Restricted Alternatives Tests in Competing Risk Analyses

CICILIA YUKO WADA. Restricted Alternatives Tests in Competing Risk Analyses. (Under the direction of Dr. P.K. SEN) The objective of the present study is to derive a union-intersection test statistic for subhypotheses against restricted alternatives in a competing risk situation with k causes of failure and p concomitant variables. Asymptotic properties of the proposed tests are investigated and compared to those of the usual score test. For the Cox regression model involving p concomitant variables and two treatments, testing of the subhypotheses against orthant restricted alternatives based on partial likelihood is considered. Roy's union-intersection principle is applied and the Kuhn-Tucker-Lagrange minimization technique is utilized for the derivation of the proposed test. The distribution of the proposed test under the null and under "local" alternatives is studied. The asymptotic relative efficiency of the proposed test with respect to the classical score test is investigated. The above derivation is extended to the comparison of r+l subsamples by considering tests of subhypotheses against restricted alternatives, such as the orthant alternative, the ordered orthant alternative and finally the ordered alternative. Asymptotic properties of these tests are also studied. The derivation of the tests using the same approach is also considered when the logistic model and a dependent parametric model are utilized to assess hypotheses of no difference between the two treatments against the restricted alterna.tive that one treatment is superior to the a.nother. A numerical illustration of the Cox regression model in a competing risk situation with two causes of failure, two treatments and with two covariates is performed. MonteCarlo sim ulation is utilized to show the power superiority of the proposed test compared to the score test.