Smoothing Techniques and Semiparametric Regression Models for Recurrent Event Data

Abstract

Recurrent event data are frequently encountered in biomedical and clinical studies where the event of interest can happen for multiple times, such as recurrent hospitalizations and recurrent infections. The analysis of recurrent event data can be based on the gap times between consecutive events or on the total time to event. In this dissertation, we improve the estimation and inference procedures of the accelerated failure time model for recurrent gap time data using the induced smoothing technique in the first project, and we focus on regression models on the rate function of the recurrent event process in the second and the third projects. The semiparametric accelerated failure time (AFT) model is especially appealing in analyzing recurrent gap time data owing to its direct interpretation of covariate effects. In general, estimation of the semiparametric AFT model is challenging because the rank-based estimating function is a non-smooth step function. In the first project, we extend the induced smoothing approach to the AFT model for recurrent gap time data. Our proposed smooth estimating function permits the application of standard numerical methods for both the regression coefficients estimation and the standard error estimation. The proposed method is applied to the data analysis of repeated hospitalizations for patients in the Danish Psychiatric Center Register. In the second project, we focus on the semiparametric additive rates model where the regression coefficients quantify the absolute difference in the occurrence rate of the recurrent events between different groups. The model estimation requires the values of time-dependent covariates being observed throughout the entire follow-up period. In practice, however, time-dependent covariates are usually only measured at intermittent follow-up visits. To solve this problem, we propose to kernel smooth functions involving time-dependent covariates across subjects in the estimating function. In the third project, we extend the kernel smoothing approach to the additive-multiplicative rates model with intermittently observed time-dependent covariates. The additive-multiplicative rates model allows some covariates to have additive effects and others to have multiplicative effects. The proposed methods are illustrated by analyzing data from an epidemiologic study which aims to evaluate the effect of streptococcal infections on recurrent pharyngitis episodes.