A Test for Bivariate Symmetry of Dependent Competing Risks

✍ Scribed by J. V. Deshpande

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 504 KB
• Volume: 32
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710320614

✦ Synopsis

In the competing risks set up with two dependent competing risks let F(z, y) be the joint probability distribution of (X, Y), the notional times to failure under the two risks. Actual independent obaervations are ( T i , & ) , i=l, 2, ..., n where Tf=min(Xi, Yi) and & = I ( X c a Y f ) . To test Ho: F ( z , y) =F(y. 2) for all 2. y, against HI: S,(t) %S2(t) where Sl(t) = P ( T d t , 6 = 1) and Sz(t) = = P (T st, 6 = 0), it is proposed to uee the Wilcoxon eigned rank type statistic J,= 2 6f (n + 1 -&)

where Rf = Rank (!Pi) among (TI, T2, ..., Tn). The J , teat is seen to be generally more efficient than the sign test except in case of alternatives under which T and 6 are indepondent, in which case the opposite is true. n (-1