Selection bias due to omitting interactions from inverse probability weighting

Inverse probability weighting (IPW) is often used to adjust for selection bias, typically using a simple logit model without interactions as a missingness model. However, the size of the selection bias depends on the interaction between exposure and outcome in their effect on selection - implying that it may be important to include interactions in the IPW model. Via a simulation and a real-data application we compare the performance of IPW with and without interaction terms to estimate a regression coefficient. The simulation study shows that IPW including interactions gives less biased estimates than IPW without interactions in all scenarios studied. Importantly, IPW using a logit model with no interactions often gives estimates close to the complete case analysis (CCA) - perhaps giving false reassurance that results are robust to selection bias. The real-data application investigates the association between unemployment and sleep duration, using data from Understanding Society. IPW including interactions suggests that unemployment is associated with a reduction in sleep duration of around 23 (9, 38) minutes, compared to 27 (14, 40) minutes for IPW without interactions, and 31 (19, 43) minutes for CCA. We strongly recommend including interactions in missingness models to adjust for selection bias.