On the ratio of hazard functions in the presence of a nuisance covariate

A common practice in the analysis of clinical trials is the assumption of proportional hazards given the covariates. When this assumption is appropriate but an important covariate is omitted, the ratio of the hazards is shown to be less than the constant proportion (assumed to be greater than 1). In certain cases it can even be less than 1. Limiting behavior of this ratio is also considered and is shown to be dependent on the left-hand tail of the distribution of the covariate.