Diagnostic checks in mixture cure models with interval-censoring

Abstract

Models for interval-censored survival data presenting a fraction of "cure" or "immune" patients have recently been proposed in the literature, particularly extending the mixture cure model to interval-censored data. However, little is known about the goodness-of-fit of such models. In a mixture cure model, the survival distribution of the entire population is improper and expressed in terms of the survival distribution of uncured individuals, i.e. the latency part of the model, and the probability to experience the event of interest, i.e. the incidence part. To validate a mixture cure model, assumptions made on both parts need to be checked, i.e. the survival distribution of uncured individuals, the link function used in the latency and the linearity of the covariates used in the both parts of the model. In this work, we investigate the Cox-Snell and deviance residuals and show how they can be adapted and used to perform diagnostics checks when all subjects are right- or interval-censored and some subjects are cured with unknown cure status. A large simulation study investigates the ability of these residuals to detect a departure from the assumptions of the mixture model. Developed techniques are applied to a real data set about Alzheimer's disease.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup

“…Model-checking is often of interest but challenging in the mixture cure model. 32,39,40 For example, Müller et al. 32 and Scolas et al.…”

“…32 and Scolas et al. 40 developed some diagnostic methods under right-censored and interval-censored data, respectively. Extending the above methods to the case of partly interval censoring is desirable but requires further investigation.…”

On the use of the modified power series family of distributions in a cure rate model context

“…where f pop ðÁ; i , kÞ and S pop ðÁ; i , kÞ come from equations (4) and (2), respectively, with given in equation (5). Parameter estimation can be performed based on the maximum likelihood method.…”

“…Some recent works showing the intense activity in this line are presented in Rocha et al., 1 Moodie et al., 2 Gressani and Lambert, 3 Chen and Du, 4 Scolas et al. 5 and Ramires et al. 6 At this moment, we can find many diseases that previously did not have possibility of cure, but nowadays patients treated for such diseases can live for a long time.…”

“…Survival models that incorporate a proportion of cured subjects are becoming increasingly popular in the analysis of data from clinical trials and other studies, mainly due to advances in Medicine. Some recent works showing the intense activity in this line are presented in Rocha et al, 1 Moodie et al, 2 Gressani and Lambert, 3 Chen and Du, 4 Scolas et al 5 and Ramires et al 6 At this moment, we can find many diseases that previously did not have possibility of cure, but nowadays patients treated for such diseases can live for a long time. For this reason, cure rate models have attracted increasing interest over the last years.…”