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Biometrika 1998 85(1):189-200; doi:10.1093/biomet/85.1.189
© 1998 by Biometrika Trust
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A goodness-of-fit test for association in a bivariate survival model

JOANNA H SHIH

National Heart, Lung, and Blood Institute, Office of Biostatistics Research, Two Rockledge Centre Room 8217, 6701 Rockledge Drive, Bethesda, Maryland 20892-7938, U.S.A. jshih{at}helix.nih.gov

We propose a simple test of constant conditional hazard ratio in the Clayton model (1978) by comparing the unweighted and weighted concordance estimators of the association parameter. If the Clayton model holds, the difference of these two estimates converges to zero. The proposed test is consistent against alternatives under which the two concordance estimators converge to different values. We derive an explicit formula for the asymptotic variance and derive the asymptotic distribution of the test statistic under the Clayton model. Then we extend the test statistic to incorporate censoring. The proposed test is expected to perform well for a general class of alternatives with monotone conditional hazard ratio. We examine the finite sample properties of the test statistic through simulations.

Key Words: Clayton model • Concordance • Conditional hazard ratio • Frailty


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