Semiparametric Analysis of the Proportional Likelihood Ratio Model and Omnibus Estimation Procedure (original) (raw)
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This paper develops a new empirical likelihood method for semiparametric linear regression with a completely unknown error distribution and right censored survival data. The method is based on the Buckley-James (1979) estimating equation. It inherits some appealing properties of the complete data empirical likelihood method. For example, it does not require variance estimation which is problematic for the Buckley-James estimator. We also extend our method to incorporate auxiliary information. We compare our method with the synthetic data empirical likelihood of Li and Wang (2003) using simulations. We also illustrate our method using Stanford heart transplantation data.
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Methodologies developed for left-truncated right-censored failure time data can mostly be categorized according to the assumption imposed on the truncation distribution, i.e., being completely unknown or completely known. While the former approach enjoys robustness, the latter is more efficient when the assumed form of the truncation distribution can be supported by the data. Motivated by data from an HIV/AIDS study, we consider the middle ground and develop methodologies for estimation of a regression function in a semiparametric setting where the truncation distribution is parametrically specified while the failure time, censoring and covariate distribution are left completely unknown. We devise an estimator for the regression function based on a local pseudo-likelihood approach that properly accounts for the bias induced on the response variable and covariate(s) by the sampling design. One important spin-off from these results is that they yield the adjustment for length-biased sampling and right-censoring; the so-called stationary case. We study the small and large sample behaviour of our estimators. The proposed method is then applied to analyze a set of HIV/AIDS data.
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Journal of Statistical Computation and Simulation, 2007
The empirical likelihood ratio method is a general nonparametric inference procedure that has many desirable properties. Recently, the procedure has been generalized to several settings including testing of weighted means with right censored data. However, the computation of the empirical likelihood ratio with censored data and other complex settings is often non-trivial. We propose to use a sequential quadratic programming (SQP) method to solve the computational problem. We introduce several auxiliary variables so that the computation of SQP is greatly simplified. Examples of the computation with null hypothesis concerning the weighted mean are presented for right and interval censored data.
Computational Statistics & Data Analysis, 2018
The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.
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Robust and efficient estimation in the parametric proportional hazards model under random censoring
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Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semiparametric Cox model is widely used to study different types of data arising from applied disciplines like medical science, biology, reliability studies and many more. A fully parametric version of the Cox regression model, if properly specified, can yield more efficient parameter estimates leading to better insight generation. However, the existing maximum likelihood approach of generating inference under the fully parametric Cox regression model is highly non-robust against data-contamination which restricts its practical usage. In this paper we develop a robust estimation procedure for the parametric Cox regression model based on the minimum density power divergence approach. The proposed minimum density power divergence estimator is seen to produce highly robust estimates under data contamination with only a slight loss in efficiency under pure data. Further, they are always seen to generate more precise inference than the likelihood based estimates under the semi-parametric Cox models or their existing robust versions. We also sketch the derivation of the asymptotic properties of the proposed estimator using the martingale approach and justify their robustness theoretically through the influence function analysis. The practical applicability and usefulness of the proposal are illustrated through simulations and a real data example.
Biometrics, 2013
The proportional hazards assumption in the commonly used Cox model for censored failure time data is often violated in scientific studies. Yang and Prentice (2005) proposed a novel semiparametric two-sample model that includes the proportional hazards model and the proportional odds model as sub-models, and accommodates crossing survival curves. The model leaves the baseline hazard unspecified and the two model parameters can be interpreted as the shortterm and long-term hazard ratios. Inference procedures were developed based on a pseudo score approach. Although extension to accommodate covariates was mentioned, no formal procedures have been provided or proved. Furthermore, the pseudo score approach may not be asymptotically efficient. We study the extension of the short-term and long-term hazard ratio model of Yang and Prentice (2005) to accommodate potentially time-dependent covariates. We develop efficient likelihood-based estimation and inference procedures. The nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Extensive simulation studies demonstrate 1 that the proposed methods perform well in practical settings. The proposed method captured the phenomenon of crossing hazards in a cancer clinical trial and identified a genetic marker with significant long-term effect missed by using the proportional hazards model on age-at-onset of alcoholism in a genetic study.
Efficient semiparametric estimators via modified profile likelihood
Journal of Statistical Planning and Inference, 2005
A new strategy is developed for obtaining large-sample efficient estimators of finite-dimensional parameters within semiparametric statistical models. The key idea is to maximize over a nonparametric log-likelihood with the infinite-dimensional nuisance parameter replaced by a consistent preliminary estimator˜ of the Kullback-Leibler minimizing value for fixed . It is shown that the parametric submodel with Kullback-Leibler minimizer substituted for is generally a least-favorable model. Results extending those of Severini and Wong (Ann. Statist. 20 (1992) 1768) then establish efficiency of the estimator of maximizing log-likelihood with replaced for fixed by˜ . These theoretical results are specialized to censored linear regression and to a class of semiparametric survival analysis regression models including the proportional hazards models with unobserved random effect or 'frailty', the latter through results of Slud and Vonta (Scand. J. Statist. 31 characterizing the restricted Kullback-Leibler information minimizers.
Estimation of the additive hazards model with interval‐censored data and missing covariates
Canadian Journal of Statistics, 2020
The additive hazards model is one of the most commonly used regression models in the analysis of failure time data and many methods have been developed for its inference in various situations. However, no established estimation procedure exists when there are covariates with missing values and the observed responses are interval-censored; both types of complications arise in various settings including demographic, epidemiological, financial, medical and sociological studies. To address this deficiency, we propose several inverse probability weight-based and reweighting-based estimation procedures for the situation where covariate values are missing at random. The resulting estimators of regression model parameters are shown to be consistent and asymptotically normal. The numerical results that we report from a simulation study suggest that the proposed methods work well in practical situations. An application to a childhood cancer survival study is provided.