Assessing etiological heterogeneity for multinomial outcome with two-phase outcome-dependent sampling design

Etiological heterogeneity occurs when distinct sets of events or exposures give rise to different subtypes of disease. Inference about subtype-specific exposure effects from two-phase outcome-dependent sampling data requires adjustment for both confounding and the sampling design. Common approaches to inference for these effects do not necessarily adjust appropriately for these sources of bias, or allow for formal comparisons of effects across different subtypes. We show that using inverse probability weighting (IPW) to fit a multinomial model to yield valid inference with this sampling design for subtype-specific exposure effects, and contrasts thereof. We compare the IPW approach to common regression-based methods for assessing exposure effect heterogeneity using simulations. The methods are applied to estimate subtype-specific effects of various exposures on breast cancer risk in the Carolina Breast Cancer Study (1993-2001).