Explained variation for survival and recurrent event data

Abstract

Explained variation measures are used to quantify the amount of information in a model and especially how useful the model might be when predicting future observations. Such measures are useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. The rst part of this thesis considers explained variation for survival data and we investigate how individual observations in a data set can in uence the value of various proposed statistics . In uence of a subject is a measure of the e ect on estimates of deleting him/her from the data set. In uence on regression coe cients has had much attention but there has not been work in in uence for explained variation for survival data analysis or other measures of predictive accuracy. Generally in reasonable size data sets the deletion of a single subject has no e ect on conclusions. However, examination of distance between measures with and without the subject can be useful in distinguishing abnormal observations. In the second part of the thesis we investigate how measures of explained variation for survival data can be extended to recurrent event data. We describe an existing rank-based measure and we investigate a new statistic based on observed and expected event count processes. Both methods can be used for all models. Adjustments for missing data are proposed for the count measure and demonstrated through simulation to be e ective. We compare the population values of the two statistics and illustrate their use in comparing an array of non-nested models for data on recurrent episodes of infant diarrhea. There is evidence that the rank-based method is robust to ignored random e ects and also to the presence of unusual observations. The count-based method more directly compares observed and expected intensities. We assess in uence of individual observation on these measures.