Assessing Etiologic Heterogeneity for Multinomial Outcome with Two-Phase Outcome-Dependent Sampling Design

Etiologic 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 appropriately adjust for these sources of bias, or allow for formal comparisons of effects across different subtypes. Herein, using inverse probability weighting (IPW) to fit a multinomial model is shown to yield valid inference with this sampling design for subtype-specific exposure effects and contrasts thereof. The IPW approach is compared 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. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement S.A.R. was supported by The Chancellor's Fellowship from The Graduate School at the University of North Carolina at Chapel Hill. M.G.H. was supported by R01 AI085073. M.I.L. and M.A.T. were supported by P50 CA058223. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The study was approved by the Office of Human Research IRB at the University of North Carolina at Chapel Hill, and informed consent was obtained from each participant. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced in the present study are available upon reasonable request to the authors.