Semiparametric Functional Temporal Process Regression of Prevalence Outcomes

Abstract

We develop novel semiparametric methods for flexibly modeling a prevalence indicator process observed over follow-up time. The proposed methods are motivated by various settings arising in end-stage renal disease (ESRD) and end-stage liver disease (ESLD).

In Chapter 1, we consider the response Survival-Out-of-Hospital, defined as a temporal process taking the value 1 when the subject is currently alive and not hospitalized, and 0 otherwise. The semiparametric model we consider assumes multiplicative covariate effects and leaves unspecified the baseline probability of being alive-and-out-of-hospital. Asymptotic properties are derived, and simulation studies are performed. The proposed methods are applied to the Dialysis Outcomes and Practice Patterns Study (DOPPS), a prospective international ESRD study.

In Chapter 2, we extend the methods from Chapter 1 to accommodate dependent censoring. We derive a modification of Inverse Probability of Censoring Weighting which offers improved stability and reduced computational burden relative to the traditional IPCW. We show that the regression estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. The methods are used to model the probability of being alive and active on the liver transplant waiting list, which can be dependently censored by liver transplantation.

In Chapter 3, we jointly model prevalence conditional on survival, and the death hazard. A frailty is shared by the prevalence and hazard models, with the frailty effect scaled in the latter. We propose an iterative procedure for estimating the regression parameters by updating frailties from their implied estimating equations. The scale parameter and random effect variance are estimated by numerical integration. The algorithm is asymptotically equivalent to an EM algorithm which treats the frailty terms as missing data. We apply the methods to DOPPS data.