Cure rate model with interval censored data

Abstract

In cancer trials, a significant fraction of patients can be cured, that is, the disease is completely eliminated, so that it never recurs. In general, treatments are developed to both increase the patients' chances of being cured and prolong the survival time among non-cured patients. A cure rate model represents a combination of cure fraction and survival model, and can be applied to many clinical studies over several types of cancer. In this article, the cure rate model is considered in the interval censored data composed of two time points, which include the event time of interest. Interval censored data commonly occur in the studies of diseases that often progress without symptoms, requiring clinical evaluation for detection (Encyclopedia of Biostatistics. Wiley: New York, 1998; 2090-2095). In our study, an approximate likelihood approach suggested by Goetghebeur and Ryan (Biometrics 2000; 56:1139-1144) is used to derive the likelihood in interval censored data. In addition, a frailty model is introduced to characterize the association between the cure fraction and survival model. In particular, the positive association between the cure fraction and the survival time is incorporated by imposing a common normal frailty effect. The EM algorithm is used to estimate parameters and a multiple imputation based on the profile likelihood is adopted for variance estimation. The approach is applied to the smoking cessation study in which the event of interest is a smoking relapse and several covariates including an intensive care treatment are evaluated to be effective for both the occurrence of relapse and the non-smoking duration.

Interval censoring

“…The readers are referred to Huang and Wellner [50] for a rigorous study of the efficiency and asymptotic properties of the MLE based on case II interval-censored data. A few generalizations of model (4) have been proposed for interval-censored data [3] and among them, Kim and Jhun [51] recently studied the situation where there exists a group of cured subjects or the subjects who may never experience the survival event of interest.…”

Nonparametric versus Parametric Estimation of the Cure Fraction Using Interval Censored Data

“…In such cases, the survival data is described as interval survival data and can be used in the general situation which can take place in the survival studies (Gomez et al, 2004;Sun, 2005;Doehler and Davidian, 2008;Sen and Tan, 2008). Therefore, right and left censoring are special cases of the interval censored data (Kim et al, 2008). Downloaded by [Stanford University Libraries] at 16:32 13 October 2012…”

Some asymptotic properties for a smooth kernel estimator of the conditional mode under random censorship

“…For their part, Perdoná and LouzadaNeto (2008) studied a modified Weibull distribution model and gave an application to both a dataset of HIV-contaminated children and to the problem of misclassification of the cause of death. Let us also quote Kim and Jhun (2008) who addressed a cure rate model with interval censored data. The problem of estimating the unconditional/conditional mode of the probability density has given way to a large amount of related statistics literature.…”