Exact inference in the proportional hazard model: possibilities and limitations

It is suggested that inference under the proportional hazard model can be carried out by programs for exact inference under the logistic regression model. Advantages of such inference is that software is available and that multivariate models can be addressed. The method has been evaluated by means of coverage and power calculations in certain situations. In all situations coverage was above the nominal level, but on the other hand rather conservative. A different type of exact inference is developed under Type II censoring. Inference was then less conservative, however there are limitations with respect to censoring mechanism, multivariate generalizations and software is not available. This method also requires extensive computational power. Performance of large sample Wald, score and likelihood inference was also considered. Large sample methods works remarkably well with small data sets, but inference by score statistics seems to be the best choice. There seems to be some problems with likelihood ratio inference that may originate from how this method works with infinite estimates of the regression parameter. Inference by Wald statistics can be quite conservative with very small data sets.