Accelerated failure time models for recurrent event data analysis and joint modeling

There are two commonly encountered problems in survival analysis: (a) recurrent event data analysis, where an individual may experience an event multiple times over follow-up; and (b) joint modeling, where the event time distribution depends on a longitudinally measured internal covariate. The proportional hazards (PH) family offers an attractive modeling paradigm for recurrent event data analysis and joint modeling. Although there are well-known techniques to test the PH assumption for standard survival data analysis, checking this assumption for joint modeling has received less attention. An alternative framework involves considering an accelerated failure time (AFT) model, which is particularly useful when the PH assumption fails. Note that there are AFT models that can describe data with wide ranging characteristics but have received far less attention in modeling recurrent event data and joint analysis of time-to-event and longitudinal data. In this paper, we develop methodology to analyze these types of data using the AFT family of distributions. Fitting these models is computationally and numerically much more demanding compared to standard survival data analysis. In particular, fitting a joint model is a computationally intensive task as it requires to approximate multiple integrals that do not have an analytic solution except in very special cases. We propose computational algorithms for statistical inference, and develop a software package to fit these models. The proposed methodology is demonstrated using both simulated and real data.