In data analysis involving the proportional-hazards regression model due to Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220), the test criteria commonly used for assessing the partial contribution to survival of subsets of concomitant variables are the classical likelihood ratio (LR) and Wald statistics. This paper presents an investigation of three other test criteria with potentially major computational advantages over the classical tests, especially for stepwise variable selection in moderate to large data sets. The alternative criteria considered are Rao's efficient score statistic and two other score statistics. Under the Cox model, the performance of these tests is examined empirically and compared with the performance of the LR and Wald statistics. Rao's test performs comparably to the LR test in all the cases considered. The performance of the other criteria is competitive in many cases. The use of these statistics is illustrated in a study of coronary artery disease.