Grants and Contracts Details
Description
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.
Status | Finished |
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Effective start/end date | 6/1/06 → 5/31/09 |
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