Basic Aspects of Confounding Adjustment

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R H H Groenwold and Aspects of confounding 182:5 E5–E7 Methodology O M Dekkers adjustment Editorial

METHODOLOGY FOR THE ENDOCRINOLOGIST Basic aspects of confounding adjustment

Rolf H H Groenwold1,2 and Olaf M Dekkers1,3 Correspondence 1Department of Clinical Epidemiology, Leiden University Medical Center, Leiden, the Netherlands, 2Department of should be addressed Biomedical Data Sciences, Leiden University Medical Center, Leiden, the Netherlands, and 3Department of to R H H Groenwold Endocrinology, Leiden University Medical Center, Leiden, the Netherlands Email [email protected]

Abstract

The results of observational studies of causal effects are potentially biased due to confounding. Various methods have been proposed to control for confounding in observational studies. Eight basic aspects of confounding adjustment are described, with a focus on correction for confounding through covariate adjustment using regression analysis. These aspects should be considered when planning an observational study of causal effects or when assessing the validity of the results of such a study. European Journal of Endocrinology (2020) 182, E5–E7

Introduction

Observational studies of potential risk factors for diseases or methods, and instrumental variable analysis. We refer observational studies into the effects of medical treatments to the literature for more details on these methods (1). often aim at making causal claims about the risk factor (or Hereafter, we focus on covariate adjustment, meaning

European Journal of Endocrinology treatment) of interest. Is an elevated growth hormone (GH) the correction for confounding by adding confounders as level a risk factor for mortality? Does medical reduction of covariates in a regression model, because that method is GH levels reduce this risk? These are both typical causal most commonly used in clinical research (2). questions. To attribute observed differences in the outcome to different levels of the exposure (e.g. high vs low GH levels), these groups should differ only in their exposure levels Basic aspects and should be comparable regarding other characteristics 1. Common cause affecting the outcome. In case of absence of such comparability, an observed relation (or lack thereof) may be Confounders are variables that are related to exposure incorrectly attributed to the exposure and the association and, independent of exposure, also affect the outcome. is confounded. Here, we describe eight basic principles of If such variables are ignored, this may lead to incorrect confounding adjustment that should be considered when estimates of the exposure-outcome relation. More formally, planning or when assessing an observational study of causal confounders are common causes of exposure and outcome effects. This list of principles is not exhaustive, nor do we (3). For example, in acromegaly, tumour size is a common pretend that all details of the listed aspects are covered. We cause of GH levels and mortality, as larger tumours have refer to the references for further reading on confounding higher GH levels and also a higher mortality risk (higher adjustment. We use the potential causal relation between risk of ACTH-deficiency). When adjusting for confounding, GH levels, its treatment, and mortality to exemplify. neither mediators of the exposure effect, nor consequences Various methods have been proposed to control of exposure and outcome should be adjusted for (4). While for confounding in observational studies, ranging from adjusting for tumour size (confounder) is appropriate, matching to covariate adjustment, propensity score adjusting for glucose levels is not, as these are affected by

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-20-0075 European Journal of Endocrinology https://eje.bioscientifica.com relation ofinterest. (partly) mediatedbyglucoselevel, whichisamediatorofthe and mortality.Theeffectofgrowth hormoneonmortalityis confounder oftherelationbetween growthhormonelevels hormone andmortalityinacromegaly. Tumorsizeisa Diagram representingthecausalrelationbetweengrowth Figure 1 confounding effectneedtobeconsidered( outcome, alsothenumberofconfoundersandtheir considerations aboutthedistributionsofexposureand with confoundingadjustmentarerare.Inadditionto studies Formal samplesizecalculationsforobservational 3. Sample size sufficient tocontrolforconfounding( graphs (DAGs)tofindaminimalsetofconfoundersthatis Formal rulescan be appliedtoso-calleddirected acyclic whereas glucoseisamediatorandnotconfounder. association betweenGHlevelsandmortalityinacromegaly, can beseenthattumourvolumeisaconfounderofthe should beconsideredasconfounders( discussions amongresearchers aboutwhethervariables An exampleisgivenin mediators, andconsequencesofexposureoutcome. can be helpful to distinguish between confounders, Diagrams representingrelationsbetweendifferentvariables 2. Identification ofconfounders expertise isindispensableforidentifyingconfounders. measurements (see6.)maybehelpful.Regardless,clinical instrument, causaldiagrams(seepoint2.)orthetimingof about whetheravariableis,forexample,mediatoror to residualconfounding(see7.)( and amplify any bias due (i.e. wider confidence intervals) because itmayincreasetheuncertaintyineffectestimates instruments orinstrumentalvariables),isinappropriate, of exposure,yetdonotaffecttheoutcome(so-called GH levels.Also,adjustmentforvariablesthatarepredictive Methodology Editorial Fig. 1 . Such diagrams help to guide . Suchdiagramshelptoguide 5 O MDekkers R HGroenwoldand ). In case of uncertainty ). Incaseofuncertainty 4 ). 6 ). From 7 ). When Fig. 1 it it In general, it is advised not to use data-driven methods for the In general,itisadvisednottousedata-drivenmethodsforthe 4. Confounder selection might beaviableoptionforconfoundingadjustment. likely low, thussuggestingthatpropensityscoremethods confounders willbelarge,whilethenumberofeventsis drugs onmortalityinacromegaly, thenumberofpotential studyassessingtheeffectofGHlowering observational exposed andunexposedarelarger. Forexample,inan events isrelativelysmall,whiletheproportionsofboth are a reasonable alternative when the proportion of be considered.Particularlypropensityscoremethods or alternativeconfoundingadjustmentmethodscould (potentially leadingtoresidualconfounding,see7.), (if possible), the numberofconfounders reduced models. Inthatcase,thesamplesizeshouldbeincreased whichever issmallest),thismayleadtoinstablestatistical compared tothenumberofevents(ornon-events, the numberofconfoundingvariablesisrelativelylarge over time,inwhichcasethe timingofmeasurements Many variables–includingpotential confounders–change 6. Timing ofmeasurements than theexposure-outcomerelation( outcome mayhaveadifferentsetofconfoundingvariables because therelationsbetweeneachconfounderand relations donotnecessarilyhaveacausalinterpretation, is oflowquality. However, confounder–outcome observed mortality, it mayindicatethat the tumoursizemeasurement For example,iflargertumoursizeappearstolowerrisk of informative abouttheapparentvalidityorqualityofdata. confounder-outcome relation maybe of theobserved and thedesignofstudy( has itsownsetofconfounders,dependingonclinicalcontext Each research question and each exposure-outcome relation 5. No uniquesetofconfounders will bedismissedbyachange-in-estimateapproach. may wellbesubstantial( sum ofseveralconfounderswithweakconfoundingeffects confounding effectofasinglevariablemaybelimited,the other disadvantage is that, although the magnitude of the and commoneffectsofexposureoutcome(see1).The distinguish betweenconfounders,mediators,instruments, main reasonisthatdata-drivenmethodsgenerallycannot selection by the change-in-estimate criterion ( confounder-exposurerelations)or (based onobserved selection ofconfounders,notablyunivariatepreselection adjustment Aspects ofconfounding Downloaded fromBioscientifica.com at09/24/202105:29:19AM 9 10 ). Theseconfounders,however, ). The direction and magnitude ). Thedirectionandmagnitude 11 182 ). :5 8 ). The ). The E6 via freeaccess European Journal of Endocrinology References Scientific Research(ZonMW-Vidiproject917.16.430)andtheLUMC. This work was supported by grants from the Netherlands Organization for Funding is listedasanauthor.RGreportsnoconflictsofinterest. he which on paper, this for process editorial or review the in involved not was He Endocrinology. of Journal European for Editor Deputy a is D M O Declaration ofinterest be requiredtoaddressthesesources ofbias. error andmissingdata.Additionalorothermethodsmay studies, including measurement bias in observational Apart fromconfounding,theremaybeothersources of 8. Othersourcesofbias about residualconfounding( have beenproposedtoguidequantitativediscussions ( impact ofresidualconfoundingishardlyeverdiscussed continuous variables( assumptions andconsideralternativeapproachestomodel ( continuous confoundersmayresultinresidualconfounding imperfect. Also, incorrectlymodelling or categorizing are (partially)lacking,adjustmentforthisvariableremains score methods.If,forexample,dataonACTH-deficiency methods tohandleconfounding,includingpropensity measured confoundersisnotcontrolledbyconventional Residual confounding due to unmeasured or inaccurately 7. Residual confounding adjustment forconfoundingbecomeschallenging( deficienciesareconsidered), newly occurringpituitary studies oftime-dependentexposures(forexamplewhen should, ingeneral,notbeadjustedfor. Particularly, in after treatment willbe affected by medication use and levels canbeconsideredaconfounder, whileGHlevels effect ofmedicaltreatmentinacromegaly, baselineGH thus bemediators( after exposurestartedcouldbeaffectedbyand qualify as a confounder, whereas variables measured start ofexposure(orbeforeismeasured)could becomes relevant.Variables thataremeasuredbeforethe 14 12 1 Methodology Editorial , ), whichunderlinestheneedtocheckmodelling Klungel OH, Martens EP, Psaty BM,Grobbee DE,Sullivan SD, Stricker BH, Leufkens HG&deBoer A. Methodstoassessintended 15 ), even though various forms of sensitivity analysis ), even though various forms of sensitivity analysis 4 ). Forexample,whenstudyingthe 13 ). Unfortunately, thepotential 16 ). O MDekkers R HGroenwoldand 3 ). Accepted 17February2020 Received 27January2020

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