An Analysis of Comparative Carcinogenesis Experiments Based on Multiple Times to Tumor

210

225

Recurrent event data are frequently encountered in longitudinal follow-up studies. In statistical literature, noninformative censoring is typically assumed when statistical methods and theory are developed for analyzing recurrent event data. In many applications, however, the observation of recurrent events could be terminated by informative dropouts or failure events, and it is unrealistic to assume that the censoring mechanism is independent of the recurrent event process. In this article we consider recurrent events of the same type and allow the censoring mechanism to be possibly informative. The occurrence of recurrent events is modeled by a subject-specific nonstationary Poisson process via a latent variable. A multiplicative intensity model is used as the underlying model for nonparametric estimation of the cumulative rate function. The multiplicative intensity model is also extended to a regression model by taking the covariate information into account. Statistical methods and theory are developed for estimation of the cumulative rate function and regression parameters. As a major feature of this article, we treat the distributions of both the censoring and latent variables as nuisance parameters. We avoid modeling and estimating the nuisance parameters by proper procedures. An analysis of the AIDS Link to Intravenous Experiences cohort data is presented to illustrate the proposed methods.

Section: Introductionmentioning

confidence: 99%

Analyzing Recurrent Event Data With Informative Censoring

Wang

Qin

Chiang

2001

210

225

“…Here S * (t) = 1 − θ (1 − S(t)), with a cure fraction of 1 − θ. An alternative K-site cancer model discussed by Gail, Santner, and Brown (1980) suggests that for each patient, an unknown N out of K dominant mutation sites within a disease location become mutated, with K fixed a priori based on scientific considerations. This implies a BG(K) model in which N ~ Bin(K, θ) and m(t) = (1 − θ (1 − e t )) K , yielding S * (t) = (1 − θ (1 − S(t))) K with a cure fraction of (1 − θ) K .…”

Section: First-activation Schemementioning

confidence: 99%

Flexible Cure Rate Modeling Under Latent Activation Schemes

Cooner

Banerjee

Carlin

et al. 2007

147

168

With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, Ibrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework's ability to distinguish among underlying mechanisms that lead to relapse and cure.

“…We discuss the physical interpretations, new stochastic formulations and the relationships among the following models of recurrent events data: the frailty model (Oakes (1992), Sinha 1993 andHougaard (2000)), the M-site model (Gail et al, 1980) and the time-varying correlated frailty model (Herdersen and Shimakura, 2003). Despite the recent interest and research activity in Bayesian survival analysis (e.g., Sinha and Dey (1998), Walker, et al (1999), Dey, Mueller and Sinha (1998) and Ibrahim, Chen and Sinha (2001)), the current Bayesian literature on recurrent events data is very limited.…”

Section: Introductionmentioning

confidence: 99%

Current Methods for Recurrent Events Data With Dependent Termination

Sinha

Maiti

Ibrahim

et al. 2008

SummaryThere has been a recent surge of interest in modeling and methods for analyzing recurrent events data with risk of termination dependent on the history of the recurrent events. To aid the future users in understanding the implications of modeling assumptions and modeling properties, we review the state of the art statistical methods and present novel theoretical properties, identifiability results and practical consequences of key modeling assumptions of several fully specified stochastic models. After introducing stochastic models with noninformative termination process, we focus on a class of models which allows both negative and positive association between the risk of termination and the rate of recurrent events via a frailty variable. We also discuss the relationship as well as the major differences between these models in terms of their motivations and physical interpretations. We discuss associated Bayesian methods based on Markov chain Monte Carlo tools, and novel model diagnostic tools to perform inference based on fully specified models. We demonstrate the usefulness of current methodology through an analysis of a data set from a clinical trial. In conclusion, we explore possible future extensions and limitations of the methodology.