Regression splines in the quasi-likelihood analysis of recurrent event data

In many longitudinal studies of recurrent events there is an interest in assessing how recurrences vary over time and across treatments or strata in the population. Usual analyses of such data assume a parametric form for the distribution of the recurrences over time. Here, we consider a semiparametric model for the analysis of such longitudinal studies where data are collected as panel counts. The model is a non-homogeneous Poisson process with a multiplicative intensity incorporating covariates through a proportionality assumption. Heterogeneity is accounted for in the model through subject-specific random effects. The key feature of the model is the use of regression splines to model the distribution of recurrences over time. This provides a flexible and robust method of relaxing parametric assumptions. In addition, quasi-likelihood methods are proposed for estimation, requiring only first and second moment assumptions to obtain consistent estimates. Simulations demonstrate that the method produces estimators of the rate with low bias and whose standardized distributions are well approximated by the normal. The usefulness of this approach, especially as an exploratory tool, is illustrated by analyzing a study designed to assess the effectiveness of a pheromone treatment in disturbing the mating habits of the Cherry Bark Tortrix moth.