Survival Analysis with Long-Term Survivors

The aim of this book is to suggest and exemplify a systematic methodology for analysing survival data which contains "immune", or "cured" individuals, denoted generically as "long-term survivors". Such data occurs in medical and epidemiological applications, where the intention may be to identify whether or not cured or immune individuals are present in a population, perhaps as a result of treatments given; in the analysis of recidivism data in criminology, where the intentions are similar with respect to prisoners released from and possibly returning to prison; and in many other areas where followup data is available on individuals, with the possibility that not all suffer the event under investigation. Both nonparametric and parametric methods are proposed and developed. The effects of covariate information can be assessed via a kind of generalised linear framework in the parametric analyses. The proposed methodologies are supported by asymptotic analyses and simulations of real situations. While these theoretical underpinnings are presented in reasonable rigour and detail, the book is aimed very much at the practitioner who wishes to analyse survival data with (or even without) immunes. Formulating Tests for the Presence of Immunes and SufficientFollow-up.

Properties of the Kaplan-Meier Estimator.

Nonparametric Estimation and Testing.

Parametric Models for Single Samples.

The Use of Concomitant Information.

Large Sample Properties of Parametric Models: Single Samples.

Large-Sample Properties of Parametric Models with Covariates.

Further Topics.

References.

Statistical Tables.

Index. "The book contains an admirable blend of theory and practice beingclearly explained and illustrated with realistic examples ofsurvival analyses from medical and criminological studies."

"...an introduction to the analysis of survival data..." (Quarterlyof Applied Mathematics, Vol. LVIII, No. 4,December 2000) About the Authors Ross Maller received his PhD from the Australian National University and after many years with CSIRO is currently Associate Professor in the Department of Mathematics, University of Western Australia. Xian Zhou is currently at the Department of Mathematics, University of Western Australia. Survival Analysis with Long-Term Survivors Ross Maller and Xian Zhou University of Western Australia The data analytic methods routinely applied in the analysis of recidivism data in criminology have been expanded to include immune individuals. This book describes the theory and methods of incorporating them. The analysis of survival data via a model-fitting paradigm consists of the estimation of the parameters of a hypothesised model and the testing of hypotheses concerning these parameters. The effects of covariates are assessed by asymptotic analyses. The accuracy and power of the asymptotic results are assessed by simulations of real situations. The authors develop the theoretical results required and exemplify the methodology by analysis of a variety of data sets. Probabilistic tools such as the law of large numbers and the central limit theorem are applied. The book will be of particular interest to criminologists, epidemiologists and biostatisticians.