An additive-multiplicative model for longitudinal data with informative observation times

Designed clinical studies often assess outcomes at pre-planned time points. In most situations, standard statistical models, such as generalized linear mixed models and generalized additive models, are sufficient to depict the temporal trends of the outcome and produce valid inference. Complicating factors, however, do exist in practical data analyses. One complication arises when the outcome and observational processes are interdependent, that is, the observational process is informative; another challenge is patient characteristics may influence the longitudinally observed outcomes in non-additive ways, for example, by multiplicative factors. In this research, we extend the standard longitudinal models to accommodate informative observation through a more flexible modeling structure—one with additive-multiplicative components that do not require explicit specification of the dependency structure between the outcome and observation processes. Along this vein, we provide the essential theory for inference in such models. Simulation studies showed the proposed method performs well for finite-sample scenarios, and the method was applied to analyze a motivating example from an alcohol-associated hepatitis observational study.