Premium
Restricted tests for testing independence of time to failure and cause of failure in a competing‐risks model
Author(s) -
Dykstra Richard,
Kochar Subhash,
Robertson Tim
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315673
Subject(s) - censoring (clinical trials) , statistics , test statistic , mathematics , likelihood ratio test , independence (probability theory) , monotonic function , hazard , hazard ratio , monotone polygon , statistic , null hypothesis , econometrics , statistical hypothesis testing , confidence interval , mathematical analysis , chemistry , geometry , organic chemistry
We consider the competing‐risks problem without making any assumption concerning the independence of the risks. Maximum‐likelihood estimates of the cause‐specific hazard rates are obtained under the condition that their ratio is monotone. We also consider the likelihood‐ratio test for testing the proportionality of two cause‐specific hazard rates against the alternative that the ratio of these two hazard rates is monotonic. This testing problem is equivalent to testing independence against likelihood‐ratio dependence of the time to failure and the cause of failure in the competing‐risks setup. We allow for random censoring on the right. The asymptotic null distribution of the test statistic is obtained and is found to be of the chi‐bar‐square type. The problem is extended to the case of more than two risks. A numerical example is given to illustrate the procedure.