Semiparametric regression analysis for alternating recurrent event data

Alternating recurrent event data arise frequently in clinical and epidemiologic studies, where 2 types of events such as hospital admission and discharge occur alternately over time. The 2 alternating states defined by these recurrent events could each carry important and distinct information about a patient's underlying health condition and/or the quality of care. In this paper, we propose a semiparametric method for evaluating covariate effects on the 2 alternating states jointly. The proposed methodology accounts for the dependence among the alternating states as well as the heterogeneity across patients via a frailty with unspecified distribution. Moreover, the estimation procedure, which is based on smooth estimating equations, not only properly addresses challenges such as induced dependent censoring and intercept sampling bias commonly confronted in serial event gap time data but also is more computationally tractable than the existing rank-based methods. The proposed methods are evaluated by simulation studies and illustrated by analyzing psychiatric contacts from the South Verona Psychiatric Case Register.