Semiparametric regression analysis of recurrent events

Abstract

In this Dissertation, we mainly concern the effects of covariates on the underlying recurrent event process. Two topics are considered: Recurrent event data are data in which the event of interest can occur repeat-edly and the successive event times are available. We study the semiparametric regression model with random effects for recurrent event data in the presence of informative censoring times. For inference, we propose using the maximum likelihood approach for estimation of the underlying baseline intensity function and regression parameters. The proposed estimates are consistent and have asymptotically a normal distribution. Also the maximum likelihood estimators of regression parameters are asymptotically efficient. The finite sample properties of the proposed estimates are investigated through simulation studies. An illustrative example from a clinical trial is provided. Panel count data deal with the recurrent events in discrete times. We study the semiparametric regression analysis of panel count data when certain covariate effects may be much more complex than linear effects. To explore the nonlinear interactions between covariates, we propose a class of partially linear models with possibly varying coefficients for the mean function of the counting processes with panel count data. The functional coefficients are estimated by B-spline function approximations. The estimation procedures are based on maximum pseudo-likelihood and likelihood approaches and they are easy to implement. The asymptotic properties of the resulting estimators are established, and their finite-sample performance is assessed by Monte Carlo simulation studies. We also demonstrate the value of the proposed method by the analysis of a cancer data set, where the new modeling approach provides more comprehensive information than the usual proportional mean model.