Grants and Contracts Details
The empirical likelihood (EL) method is a nonparametric inference method with asymptotic properties that are in general similar to the parametric maximum likelihood. For example, there are EL versions of likelihood ratio tests and Wilks' theorem. Like its parametric equivalent, the EL approach often provides an efficient and practical inference tool in situations where other inferential methods do not succeed. An application where its versatility is particularly appreciated is censored quantile regression. Without censoring, quantile regression (QR) has appeared as an alternative to the least squares method in many areas of application, as it provides more complete information about the conditional distribution of the response, while accommodating a quite general heterogeneity in the model and the error distributions. It is especially useful when tails of the distribution or abnormal cases such as low birth weight, high ozone concentration or high yield stock are under question and quantiles are of direct interest. In many applications, the response is censored, and it is unknown how inference about the censored QR can be achieved. The objectives of this proposal are: to propose a new EL approach for the accelerated failure time (AFT) model based on the sample points casewise and to extend the EL inference of censored regression beyond least squares by considering the EL method with censored quantile regression in various settings. The EL approach based on the sample points is innovative. It will extend the domain of the EL inference greatly, as it has a less stringent requirement that the sample points are i.i.d., and permits quite a general form of heteroscedasticity. The intellectual merit of the proposed research is that it will advance quantile analysis in censored regression and extend the domain of EL inference with the new approach. Its impact can be immediately seen in its readily applicable results to other semi- or non-parametric extensions of linear AFT models with various smoothing techniques. The broader impact of the proposed research is that the results will be widely applicable to many scientific, medical and economical problems for which a lack of inference tools has precluded censored quantile regression. Censored QR can investigate the conditional distribution of, for example, the survival time of epithelial ovarian cancer patients, conditioning on a certain biomarker, without having to assume that the relation with the biomarker is the same for, say, the upper quartile of the survival times, as for the median or the 10th percentile. This is not usually permitted in most of the parametric or semi-parametric censored regression analyses. With the proposed EL inference method, one may find that the prognostic values of the biomarker are only significant, for example, for those who die exceptionally early (lower conditional quantiles) or exceptionally late (upper conditional quantiles) in comparison to others in the same reference group. Thereby censored QR analysis together with EL inference can better inform health professionals of the effects of the biomarker and provide a useful prognostic tool for the survival times of the cancer patients.
|Effective start/end date
|6/1/06 → 5/31/09
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