Practical Methods for Analysing Dependent Survival Data

Newell, John (1999) Practical Methods for Analysing Dependent Survival Data. PhD thesis, University of Glasgow.

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Abstract

Survival data arises when there is interest in the length of time until a particular event occurs e.g. death due to cancer. Typically, observations are assumed to be statistically independent of each other. This assumption however is violated in many situations which are not as uncommon as one might think. The overall aim of this thesis is to provide practical methods for analysing dependent survival data. All the methods described in this thesis are illustrated using paired survival data from an Orthodontic study and matched survival data from a Melanoma study. Chapter 1 gives a brief background to survival data, common censoring mechanisms and estimation of the survivor function. A review of some of the standard techniques for summarising survival data is given with particular emphasis on non-parametric estimators of the survivor function. A discussion of situations where the assumption of independence between observations is likely to be invalid is given in Chapter 2 where Multiple Event and Cluster Survival studies are introduced. This thesis, however, primarily concerns analysing dependent survival data from cluster studies (i.e. where a failure process acts concurrently on individuals in a cluster). Such studies are of two types, namely paired studies (e.g. time to cataract in left/right eye) and matched studies where the individuals are matched by design (e.g. comparing time to death ). Both matched and paired survival studies will have a pair of observation times recorded which represent the two 'arms' of the primary variable of interest. In addition to these, additional information may be recorded also in the form of covariates, or prognostic indicators. Matched survival studies will, by definition, have the variables used for the matching present and some additional unmatched covariates, or prognostic indicators, may also be recorded for each individual. Graphical and analytical methods for assessing the quality of matching in matched survival studies were given also. Paired studies, by definition, are unlikely to have any matching variables available but may have 'unit' covariate information recorded for each individual e.g. sex or age. Two example data sets are introduced (matched survival data from a Melanoma study and paired survival data from an Orthodontic study) which will be used to illustrate the various methods presented in the following chapters. Chapter 3 presents techniques for graphically displaying dependent survival data, including bivariate survival scatterplots and survival ratio plots. A review of several nonparametric estimators of the bivariate survival function is given with methods for generating reference ranges for such three-dimensional plots. In addition, two methods to graphically assess the independent effect on survival of any continuous covariates are discussed. The first uses a form of kernel estimation to construct an estimator of a percentile of the survivor function as a function of the covariate while the second uses a tree-based approach. Chapter 4 concerns the comparison of the survival distributions of the two arms of the primary variable (i.e. ignoring all covariates but the primary variable) where a review of several nonparametric paired 'log-rank' tests is given. Two new approaches for comparing survival in paired/matched survival studies are described and illustrated. The first is a simple test of symmetry based on 'pair performance'. The second is based on estimating the distribution of the (pairwise) difference in survival, using a parametric approach (by providing an interval estimate for the mean difference in survival time) and a nonparametric approach (by providing an interval estimate for an appropriate quantile e.g. the median difference). Methods for incorporating covariates into the analysis, while at the same time taking the dependency structure of the data into account are presented in chapter 5. (Abstract shortened by ProQuest.).

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: Tom Aithison
Keywords: Biostatistics, Statistics
Date of Award: 1999
Depositing User: Enlighten Team
Unique ID: glathesis:1999-76463
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Nov 2019 14:18
Last Modified: 19 Nov 2019 14:18
URI: http://theses.gla.ac.uk/id/eprint/76463

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