Analysis of 1:1 Matched Cohort Studies and Twin …

1 [ ] 2 Oct 2012 Statistical Science2012, Vol. 27, No. 3, 395 411 Institute of Mathematical Statistics, 2012 Analysis of 1:1 Matched Cohort Studiesand Twin Studies , with Binary Exposuresand Binary OutcomesArvid Sj olander, Anna L. V. Johansson, Cecilia Lundholm, Daniel Altman,Catarina Almqvist and Yudi improve confounder adjustments, observational studiesare often Matched on potential confounders. While Matched case-controlstudies are common and well covered in the literature, our focus hereis on Matched Cohort Studies , which are less common and sparsely dis-cussed in the literature. Matched data also arise naturallyin twin stud-ies, as a Cohort of exposure discordant twins can be viewed as beingmatched on a large number of potential confounders. The Analysis oftwin Studies will be given special attention. We give an overview of vari-ous Analysis methods for Matched Cohort Studies with binaryexposuresand binary outcomes.

2 In particular, our aim is to answer the followingquestions: (1) What are the target parameters in the common analysismethods? (2) What are the underlying assumptions in these methods?(3) How do the methods compare in terms of statistical power?Key words and phrases: Cohort Studies , likelihood, Sj olander is Student, Department ofMedical Epidemiology and Biostatistics, KarolinskaInstitutet, Solna, Sweden L. V. Johansson is Statistician, Department ofMedical Epidemiology and Biostatistics, KarolinskaInstitutet, Solna, Sweden Lundholm is Statistician, Department of MedicalEpidemiology and Biostatistics, Karolinska Institutet,Solna, Sweden DanielAltman is Associate Professor, Department of MedicalEpidemiology and Biostatistics, Karolinska Institutet,Solna, Sweden, and Associate Professor, Division ofObstetrics and Gynecology, Department of ClinicalSciences, Danderyd Hospital, Karolinska Institutet,Stockholm, Sweden Almqvist is Associate Professor, Departmentof Medical Epidemiology and Biostatistics, KarolinskaInstitutet, Solna, Sweden, and Associate Professor,Astrid Lindgren Children s Hospital and Department ofWoman and Child Health, Karolinska Institutet,Stockholm, Sweden Pawitan is Professor, Department of MedicalEpidemiology and Biostatistics, Karolinska Institutet.

3 Solna, Sweden INTRODUCTIONA common goal of epidemiological research is toestimate the causal effect of a particular exposureon a particular outcome. The common tool is anobservational study, utilizing, for example, hospitaldata, Cohort data or health register data. In observa-tional Studies , the exposure-outcome association isinvariably confounded by factors that induce spuri-ous ( , noncausal) associations. For example, agemay confound an exposure-outcome association ifolder people are more often exposed and more likelyto develop the outcome. Without adjustment forage, that is, if the confounding influence by age is notaccounted for in the Analysis , there may be an asso-ciation of exposure and outcome, even in the absenceof a causal effect. Hence, the exposure-outcome asso-This is an electronic reprint of the original articlepublished by theInstitute of Mathematical StatisticsinStatistical Science,2012, Vol.

4 27, No. 3, 395 411. Thisreprint differs from the original in pagination andtypographic SJ OLANDER ET cannot, in general, be given a causal interpre-tation, unless all confounders are properly are several strategies to adjust for potentialconfounders in the Analysis , for example, stratifica-tion or regression modeling. Essentially, these meth-ods solve the problem of confounding by comparingthe exposed and unexposed within levels of the con-founders, thus balancing the confounders across lev-els of the exposure and comparing like with like. Ifthere is a strong association between the confound-ers and the exposure, or between the confoundersand the outcome, these strategies are often ineffi-cient. In particular, some strata may contain fewexposed subjects or few cases ( , subjects that de-veloped the outcome); the lack of balance may leadto unstable estimates for these common method to increase the efficiency isto match the study on potential confounders.

5 For ex-ample, Matched case-control Studies are constructedso that for each case, a fixed number of controlsare selected, having the same confounder levels asthe case. When each case is Matched to one con-trol, we say that the study is 1:1 Matched . In case-control Studies , matching forces the ratio of casesto controls to be constant across all strata of thematched factors, which implies that the associationbetween the confounders and the outcome is case-control Studies are commonplace, andwell covered in the literature ( ,Breslow and Day,1980;Jewell,2004;Woodward,2005). A matchedcohort study can be constructed in a similar fash-ion; for each exposed subject, a fixed number ofunexposed subjects are selected, having the sameconfounder levels as the exposed. In Cohort Studies ,matching forces the ratio of exposed to unexposedto be constant across all strata of the Matched fac-tors, which implies that the association between theconfounders and the exposure is broken.

6 Matchedcohort Studies are relatively rare, and the literatureis sparse and typically rather brief ( , Cummingset al.,2003). The reason, we believe, is mainly due toavailable data sources. Matched Cohort Studies aresuitable for situations where a researcher has accessto large population data sources with exposure data also arise naturally in twin nature, a large number of potential confoundersare shared ( , having constant levels) within eachtwin pair, for example, genetic factors, maternal uter-ine environment, gestational age, etc. It follows thata Cohort of exposure discordant twin pairs ( , pairsin which one of the twins is exposed, and the othertwin is unexposed) can be viewed as being 1:1 matchedon all shared confounders. In such a Cohort there isno association between the shared confounders andthe exposure. An attractive feature of twin studiesis that the shared confounders often include factorswhich are normally very difficult to match on, oreven to measure.

7 For example, monozygotic twinshave identical genes and can thus can be viewed asbeing Matched on the whole genome. However, a twinstudy is not simply a special case of a regular 1:1matched Cohort study; whereas the latter only con-tains exposure discordant pairs, the former also con-tains pairs which are concordant in the exposure. Be-cause of their unique and attractive properties, twinstudies will be given special attention in this aim of this paper is to give a detailed overviewof different Analysis methods for Matched cohortstudies with binary exposures and binary particular, our aim is to answer the followingquestions: (1) What are the target parameters in thecommon Analysis methods? (2) What are the under-lying assumptions in these methods? (3) How do themethods compare in terms of statistical power?We illustrate the methods with two examples. Thefirst example is a register-based study on the ef-fect of hysterectomy on the risk for cardiovasculardisease (CVD) in Swedish women (Ingelsson et al.)

8 ,2010). The study is Matched on birth year, year ofhysterectomy and county of residence at year of hys-terectomy, so that for each hysterectomized woman(exposed), three nonhysterectomized women at sameage and year were selected from the general popu-lation. The second study is a population-based twinstudy of the association between fetal growth andchildhood asthma ( Ortqvist et al.,2009).The paper is organized as follows. In Section2we review the concepts of marginalization, condi-tioning and standardization. In Section3we definea Matched Cohort study. In Section4we describethe most common Analysis methods for Matched co-horts. These methods can also be used to analyzethe exposure discordant pairs in twin Studies . InSection5we demonstrate how these methods canbe adapted for inclusion of the exposure concordantpairs in twin Studies as well. In Section6we carryout a simulation study.

9 In Section7we provide thetwo illustrating examples. We will restrict our atten-tion to 1:1 matching, and we will not consider ad-ditional covariate adjustments. Extensions to othermatching schemes and adjustments for additionalcovariates are discussed in Cohort STUDIES32. MARGINALIZATION, CONDITIONINGAND STANDARDIZATIONWe first establish the notations and briefly reviewthe concepts of marginalization, conditioning andstandardization, which are crucial for the under-standing of matching and confounder thorough discussions can be found in standardepidemiological textbooks ( , Rothman et al.,2008). LetXdenote the binary exposure of interest(0/1), letYdenote the binary outcome of interest(0/1) and letZdenote a set of potential confoundersfor the association betweenXandY. We use Pr( )generically for both probabilities (population pro-portions) and densities, and we useE( ) for expectedvalue (population average).

10 We useV1 V2|V3asshorthand for V1andV2conditionally independent,givenV3. We use (log) odds ratios to quantify theX Yassociation. Other possible options would berisk differences or risk ratios. There are two reasonsfor focusing on odds ratios. First, regression mod-els for odds ratios can be conveniently fitted with-out restrictions; see Second, in appliedscenarios, it is often desirable to make results com-parable with case control Studies , in which only oddsratios are unadjusted Analysis targets the marginal(overZ) association betweenXandY, for exam-ple, through the marginal odds ratioORm=Pr(Y= 1|X= 1)Pr(Y= 0|X= 0)Pr(Y= 0|X= 1)Pr(Y= 1|X= 0).We define m= log(ORm). In the presence of con-foundersZ,ORmfails to have a causal interpreta-tion. In particular, it may differ from 1 in the ab-sence of a causal influence ofZcan be eliminated by condi-tioning onZ, as in the conditional odds ratioORc(Z) =Pr(Y= 1|X= 1,Z)Pr(Y= 0|X= 0,Z)Pr(Y= 0|X= 1,Z)Pr(Y= 1|X= 0,Z).