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الخلاصة
This thesis examines several exploratory methods for data that is subject to right censoring. An exploratory method is one that examines the observed data for relationships that exist in it. This may be contrasted with methods that assume the data arises from a given model and check whether the model is correct. Graphical methods play an important role in exploratory analysis. Several new plots for censored data are developed and some revisions are suggested for existing plots.
A second way in which data can be explored is to model the data with a very flexible model. The methods of spline smoothing and local likelihood fit into this class of exploratory technique. Applications of the method of local likelihood to the full likelihood based on a proportional hazards model are given. Another flexible model is the estimation of conditional distribution functions. Estimating conditional distribution functions for all observed values of the covariate can provide useful information about how the response depends upon the covariate. The estimates of conditional distribution functions may then be used to estimate conditional means, variances, and a variety of other statistics. These methods are studied with regard to censored data.
Since the methods are exploratory and in some sense data-driven inference about the estimated covariate effects is not possible. However, it will sometimes be possible to use a method such as local likelihood to control for one covariate and allow for inference about another covariate. Such a method based on the permutation test is proposed for local likelihood estimation in the proportional hazards model.
