Monte Carlo methods are used to examine the small-sample properties of 11 test statistics that can be used for comparing several treatments with respect to their mortality experiences while adjusting for covariables. The test statistics are investigated from three distinct models: the parametric, semiparametric and rank analysis of covariance (Quade, 1967) models. Four tests (likelihood ratio, Wald, conditional and unconditional score tests) from each of the first two models and three tests (based on rank scores) from the last model are discussed. The empirical size and power of the tests are investigated under a proportional hazards model in three situations: (1) the baseline hazard is correctly assumed to be Exponential, (2) the baseline hazard is incorrectly assumed to be Exponential, and (3) a treatment-covariate interaction is omitted from the analysis.