A Stochastic Study of the Life Table and Its Applications. III. The Follow-Up Study with the Consideration of Competing Risks

Statistical studies falling into the general category of life testing and medical follow-up have as their common immediate objective the estimation of life expectation and survival rates for a defined population at risk. Usually such a study must be brought to a close before all the information on survival (of patients, electric bulbs, automobiles, etc.) is complete, and thus the study is said to be truncated. Whether the investigation is basically concerned with life testing or with medical follow-up, the nature of the problem is the same, although differences in sample size may call for different approaches. Thus methods developed for life testing may be applied to follow-up studies when the underlying conditions are met, and vice versa. In this study cancer survival data utilizing a large sample will be used as illustrative material, and we shall accordingly use the terminology of the medical follow-up study as a matter of convenience. We are concerned then with a typical follow-up study in which a group of individuals with some common morbidity experience are followed from a well-defined zero point, such as date of hospital admission. Perhaps we wish to evaluate a certain therapeutic measure by comparing the expectation of life and survival rates of treated and untreated patients. Or we may wish to compare the expectation of life of treated and presumably cured patients with that of normal persons. When the period of observation is ended, there will usually remain a number of individuals on whom the mortality data in a typical study will be incomplete. Of first importance among these are the 'This study was completed while the author was a Special Research Fellow of the National Heart Institute, Public Health Service, U. S. Department of Health, Education and Welfare. 2Parts of this paper were presented at the joint meeting of the American Statistical Association, the Institute of Mathematical Statistics, and the Biometric Society in Washington, D. C., December 29, 1959.