Sibling Comparison Designs Bias From Non-Shared Confounders and Measurement Error

Twins, full siblings, and half-siblings are increasingly used as comparison groups in matched cohort and matched casecontrol studies. The “within-pair” estimates acquired through these comparisons are free from confounding from all factors that are shared by the siblings. This has made sibling comparisons popular in studying associations thought likely to suffer confounding from socioeconomic or genetic factors. Despite the wide application of these designs in epidemiology, they have received little scrutiny from a statistical or methodological standpoint. In this paper we show, analytically and through a series of simulations, that the standard interpretation of the models is subject to several limitations that are rarely acknowledged. Although within-pair estimates will not be confounded by factors shared by the siblings, such estimates are more severely biased by non-shared confounders than the unpaired estimate. If siblings are less similar with regard to confounders than to the exposure under study, the within-pair estimate will always be more biased than the ordinary unpaired estimate. Attenuation of associations due to random measurement error in exposure will also be higher in the within-pair estimate, leading within-pair associations to be weaker than corresponding unpaired associations, even in the absence of confounding. Implications for the interpretation of sibling comparison results are discussed. (Epidemiology 2012;23: 713–720) Sibling comparison designs, such as the co-twin control design, have been considered simple, yet ingenious, extensions of the matched case-control design. Instead of explicitly matching on a set of measured variables, the use of siblings as controls will automatically match on many unmeasured factors, including cultural background, parental characteristics and child-rearing practices, and—particularly for monozygotic twins—genetics. This promise of adjustment for a wide range of unmeasured, even unknown, confounders has made co-twin control methods popular, especially in etiologic research on controversial topics. Recent applications include the associations of body mass index with mortality, sexual orientation with mental disorder, and birth weight with cardiovascular disease. Twins are relatively rare, and the degree to which associations among twins are generalizable to the entire population has been questioned. Recent commentaries have therefore advocated matching of other relatives, primarily fulland half-siblings. Indeed, sibling comparisons have already been used in economics research for at least 30 years, and recent applications in epidemiology include the association of mother’s smoking during pregnancy with offspring psychologic traits, and the association of birth weight with intelligence. Methodologic aspects of sibling-comparison designs have been relatively unexplored. Common analytic strategies for paired data include the flexible between-within model and conditional logistic regression. In the absence of nonshared confounding and other biases, these methods produce estimates of the causal effect of exposure free from confounding by factors shared by the siblings. The absence of bias is rather unlikely in real applications, but what impact these biases might have on sibling comparisons has, to our knowledge, not been discussed in the epidemiologic literature. In contrast, economists have long been aware that random measurement error and omitted variables can have specific influence on within-pair estimates under a linear model. We explore the impact of 2 common sources of bias: confounding by factors not perfectly shared by siblings, and random measurement error of exposure. We will show, analytically and with simulations, how sibling comparison methods in these situations may actually lead to increased bias. Specifically, we give a brief summary of how sibling comSubmitted 12 June 2011; accepted 12 March 2012; posted 9 July 2012. From the Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden; Centre for Violence Prevention, Karolinska Institutet, Stockholm, Sweden; and Department of Epidemiology, Harvard School of Public Health, Boston, MA. Conflicts of Interest and Source of Funding: T.F. and R.K-H. are supported by the Swedish Prison and Probation Service R&D. SÖ is supported by the Swedish Council for Working Life and Social Research 2011–1477 . AS is supported by the Swedish Research Council 2008–5375 . The authors report no conflict of interest. Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (www.epidem.com). This content is not peer-reviewed or copy edited; it is the sole responsibility of the author. Correspondence: Thomas Frisell, Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, PO Box 281, 171 77, Stockholm, Sweden. E-mail: Thomas.Frisell@ki.se. Copyright © 2012 by Lippincott Williams & Wilkins ISSN: 1044-3983/12/2305-0713 DOI: 10.1097/EDE.0b013e31825fa230 Epidemiology • Volume 23, Number 5, September 2012 www.epidem. com | 713 parisons are analyzed and explain why the designs may lead to increased bias. Next, we show the impact analytically under a linear model, and we illustrate the impact through simulations under a logistic model where the outcome and exposure are dichotomous. We end with a discussion of how results from sibling comparisons may be interpreted in light of the caveats raised here. STATISTICAL ANALYSES OF SIBLING COMPARISON DESIGNS For binary outcomes, the sibling comparison is often considered an extension of the matched case-control design. Sibling-pairs discordant for the studied outcome are selected, and the association of exposure with outcome in the paired data is analyzed using McNemar’s test or conditional logistic regression. Because the analysis is essentially stratified by sibling pair, only pairs that also differ in exposure level will contribute to the estimated association. Although conditional logistic regression is the method of choice in cross-sectional case-control settings, most sibling comparison studies are nested in a larger cohort or population register and may thus be analyzed using the more general between-within model. To describe this model, let Yij and Xij be the outcome and exposure, respectively, of individual j in pair i. The pairs are symmetric, so the ordering of j is exchangeable. First consider an ordinary generalized linear regression model, ignoring the fact that the data consist of pairs: g{E Yij Xij } Xij (1) The between-within model is a simple extension of this, where the individual’s exposure and the siblings’ mean exposure are included as independent variables: g{E Yij Xij, X i } BW WXij BX i (2) where X i is the average exposure in pair i. The link function, g{}, puts the sibling comparison in a generalized linear model framework. Different link functions enable for instance linear, logistic, and log-linear regression. The exposure-outcome association is split into 2 parts: a within-effect W and a between-effect B. When the exposure is dichotomous, the between-within model will give the same result as analyzing only exposure-discordant twin pairs. Recently, we showed that in the absence of nonshared confounders, the within effect may be interpreted as a causal exposure effect in the subpopulation consisting of exposure discordant pairs. The between-effect contains information on how strongly factors shared by the family affect the exposure-outcome association. However, this information is generally considered difficult to interpret and is ignored in most applications. Although some sibling comparison studies estimate only within effects, most aim to evaluate the presence and degree of confounding due to shared factors by comparing the unpaired estimate, , to W. The customary interpretation has been that if W there is no confounding by shared factors; if is different from W, there is at least some confounding by shared factors; and if W 0, the entire association is caused by shared confounders. As we will show in the following sections, none of these conclusions is necessarily true. HOW SIBLING COMPARISON DESIGNS CAN INCREASE BIAS To understand how sibling comparison designs could increase bias, it may help to consider a hypothetical situation in which the exposure, confounder, and outcome are binary, there is no causal effect of exposure on outcome, and the exposure and outcome are both influenced by sibling-shared risk factors, but the confounder is not. As noted earlier in the text, the only pairs that contribute to the estimated “withinpair” association are those discordant in exposure. Although such discordant pairs may share many causes of the exposure, the fact these pairs are differently exposed implies a selection of pairs that also differ in nonshared causes of the exposure, including common causes of both exposure and outcome. In other words, with regard to nonshared confounders, the members of exposure-discordant pairs (although they are siblings) are likely to differ more from each other than 2 randomly selected persons from the same population having the same exposure levels. If the effect of the confounder is to increase both the probability of being exposed and the probability of developing the outcome, unexposed persons are less likely to have the confounder, and consequently less likely to develop the outcome. When picked as part of a discordant pair, a sibling is also selected to be different from the exposed relative, further reducing their likelihood of having the confounder. As an effect, the confounder-exposure association will be strengthened, thus increasing any spurious association due to nonshared confounding bias. This problem can be illustrated using causal diagrams. Suppose that the data-generating mechanism is given by the causal diagram in the Figure. X is the exposure of interest, Y is the outcome, and C denotes the fu