A Weighted Likelihood Approach to Problems in Survival Data

This work is motivated by the need to perform the appropriate “robust” analysis on right-censored survival data. As in other domains of application, modelling and analysis of data generated by medical and biological studies are often unstable due to the presence of outliers and model misspecification. Use of robust techniques is helpful in this respect, and has often been the default in such situations. However, a large contaminating set of observations can often mean that the group is generated systematically by a model which is different from the one to which the majority of the data are attributed, rather than being stray outliers. The method of weighted likelihood estimating equations might provide a solution to this problem, where the different roots obtained can indicate the presence of distinct parametric clusters, rather than providing a single robust fit which ignores the observations incompatible with the major fitted component. Efron’s (J. Am. Stat. Assoc. 83, 402, 414–425, 1988) head-and-neck cancer data provide an ideal scenario for the application of such a method. A recently developed variant of the weighted likelihood method provides a nice illustration of the presence of different clusters in Efron’s data, and highlights the benefits of the weighted likelihood method in relation to classical robust techniques.