Winnett, Angela Susan; (1999) Flexible estimators of hazard ratios for exploratory and residual analysis. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In analysis of censored survival data extensive use is made of models, in particular the Cox model, which assume a parametric form for the hazard ratio. The assumed form is often inappropriate and methods are needed for estimating hazard ratios with greater flexibility. Such methods could be used for model checking, graphical presentation, and for suggesting more appropriate parametric models. While in areas such as ordinary linear regression there are clear and well understood methods for checking models and exploring flexible alternatives, in hazard ratio estimation corresponding approaches are less well developed and both properties and application are still unclear. This thesis develops flexible estimators which have desirable theoretical properties, are useful in practice and are easy to interpret. The practical methodology is developed through an approach to estimation using Cox model residuals - flexible hazard ratios are estimated as extensions of the Cox model, using residuals, adjusted, smoothed, and iterated. Theoretical results are found for the properties of the iterated estimates, leading to practical guidelines for exploratory and residual analysis in existing software. The methodology is relevant for applications in a wide range of areas, but particularly for analysis of clinical data. An application is presented in an analysis of data from the Medical Research Council's myelomatosis trials.

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