Joint outcome modeling using shared frailties with application to temporal streamflow data

Recently there has been tremendous interest in the development of tools for joint analysis of longitudinal data and time-to-event data. This has gained emphasis particularly in clinical studies, where longitudinal measurements on a response may be recorded along with a time-to-event outcome. Joint analysis of multiple outcomes beyond longitudinal and survival have also been considered, for example, joint analysis of a variety of generalized linear models including continuous and count data, or continuous and binomial data. With joint analysis of multiple outcomes, the interest may be analysis of one outcome conditional on the others, or, more typically, analysis of all outcomes jointly using latent random effects to link the outcomes. In this project, we study joint-outcome models with the particular application being streamflow at two stations on the prairies. Here, streamflow at the two stations is linked via an annual random effect. Smoothers are used to flexibly account for temporal trends in the model. An important aspect is determining the amount of information required in order to estimate the link parameter which connects the two processes, and we investigate this via simulation in the context of the streamflow analysis.