A note on potential gains in precision of radiation risk estimates from joint analysis

In estimating radiation-related risk of cancer and other diseases based on the RERF Life Span Study (LSS), joint analyses can be performed where multiple health outcome endpoints are combined in the same model, allowing some parameters to be estimated in common among all endpoints with possible increase in precision of radiation risk and other model parameter estimates. Using as a basis excess relative risk (ERR) and excess absolute risk (EAR) models of the type commonly used in analysis of LSS data at RERF, we use maximum likelihood theory to compute the asymptotic relative standard error of endpoint-specific radiation effect and other parameter estimates using joint analyses as compared to traditional independent analysis. We show that some gains in precision of endpoint-specific radiation risk parameter estimates can be achieved by sharing effect modifier and other model parameters, but only small or negligible gains in precision are achieved for endpoint-specific background modifying or effect modifying parameters when other model parameters are shared. The magnitude of the precision gain for radiation risk estimates depends on the number of endpoints, the baseline incidence rate of the endpoint, and the type of model being used.