Über die Autorin bzw. den Autor

David Machin:  Division of Clincial Trials and Epidemiological Sciences, National Cancer Centre, Singapore; UK Children’s Cancer Study Group, University of Leicester, UK Institute of General Practice and Primary Care, School of Health and Related Sciences, University of Sheffield, UK
Author of recently published Design of Medical Studies for Medical Research and editor of Textbook of Clinical Trials among other Wiley titles.

Yin Bun Cheung: MRC Tropical Epidemiology Group, London School of Hygiene and Tropical Medicine, UK, Division of Clinical Trials and Epidemiological Sciences, National Cancer Centre, Singapore.

Mahesh Parmar: Cancer Trials Division, MRC Clincial Trials Unit, London, UK.

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Well received in its first edition, Survival Analysis: A Practical Approach is revised, keeping to its original underlying aim, to provide an accessible and practical guide to survival analysis techniques in diverse environments.

Illustrated with many authentic examples, the book introduces basic statistical concepts and methods to construct survival curves, later developing them to encompass more specialised and complex models.

During the years since the first edition there have been several new topics that have come to the fore and many new applications. Parallel developments in computer software programmes, used to implement these methodologies, are relied upon throughout the text to bring it up to date.

This book is designed with the practitioner in mind and is aimed at medical statisticians, epidemiologists, clinicians and healthcare professionals as well as students studying survival analysis as part of their graduate or postgraduate courses and thus presents the subject in a user-friendly way.

Aus dem Klappentext

Well received in its first edition, Survival Analysis: A Practical Approach is revised, keeping to its original underlying aim, to provide an accessible and practical guide to survival analysis techniques in diverse environments.

Illustrated with many authentic examples, the book introduces basic statistical concepts and methods to construct survival curves, later developing them to encompass more specialised and complex models.

During the years since the first edition there have been several new topics that have come to the fore and many new applications. Parallel developments in computer software programmes, used to implement these methodologies, are relied upon throughout the text to bring it up to date.

This book is designed with the practitioner in mind and is aimed at medical statisticians, epidemiologists, clinicians and healthcare professionals as well as students studying survival analysis as part of their graduate or postgraduate courses and thus presents the subject in a user-friendly way.

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Survival Analysis

John Wiley & Sons

Chapter One

Summary

In this chapter we introduce some examples of the use of survival methods in a selection of different areas and describe the concepts necessary to define survival time. The chapter also includes a review of some basic statistical ideas including the Normal distribution, hypothesis testing and the use of confidence intervals, the [chi square] and likelihood ratio tests and some other methods useful in survival analysis, including the median survival time and the hazard ratio. The difference between clinical and statistical significance is highlighted. The chapter indicates some of the computing packages that can be used to analyse survival data and emphasises that the database within which the study data is managed and stored must interface easily with these.

1.1 INTRODUCTION

There are many examples in medicine where a survival time measurement is appropriate. For example, such measurements may include the time a kidney graft remains patent, the time a patient with colorectal cancer survives once the tumour has been removed by surgery, the time a patient with osteoarthritis is pain-free following acupuncture treatment, the time a woman remains without a pregnancy whilst using a particular hormonal contraceptive and the time a pressure sore takes to heal. All these times are triggered by an initial event: a kidney graft, a surgical intervention, commencement of acupuncture therapy, first use of a contraceptive or identification of the pressure sore. These initial events are followed by a subsequent event: graft failure, death, return of pain, pregnancy or healing of the sore. The time between such events is known as the 'survival time'. The term survival is used because an early use of the associated statistical techniques arose from the insurance industry, which was developing methods of costing insurance premiums. The industry needed to know the risk, or average survival time, associated with a particular type of client. This 'risk' was based on that of a large group of individuals with a particular age, gender and possibly other characteristics; the individual was then given the risk for his or her group for the calculation of their insurance premium.

There is one major difference between 'survival' data and other types of numeric continuous data: the time to the event occurring is not necessarily observed in all subjects. Thus in the above examples we may not observe for all subjects the events of graft failure (the graft remains functional indefinitely), death (the patient survives for a very long time), return of pain (the patient remains pain-free thereafter), pregnancy (the woman never conceives) or healing of the sore (the sore does not heal), respectively. Such non-observed events are termed 'censored' but are quite different from 'missing' data items.

The date of 1 March 1973 can be thought of as the 'census day', that is, the day on which the currently available data on all patients recruited to the transplant programme were collected together and summarised. Typically, as in this example, by the census day some patients will have died whilst others remain alive. The survival times of those who are still alive are termed censored survival times. Censored survival times are described in Section 2.1

The probability of survival without transplant for patients identified as transplant candidates is shown in Figure 1.1. Details of how this probability is calculated using the Kaplan-Meier (product-limit) estimate, are given in Section 2.2. By reading across from 0.5 on the vertical scale in Figure 1.1 and then vertically downwards at the point of intersection with the curve, we can say that approximately half (see Section 2.3) of such patients will die within 80 days of being selected as suitable for transplant if no transplant becomes available for them.

Historically, much of survival analysis has been developed and applied in relation to cancer clinical trials in which the survival time is often measured from the date of randomisation or commencement of therapy until death. The seminal papers by Peto, Pike, Armitage et al. (1976, 1977) published in the British Journal of Cancer describing the design, conduct and analysis of cancer trials provide a landmark in the development and use of survival methods.

The method of making a formal comparison of two survival curves with the Logrank test is described in Chapter 3.

One field of application of survival studies has been in the development of methods of fertility regulation. In such applications alternative contraceptive methods either for the male or female partner are compared in prospective randomised trials. These trials usually compare the efficacy of different methods by observing how many women conceive in each group. A pregnancy is deemed a failure in this context.

Survival time methods have been used extensively in many medical fields, including trials concerned with the prevention of new cardiovascular events in patients who have had a recent myocardial infarction (Wallentin, Wilcox, Weaver et al., 2003), prevention of type 2 diabetes mellitus in those with impaired glucose tolerance (Chiasson, Josse, Gomis et al., 2002), return of post-stroke function (Mayo, Korner-Bitensky and Becker, 1991), and AIDS (Bonacini, Louie, Bzowej, et al., 2004).

1.2 DEFINING TIME

In order to perform survival analysis one must know how to define the time-to-event interval. The endpoint of the interval is relatively easy to define. In the examples in Section 1.1, they were graft failure, return of pain, pregnancy, healing of the sore, recovery of sperm function, and death. However, defining the initial event that trigger the times is sometimes a more difficult task.

INITIAL EVENTS AND THE ORIGIN OF TIME

The origin of time refers to the starting point of a time interval, when t = 0. We have mentioned the time from the surgical removal of a colorectal cancer to the death of the patient. So the initial event was surgery and t =0 corresponds to the date of surgery. However, a quite common research situation in cancer clinical trials is that after surgery, patients are randomised into receiving one of two treatments, say two types of adjuvant chemotherapy. Should the initial event be surgery, randomisation, or the start of chemotherapy? How does one choose when there are several (starting) events that can be considered? There are no definite rules, but some considerations are as follows.

It is intuitive to consider a point in time that marks the onset of exposure to the risk of the outcome event. For example, when studying ethnic differences in mortality, birth may be taken as the initial event as one is immediately at risk of death once born. In this case, survival time is equivalent to age at death. However, in studies of hospital readmission rates, a patient cannot be readmitted until he or she is first of all discharged. Therefore the latest discharge is the initial event and marks the origin of the time interval to readmission.

In randomised trials, the initial event should usually be randomisation to treatment. Prior to randomisation, patients may have already been at risk of the outcome event (perhaps dying from their colorectal cancer before surgery can take...