Theses Doctoral

A Tale of Two Paradoxes: Reconciling Selection Bias, Collider Bias, and the Birth Weight Paradox

Levy, Natalie S.

Unexpected findings that contradict well-established relationships between exposures and outcomes are often referred to as “paradoxes” in the epidemiologic literature. For example, the “birth weight paradox” refers to the observed protective association between smoking during pregnancy and infant mortality among low birth weight infants. A recent body of literature suggests that this and several other well-known epidemiologic paradoxes can be attributed to collider bias. Collider bias results from conditioning on a variable that is caused by the exposure or shares common cause with the exposure and is caused by the outcome or shares common causes with the outcome. Several recent epidemiology textbooks and methodological studies further suggest that collider bias is the graphical representation of selection bias, suggesting that these two biases are synonymous.

This structural approach to bias is conceptually very useful for defining, describing, and identifying selection bias, but it introduces paradoxes of its own due to contradictory conclusions in the selection and collider bias methodologic literatures about their likely impact on study results in terms of magnitude, direction, and strata affected. Resolving these discrepancies is essential for our theoretical understanding of the relationship between selection and collider bias and has important practical implications for how we teach epidemiology, design studies, and evaluate and quantify the potential effects of bias on our results. For example, while patterns of collider bias coincide qualitatively with the birth weight paradox, the magnitude of collider bias would have to be substantial to reverse the sign of the association, contrary to prevailing beliefs that collider bias only minimally affects our results.

To date, the plausibility of collider bias as an explanation for the birth weight paradox has not been empirically evaluated using data in which the paradox is observed.Taken together, these inconsistencies and contradictions suggest that our understanding of selection bias and collider bias remains incomplete. The overarching goal of this dissertation was to advance the theoretical and quantitative understanding of the impact of collider bias on study results to clarify the relationship between selection and collider bias. I began by systematically reviewing the methodologic literature on selection and collider bias. I found that selection bias and collider bias are increasingly treated as synonyms, but that conclusions about the magnitude and direction of selection and collider bias, the stratum affected, and the conditions under which the effects of each type of bias were evaluated are highly inconsistent.

This suggested that divergent findings about the impact of selection and collider bias might be resolved by considering the impact of collider bias under a broader set of circumstances. I used microsimulations grounded in the sufficient component cause model to examine collider bias not under the null; interrogate why multiplicative interaction appeared central to the impact of collider bias; and clarify which stratum or strata are affected by collider bias. I identified clear patterns for the magnitude, direction, and strata affected by collider bias and successfully reconciled discrepancies with the selection bias literature. This work also enabled me to interrogate both the causal mechanisms and mathematical principles that underlie collider bias, which revealed how collider bias leads to non-exchangeability and when stratifying on a collider results in bias.

Finally, I applied this deeper understanding of the mechanisms underlying collider bias to empirically evaluate the plausibility of collider bias as an explanation for the birth weight paradox. Using microsimulations parameterized with 2015 National Center for Health Statistics Cohort Linked Birth-Infant Mortality, I identified scenarios that successfully reproduced the paradox and all observed relationships between smoking during pregnancy, infant mortality, and low birth weight. These findings strengthen the evidence for the role of collider bias in producing the paradox and shed light on the potential magnitude of unmeasured confounding and direct effects of smoking and low birth weight on infant mortality that may be required for the observed magnitude of the paradox to arise.

This work clarifies that almost all selection bias is collider bias; that the effects of collider bias vary in magnitude and direction; that selecting on a collider always leads to bias, but this bias may not occur in the stratum that coincides with our analytical sample; and that collider bias may resolve the birth weight paradox, but is unlikely to explain all epidemiologic paradoxes.


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More About This Work

Academic Units
Thesis Advisors
Schwartz, Sharon B.
Ph.D., Columbia University
Published Here
July 5, 2023