The Wald Statistic in Proportional Hazards Hypothesis Testing

✍ Scribed by Prof. Dr. Shrikant I. Bangdiwala

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 452 KB
• Volume: 31
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710310209

✦ Synopsis

Carolina 8ummry I n survivorship modelling using the proportional hazards model of Cox (1972, Journal of the Royal Statistical Society, Series B, 34, 187-220). it is often desired to test a subset of the vector of unknown regreasion parameters in the expression for the hazard rate at time t . The likelihood ratio test statistic is well behaved most situations but may be expensive t o calculate. The Wald (1943, Transections of the American Mathematical Society 64, 426-482) test Statistic is easier to calculate, but has some drawbacks. In testing a single parameter in a binomial logit model, HAUCK and DONNEB (1977, Journal of the American Statistical Association 72, 861-863) show that the

Wald statistic decreases t o zero the further the parameter estimate is from the null and that the asymptotic power of the test decreases to the significance level. The Wald statistic is extensively used in statistical software packages for survivorship modelling and it is therefore important to understand its behavior. The present work examines empirically t h e behavior of the Wald statistic under various departures from the null hypothesis and under the presence of Type I censoring and covariates in the model. It is shown via examples t h a t the Wald statistic's behavior is not as aberrant as found for the logistic model. For the single parameter case, the asymptotic non-null distribution of the Wald statist,ic is examined.