A semi-parametric approach to analysis of event duration and prevalence

Event duration and prevalence are important features for assessing outcomes of medical treatment. Although semi-parametric approaches have been well developed for analysis of recurrent events, applications to analysis of event duration, in particular the duration of multiple overlapping events, are relatively rare. Various approaches are considered using semi-parametric multiplicative models for cumulative duration and prevalence of events with time-varying coefficients, and a simple algorithm is proposed to fit the models. The relationships between parameters in the semi-parametric multiplicative models for prevalence and cumulative duration, particularly for models with time-varying treatment effects, are examined. The models can be extended to take overlapping intervals of multiple events with varying severity into account, and can be used in the presence of censoring due to informative dropouts and/or a terminal event. The approach can be implemented in standard software such as SAS. The approach was applied to a dataset of recurrent pulmonary exacerbations in patients with cystic fibrosis. Simulation was also conducted to examine the small-sample properties of the approaches.