Noncollapsibility in studies based on nonrepresentative samples

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.