Non-parametric estimation with doubly censored data

A flexible semiparametric modeling approach for doubly censored data with an application to prostate cancer

Doubly censored data often arise in medical studies of disease progression involving two related events for which both an originating and a terminating event are interval-censored. Although regression modeling for such doubly censored data may be complicated, we propose a simple semiparametric regression modeling strategy based on jackknife pseudo-observations obtained using nonparametric estimators of the survival function. Inference is carried out via generalized estimating equations. Simulations studies show that the proposed method produces virtually unbiased covariate effect estimates, even for moderate sample sizes. A prostate cancer study example illustrates the practical advantages of the proposed approach.

Nonparametric inference and uniqueness for periodically observed progressive disease models

In many studies examining the progression of HIV and other chronic diseases, subjects are periodically monitored to assess their progression through disease states. This gives rise to a specific type of panel data which have been termed "chain-of-events data"; e.g. data that result from periodic observation of a progressive disease process whose states occur in a prescribed order and where state transitions are not observable. Using a discrete time semi-Markov model, we develop an algorithm for nonparametric estimation of the distribution functions of sojourn times in a J state progressive disease model. Issues of uniqueness for chain-of-events data are not well-understood. Thus, a main goal of this paper is to determine the uniqueness of the nonparametric estimators of the distribution functions of sojourn times within states. We develop sufficient conditions for uniqueness of the nonparametric maximum likelihood estimator, including situations where some but not all of its components are unique. We illustrate the methods with three examples.

A parametric survival model with an interval-censored covariate

We present a parametric survival model whose particularity consists in the inclusion of an interval-censored covariate. The methodology is motivated by a study on injecting drug users in Badalona (Spain), most of whom suffered HIV infection as a result of their drug addiction. The study aims to examine the possible association between the elapsed time from first injecting drug use until HIV infection and the subsequent AIDS incubation period. Whereas the moment of HIV infection cannot be observed exactly and is therefore interval-censored, time until AIDS onset is doubly-censored. For the maximization of the resulting likelihood function, we use a numerical solver. Maximization is carried out by means of the mathematical programming language AMPL.