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

Publisher Website
Google Scholar
Abstract
Medical follow-up studies have as their immediate objective the estimation of life expectation and survival rates for a defined population at risk. When the study is brought to a close, there will usually remain a number or patients on whom the mortality information will be incomplete. First, there will be patients still alive at the close of the study. Second, if the investigation is concerned with mortality from a specific cause, the necessary information is incomplete and unavailable for patients who died from other causes. And third, there will usually be patients who were "lost" to the study because of follow-up failure. These three groups present a number of statistical problems in the estimation of the expectation of life and survival rates. This paper is devoted to the study of these problems. Part 1 of the paper considers the mortality experience of patients without specification as to the cause of death. Formulas are presented for the maximum-likelihood estimator of the probability of death and its asymptotic variance. Because the study is truncated, expectation of life cannot be computed by the conventional method. A simple device is suggested for obtaining the observed expectation of life and its standard error. In Part 11 the discussion is extended to the problem of competing risks. The relations between net, crude, and partial crude probabilities are reviewed and formulas developed for their estimators and the corresponding covariance matrix. The problem of "lost" cases is also considered. The last part of the paper is devoted to the application of the theoretical results to an actual medical follow-up study on patients with a diagnosis of cancer of the cervix uteri.

This publication has 1 reference indexed in Scilit:

  • Life Testing
    Journal of the American Statistical Association, 1953