The Use of Joint Models in Analysis of Aggregate Endpoints in RERF Cohort Studies

In radiation risk estimation based on the Radiation Effects Research Foundation (RERF) cohort studies, one common analysis is Poisson regression on radiation dose and background and effect modifying variables of an aggregate endpoint such as all solid cancer incidence or all non-cancer mortality. As currently performed, these analyses require selection of a surrogate radiation organ dose, (e.g., colon dose), which could conceptually be problematic since the aggregate endpoint comprises events arising from a variety of organs. We use maximum likelihood theory to compare inference from the usual aggregate endpoint analysis to analyses based on joint analysis. These two approaches are also compared in a re-analysis of RERF Life Span Study all cancer mortality. We show that, except for a trivial difference, these two analytic approaches yield identical inference with respect to radiation dose response and background and effect modification when based on a single surrogate organ radiation dose. When repeating the analysis with organ-specific doses, an interesting issue of bias in intercept parameters arises when dose estimates are undefined for one sex when sex-specific outcomes are included in the aggregate endpoint, but a simple correction will avoid this issue. Lastly, while the joint analysis formulation allows use of organ-specific doses, the interpretation of such an analysis for inference regarding an aggregate endpoint can be problematic. To the extent that analysis of radiation risk for an aggregate endpoint is of interest, the joint-analysis formulation with a single surrogate dose is an appropriate analytic approach, whereas joint analysis with organ-specific doses may only be interpretable if endpoints are considered separately for estimating dose response. However, for neither approach is inference about dose response well defined.