions, hypotheses and objectives. Can J Surg dence. Int J Technol Assess Health Care 1989;5:503-19. 2010;53:278-81.

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