A cautionary note about estimating effects of secondary exposures in cohort studies

Cohort studies are often enriched for a primary exposure of interest to improve cost-effectiveness, which presents analytical challenges not commonly discussed in epidemiology. In this paper, we use causal diagrams to represent exposure-enriched cohort studies, illustrate a scenario wherein the risk ratio for the effect of a secondary exposure on an outcome is biased, and propose an analytical method for correcting for such bias. In our motivating example, maternal smoking (Z) is a cause of fetal growth restriction (X), which subsequently affects preterm birth (Y) (i.e., Z → X → Y); strong positive associations exist between both Z, X and X, Y; and enrichment for X increases its prevalence from 10% to 50%. In the X-enriched cohort, unadjusted and X-adjusted analyses lead to bias in the risk ratio for the total effect of Z on Y. After application of inverse probability weights, the bias is corrected, with a small loss of efficiency in comparison with a same-sized study without X-enrichment. With increasing interest in conducting secondary analyses to reduce research costs, caution should be employed when analyzing studies that have already been enriched, intentionally or unintentionally, for a primary exposure of interest. Causal diagrams can help identify scenarios in which secondary analyses may be biased. Inverse probability weights can be used to remove the bias.