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LOCAL BUCKLEY-JAMES ESTIMATION FOR HETEROSCEDASTIC ACCELERATED FAILURE TIME MODEL.

ABSTRACT: In survival analysis, the accelerated failure time model is a useful alternative to the popular Cox proportional hazards model due to its easy interpretation. Current estimation methods for the accelerated failure time model mostly assume independent and identically distributed random errors, but in many applications the conditional variance of log survival times depend on covariates exhibiting some form of heteroscedasticity. In this paper, we develop a local Buckley-James estimator for the accelerated failure time model with heteroscedastic errors. We establish the consistency and asymptotic normality of the proposed estimator and propose a resampling approach for inference. Simulations demonstrate that the proposed method is flexible and leads to more efficient estimation when heteroscedasticity is present. The value of the proposed method is further assessed by the analysis of a breast cancer data set.

SUBMITTER: Pang L

PROVIDER: S-EPMC4988529 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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LOCAL BUCKLEY-JAMES ESTIMATION FOR HETEROSCEDASTIC ACCELERATED FAILURE TIME MODEL.

Pang Lei L Lu Wenbin W Wang Huixia Judy HJ

Statistica Sinica 20150101

In survival analysis, the accelerated failure time model is a useful alternative to the popular Cox proportional hazards model due to its easy interpretation. Current estimation methods for the accelerated failure time model mostly assume independent and identically distributed random errors, but in many applications the conditional variance of log survival times depend on covariates exhibiting some form of heteroscedasticity. In this paper, we develop a local Buckley-James estimator for the acc ...[more]

PMID: 27547018

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Project description:BackgroundSurvival analysis is the most appropriate method of analysis for time-to-event data. The classical accelerated failure-time model is a more powerful and interpretable model than the Cox proportional hazards model, provided that model imposed distribution and homoscedasticity assumptions satisfied. However, most of the real data are heteroscedastic which violates the fundamental assumption and consequently, the statistical inference could be erroneous in accelerated failure-time modeling. The weighted least-squares estimation for the accelerated failure-time model is an efficient semi-parametric approach for time-to-event data without the homoscedasticity assumption, which is developed recently and not often utilized for real data analysis. Thus, this study was conducted to ascertain the better performance of the weighted least-squares estimation method over the classical methods.MethodsWe analyzed a REAL dataset on Antiretroviral Therapy patients we recently collected. We compared the results from classical methods of estimation for the accelerated failure-time model with the results revealed from the weighted least-squares estimation.ResultsWe found that the data are heteroscedastic and indicated that the weighted least-square method should be used to analyze this data. The weighted least-squares estimation revealed more accurate, and efficient estimates of covariates effect since its confidence intervals were shorter and it identified more significant covariates. Accordingly, the survival of HIV positives was found to be significantly linked with age, weight, functional status, CD4 (Cluster of Differentiation agent 4 glycoproteins), and clinical stages.ConclusionsThe weighted least-squares estimation performed the best in providing more significant effects and precise estimates than the classical accelerated failure-time methods of estimation if data are heteroscedastic. Thus, we recommend future researchers should utilize weighted least-squares estimation rather than the classical methods when the homoscedasticity assumption is violated.

Project description:BackgroundSeparation or monotone likelihood may exist in fitting process of the accelerated failure time (AFT) model using maximum likelihood approach when sample size is small and/or rate of censoring is high (rare event) or there is at least one strong covariate in the model, resulting in infinite estimates of at least one regression coefficient.MethodsThis paper investigated the properties of the maximum likelihood estimator (MLE) of the regression parameters of the AFT models for small sample and/or rare-event situation and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function and the corresponding score equation is derived by adding a penalty term to the existing likelihood function, which was originally proposed by Firth (Biometrika, 1993) for the exponential family models. Further, a post-hoc adjustment of intercept and scale parameters is discussed keeping them out of penalization to ensure accurate prediction of survival probability. The penalized method was illustrated for the widely used log-location-scale family models such as Weibull, Log-normal and Log-logistic distributions and compared the models and methods uisng an extensive simulation study.ResultsThe simulation study, performed separately for each of the log-location-scale models, showed that Firth's penalized likelihood succeeded to solve the problem of separation and achieve convergence, providing finite estimates of the regression coefficients, which are not often possible by the MLE. Furthermore, the proposed penalized method showed substantial improvement over MLE by providing smaller amount of bias, mean squared error (MSE), narrower confidence interval and reasonably accurate prediction of survival probabilities. The methods are illustrated using prostate cancer data with existence of separation, and results supported the simulation findings.ConclusionWhen sample size is small (≤ 50) or event is rare (i.e., censoring proportion is high) and/or there is any evidence of separation in the data, we recommend to use Firth's penalized likelihood method for fitting AFT model.

Dataset Information

LOCAL BUCKLEY-JAMES ESTIMATION FOR HETEROSCEDASTIC ACCELERATED FAILURE TIME MODEL.

Publications

LOCAL BUCKLEY-JAMES ESTIMATION FOR HETEROSCEDASTIC ACCELERATED FAILURE TIME MODEL.

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