Recurrent events analysis with piece-wise exponential additive mixed models

Recurrent events analysis plays an important role in many applications, including the study of chronic diseases or recurrence of infections. Historically, many models for recurrent events have been variants of the Cox model. In this article we introduce and describe the application of the piece-wise exponential Additive Mixed Model (PAMM) for recurrent events analysis and illustrate how PAMMs can be used to flexibly model the dependencies in recurrent events data. Simulations confirm that PAMMs provide unbiased estimates as well as equivalence to the Cox model when proportional hazards are assumed. Applications to recurrence of staphylococcus aureus and malaria in children illustrate the estimation of seasonality, bivariate non-linear effects, multiple timescales and relaxation of the proportional hazards assumption via time-varying effects. The R package pammtools is extended to facilitate estimation and visualization of PAMMs for recurrent events data.