All subsets regression in a proportional hazards model

This paper shows that within the framework of the proportional hazards model all subsets regression can be performed with very little computational effort. A selection criterion based on a Wald statistic is motivated by an argument similar to crossvalidation in which the status of one observation is changed from uncensored to consored. This criterion is formally equivalent to Mallows's Cp and thus the problem is reduced to one readily handled by standard statistical packages. The procedure is applied to some multiple myeloma data to give results remarkably different from those obtained by previous workers using stepwise procedures. New insights are gained and the superiority of all subsets regression over stepwise regression is clearly demonstrated.