Two-stage recurrent events random effects models

We consider semiparametric random-effects models for recurrent events in the presence of a terminal event. The recurrent events have either a proportional marginal rate model (Cox in J Roy Stat Soc Ser B 34:406-424, 1972) or a proportional marginal mean model (Ghosh and Lin in Stat Sin 34: 663-688, 2002), while the marginal rate of the terminal event is given by a proportional model. The dependency between the recurrent events and the terminal event is described by two variants of random effects models that allow the processes to share the random effect, either fully or partly. The models are formulated as two-stage models, where the marginals can be fitted in an initial stage, and then subsequently random effects parameters can be estimated. The estimation of parameters does not require the choice of any tuning parameters, in contrast to procedures based on numerical integration, and the numerical procedure works well. Standard errors were computed by bootstrapping. The methods are applied to the Taichung Peritoneal Dialysis Study (Chen et al. in Biom J 57(2):215-233, 2015) that considered recurrent inflammations in dialysis patients.