Two-sample rank tests for censored data with non-predictable weights

✍ Scribed by Arnold Janssen; Georg Neuhaus

• Book ID: 104340295
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 939 KB
• Volume: 60
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00125-5

✦ Synopsis

In the two-sample testing problem for censored data a famous class of statistics, initiated by Mantel and Haenszel (J. Natl. Cancer Inst. 22 (1959), 719-748), consists of sums S = C, wj(Aj -Ej), where A, is the observed number of failures in the first sample at time tj and Ej is its conditional expectation, given the past. The weights wj determine the alternatives for which the corresponding tests are sensitive. The common method for deriving the asymptotic distribution of S is by counting process theory (Gill, Censoring and Stochastic Integrals (1980)), which demands predictability.

i.e., dependence of the past of the weights wj. In the present paper the asymptotic null-distribution of S is derived also for certain natural classes of anticipating, hence non-predictable weights. The proof works by discrete parameter martingale theory and is, thereby, easier accessible and at the same time more general than the common one under the null hypothesis. Moreover. the proof turns out to parallel the derivation of related conditional limit theorems as given in Neuhaus (Ann. Statist. 21 (1993), 1760-1779).