Semiparametric Threshold Regression Analysis for Time-to-Event Data
Kagan, Abram M
MetadataShow full item record
Threshold regression is a relatively new alternative approach to the Cox proportional hazards model when the proportional hazards assumption is violated. It is based on first-hitting-time models, where the time-to-event data can be modeled as the time at which the stochastic process of interest first hits a boundary or threshold state. In this dissertation, we develop a semiparametric threshold regression model with flexible covariate effects. Specifically, we propose a B-spline approximation method to estimate nonlinear covariate effects on both the initial state and the rate of the process. We show that the spline based estimators are consistent and achieve the possible optimal rate of convergence under the smooth assumption. Simulation studies are conducted for practical situations, and the methodology is applied to a study of osteoporotic fractures that motivated this investigation. To check the validity of threshold regression model with parametric link functions, we propose two supremum-type test processes: one is based on cumulative sums of martingale residuals; the other one is based on censoring consistent residuals. The realizations of these test stochastic processes under the assumed model can be easily generated by computer simulation. We show that both tests are consistent against model misspecification. Both model checking methods have been applied to a kidney dialysis data set.