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Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach.

ABSTRACT: In many situations in survival analysis, it may happen that a fraction of individuals will never experience the event of interest: they are considered to be cured. The promotion time cure model takes this into account. We consider the case where one or more explanatory variables in the model are subject to measurement error, which should be taken into account to avoid biased estimators. A general approach is the simulation-extrapolation algorithm, a method based on simulations which allows one to estimate the effect of measurement error on the bias of the estimators and to reduce this bias. We extend this approach to the promotion time cure model. We explain how the algorithm works, and we show that the proposed estimator is approximately consistent and asymptotically normally distributed, and that it performs well in finite samples. Finally, we analyse a database in cardiology: among the explanatory variables of interest is the ejection fraction, which is known to be measured with error.

SUBMITTER: Bertrand A

PROVIDER: S-EPMC5693403 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach.

Bertrand Aurelie A Legrand Catherine C Carroll Raymond J RJ De Meester Christophe C Van Keilegom Ingrid I

Political analysis : an annual publication of the Methodology Section of the American Political Science Association 20170103 1

In many situations in survival analysis, it may happen that a fraction of individuals will never experience the event of interest: they are considered to be cured. The promotion time cure model takes this into account. We consider the case where one or more explanatory variables in the model are subject to measurement error, which should be taken into account to avoid biased estimators. A general approach is the simulation-extrapolation algorithm, a method based on simulations which allows one t ...[more]

PMID: 29151774

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Project description:BackgroundDifferent parametric survival models can lead to widely discordant extrapolations and decision uncertainty in cost-effectiveness analyses. The use of excess hazard (EH) methods, which incorporate general population mortality data, has the potential to reduce model uncertainty. This review highlights key practical considerations of EH methods for estimating long-term survival.MethodsDemonstration of methods used a case study of 686 patients from the German Breast Cancer Study Group, followed for a maximum of 7.3 y and divided into low (1/2) and high (3) grade cancers. Seven standard parametric survival models were fit to each group separately. The same 7 distributions were then used in an EH framework, which incorporated general population mortality rates, and fitted both with and without a cure parameter. Survival extrapolations, restricted mean survival time (RMST), and difference in RMST between high and low grades were compared up to 30 years along with Akaike information criterion goodness-of-fit and cure fraction estimates. The sensitivity of the EH models to lifetable misspecification was investigated.ResultsIn our case study, variability in survival extrapolations was extensive across the standard models, with 30-y RMST ranging from 7.5 to 14.3 y. Incorporation of general population mortality rates using EH cure methods substantially reduced model uncertainty, whereas EH models without cure had less of an effect. Long-term treatment effects approached the null for most models but at varying rates. Lifetable misspecification had minimal effect on RMST differences.ConclusionsEH methods may be useful for survival extrapolation, and in cancer, EHs may decrease over time and be easier to extrapolate than all-cause hazards. EH cure models may be helpful when cure is plausible and likely to result in less extrapolation variability.HighlightsIn health economic modeling, to help anchor long-term survival extrapolation, it has been recommended that survival models incorporate background mortality rates using excess hazard (EH) methods.We present a thorough description of EH methods with and without the assumption of cure and demonstrate user-friendly software to aid researchers wishing to use these methods.EH models are applied to a case study, and we demonstrate that EHs are easier to extrapolate and that the use of the EH cure model, when cure is plausible, can reduce extrapolation variability.EH methods are relatively robust to lifetable misspecification.

Project description:The mixture cure model for analyzing survival data is characterized by the assumption that the population under study is divided into a group of subjects who will experience the event of interest over some finite time horizon and another group of cured subjects who will never experience the event irrespective of the duration of follow-up. When using the Bayesian paradigm for inference in survival models with a cure fraction, it is common practice to rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior distributions. Although computationally feasible, the iterative nature of MCMC often implies long sampling times to explore the target space with chains that may suffer from slow convergence and poor mixing. Furthermore, extra efforts have to be invested in diagnostic checks to monitor the reliability of the generated posterior samples. A sampling-free strategy for fast and flexible Bayesian inference in the mixture cure model is suggested in this article by combining Laplace approximations and penalized B-splines. A logistic regression model is assumed for the cure proportion and a Cox proportional hazards model with a P-spline approximated baseline hazard is used to specify the conditional survival function of susceptible subjects. Laplace approximations to the posterior conditional latent vector are based on analytical formulas for the gradient and Hessian of the log-likelihood, resulting in a substantial speed-up in approximating posterior distributions. The spline specification yields smooth estimates of survival curves and functions of latent variables together with their associated credible interval are estimated in seconds. A fully stochastic algorithm based on a Metropolis-Langevin-within-Gibbs sampler is also suggested as an alternative to the proposed Laplacian-P-splines mixture cure (LPSMC) methodology. The statistical performance and computational efficiency of LPSMC is assessed in a simulation study. Results show that LPSMC is an appealing alternative to MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.

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Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach.

Publications

Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach.

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