Noncollapsibility in studies based on nonrepresentative samples

Abstract

Background: It is common to use nonrepresentative samples in observational epidemiologic studies, but there has been debate about whether this introduces bias. In this article, we consider the consequences on noncollapsibility of a sample selection related to a relevant outcome-risk factor.

Methods: We focused on the odds ratio and defined the noncollapsibility effect as the difference between the marginal and the conditional (with respect to the outcome-risk factor) exposure-outcome association. We consider a situation in which the aims of the study require the estimate of a conditional effect.

Results: Using a classical numerical example, which assumes that all variables are binary and that the outcome-risk factor is not an effect modifier, we illustrate that in the selected sample the noncollapsibility effect can either be larger or smaller than in the population-based study, according to whether the selection moves the prevalence of the risk factor closer to or away from 50%. When the outcome-risk factor is also a confounder, the magnitude of the noncollapsibility effect in the selected sample depends on the effects of the selection on both noncollapsibility and confounding.

Conclusions: When a key outcome-risk factor is unmeasured, in presence of noncollapsibility neither a population-based nor a selected study can directly estimate the conditional effect; whether the computable marginal is closer to the conditional in the selected or in the population-based study depends on the underlying population and the selection process.

Keywords: Cohort study; Odds ratios; Selection bias.