Full likelihood inferences in the Cox model: an empirical likelihood approach (original) (raw)
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A solution to the problem of monotone likelihood in Cox regression
2001
Summary. The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to±∞. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory.
Scandinavian Journal of Statistics, 2009
The Cox model with time-dependent coefficients has been studied by a number of authors recently. In this paper, we develop empirical likelihood (EL) pointwise confidence regions for the timedependent regression coefficients via local partial likelihood smoothing. The EL simultaneous confidence bands for a linear combination of the coefficients are also derived based on the strong approximation methods. The empirical likelihood ratio is formulated through the local partial loglikelihood for the regression coefficient functions. Our numerical studies indicate that the EL pointwise/simultaneous confidence regions/bands have satisfactory finite sample performances. Compared with the confidence regions derived directly based on the asymptotic normal distribution of the local constant estimator, the EL confidence regions are overall tighter and can better capture the curvature of the underlying regression coefficient functions. Two data sets, the gastric cancer data and the Mayo Clinic primary biliary cirrhosis data, are analyzed using the proposed method.
Biometrics, 2018
We develop a new method for covariate error correction in the Cox survival regression model, given a modest sample of internal validation data. Unlike most previous methods for this setting, our method can handle covariate error of arbitrary form. Asymptotic properties of the estimator are derived. In a simulation study, the method was found to perform very well in terms of bias reduction and confidence interval coverage. The method is applied to data from Health Professionals Follow-Up Study (HPFS) on the effect of diet on incidence of Type II diabetes.
Empirical Likelihood Inference on Survival Functions under Proportional Hazards Model
Journal of Biometrics & Biostatistics, 2014
Under the framework of the Cox model, it is often of interest to assess a subject's survival prospect through the individualized predicted survival function, and the corresponding pointwise or simultaneous confidence bands as well. The standard approach to the confidence bands relies on the weak convergence of the estimated survival function to a Gaussian process. Such normal approximation based confidence band may have poor small sample coverage accuracy and generally requires an appropriate transformation to improve its performance. In this paper, we propose an empirical likelihood ratio based pointwise and simultaneous confidence bands that are transformation preserving and therefore eliminate the need of any transformations. The effectiveness of the proposed method is illustrated by a simulation study and an application to the Mayo Clinical primary biliary cirrhosis dataset. Journal of Biometrics & Biostatistics Journa l o f B io m etrics & B io s ta tistics
Understanding Cox's Regression Model: A Martingale Approach
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Empirical Likelihood in Survival Analysis
In Celebration of Professor Kai-Tai Fang's 65th Birthday, 2005
Since the pioneering work of Thomas and Grunkemeier (1975) and Owen (1988), the empirical likelihood has been developed as a powerful nonparametric inference approach and become popular in statistical literature. There are many applications of empirical likelihood in survival analysis. In this paper, we present an overview of some recent developments of the empirical likelihood for survival data. We will focus our attentions on the two regression models: the Cox proportional hazards model and the accelerated failure time model.
Towards an omnibus distribution-free goodness-of-fit test for the Cox model
Statistica Sinica
A new goodness-of-fit test for Cox's proportional hazards model is introduced. The test is based on a transformation of the difference between nonparametric and Cox model specific estimators of the doubly-cumulative hazard function used by McKeague and Utikal (1991). The transformation is designed to give an asymptotically distribution-free test. The test is shown to be consistent against all alternatives except those in which the baseline hazard is linearly dependent on the covariate.
Epidemiology, 2012
While epidemiologic and clinical research often aims to analyze predictors of specific endpoints, time-to-the-specific-event analysis can be hampered by problems with cause ascertainment. Under typical assumptions of competing risks analysis (and missing-data settings), we correct the causespecific proportional hazards analysis when information on the reliability of diagnosis is available. Our method avoids bias in effect estimates at low cost in variance, thus offering a perspective for better-informed decision-making. The ratio of different cause-specific hazards can be estimated flexibly for this purpose. It thus complements an all-cause analysis. In a sensitivity analysis, this approach can reveal the likely extent and direction of the bias of a standard cause-specific analysis when the diagnosis is suspect. These two uses are illustrated in a randomized vaccine trial and an epidemiologic cohort study respectively.
A Pseudo–Partial Likelihood Method for Semiparametric Survival Regression With Covariate Errors
Journal of the American Statistical Association, 2005
This paper presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures: it is not restricted to the independent additive error model. It can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The estimator is shown to be consistent and asymptotically normal, and an estimate of the asymptotic covariance matrix is derived. Some extensions to general transformation survival models are indicated. Simulation studies are presented for a setup with a single error-prone binary covariate and a setup with a single error-prone normally-distributed covariate. These simulation studies show that the method typically produces estimates with low bias and confidence intervals with accurate coverage rates. Efficiency results relative to fully parametric maximum likelihood are also presented. The method is applied to data from the Framingham Heart Study.