r在生存分析中的应用.pdf

STATISTICS: AN INTRODUCTION USING R By . Crawley Exercises 12. SURVIVAL ANALYSIS A great many studies in statisti cs deal with deaths or with failures ponents: the numbers of deaths, the timing of death, and the risks of death to whic h different classes of individuals are exposed. The anal ysis of survival data is a major focus of the statistics business (see Kalbfleisch & Prentice 1980, Miller 1981, Fleming & Harrington 1991), and S-Plus supports a wide range of tools fo r the analysis of survival data. The main theme of this chapter is the an alysis of data that take the form of measurements of the time to death, or the time to failure of ponent. Up to now, we have dealt with mortality data by considering the pro portion of individuals that were dead at a given time . In this chapter each individual is followed until it dies, then the time of death is recorded (this will be the response variab le). Individuals that survive to the end of the experiment will die at an unknown time in the future; they are said to be censored (see below). A Monte Carlo experiment With data on time-to-death, the most important decision to be made concerns the error distribution. The key point to understand is that the variance in age at death is almost certain to increase with the mean, and he nce standard models (assuming constant variance and normal errors) will be inappropriate. You can see this at once with a simple Monte Carlo experiment. Suppose that the per-w eek probability of fa ilure of ponent is from one factory but from another. We can simulate the fate of an individual component in a given week by generating a uniformly distributed random number between 0 and 1. If the value of the random numb er is less than or e qual to (or for the second factory) ponent fails dur ing that week and its lifetime can be calculated. If the random number is larger than ponent survives to the next week. The lifetime of