On semi-competing risks data

SUMMARY We consider a variation of the competing risks problem in which a terminal event censors a non-terminal event, but not vice versa. The joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable (Day et al., 1997), with the marginal distributions unspecified. An estimator for the association parameter is obtained from a concordance estimating function. A novel plug-in estimator for the marginal distribution of the non-terminal event is shown to be uniformly consistent and to converge weakly to a Gaussian process. The assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses. Simulations demonstrate that the methods work well with practical sample sizes. The proposals are illustrated with data on morbidity and mortality in leukaemia patients.

[1]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[2]  D. Oakes,et al.  Bivariate survival models induced by frailties , 1989 .

[3]  John P. Klein,et al.  Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with BuCy2. , 1991 .

[4]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[5]  Lee-Jen Wei,et al.  Combining dependent tests with incomplete repeated measurements , 1985 .

[6]  P. Hougaard.  A class of multivanate failure time distributions , 1986 .

[7]  D. Oakes.  A Model for Association in Bivariate Survival Data , 1982 .

[8]  J. Shih,et al.  A goodness-of-fit test for association in a bivariate survival model , 1998 .

[9]  R. Day,et al.  Adaptation of bivariate frailty models for prediction, with application to biological markers as prognostic indicators , 1997 .

[10]  M. L. Moeschberger,et al.  Life Tests Under Dependent Competing Causes of Failure , 1974 .

[11]  Zhiliang Ying,et al.  A simple nonparametric estimator of the bivariate survival function under univariate censoring , 1993 .

[12]  T. Louis,et al.  Inferences on the association parameter in copula models for bivariate survival data. , 1995, Biometrics.

[13]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[14]  D. Oakes,et al.  Semiparametric inference in a model for association in bivanate survival data , 1986 .

[15]  Eric V. Slud,et al.  Dependent competing risks and summary survival curves , 1983 .

[16]  S. E. Emoto,et al.  A Weibull Model for Dependent Censoring , 1990 .

[17]  A. V. Peterson,et al.  Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[18]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[19]  John P. Klein,et al.  Estimates of marginal survival for dependent competing risks based on an assumed copula , 1995 .