Time-dependent prognostic accuracy measures for recurrent event data

In many clinical contexts, the event of interest could occur multiple times for the same patient. Considerable advancement has been made on developing recurrent event models based on or that use biomarker information. However, less attention has been given to evaluating the prognostic accuracy of a biomarker or a composite score obtained from a fitted recurrent event-rate model. In this manuscript, we propose novel measures to characterize the prognostic accuracy of a marker measured at baseline in the presence of recurrent events. The proposed estimators are based on a semiparametric frailty model that accounts for the informativeness of a marker and unobserved heterogeneity among patients with respect to the rate of event occurrence. We investigate the asymptotic properties of the proposed accuracy estimators and demonstrate these estimators' finite sample performance through simulation studies. The proposed estimators have minimal bias and appropriate coverage. The estimators are applied to evaluate the performance of a baseline forced expiratory volume, a measure of lung capacity, for repeated episodes of pulmonary exacerbations in patients with cystic fibrosis.