Effects of covariate omission and categorization when analysing randomized trials with the Cox model

When analysing the survival of patients in comparative randomized clinical trials using the Cox proportional hazards model, important prognostic factors may be included for the adjustment of the treatment effect. In this paper we examine two of the most common misspecifications of the model: (i) an important prognostic factor is omitted from the analysis; and (ii) an important prognostic factor originally present on continuous scale is included in categorized form. Both situations may emerge from the occurrence of missing values. We investigate the properties of the maximum partial likelihood estimator of the treatment effect under this kind of misspecification. The estimate of the treatment effect is found to be asymptotically biased toward zero. For its asymptotic variance we obtain a quantity with the so-called 'sandwich' structure. Thus, variance estimation by the inverse of the second-order derivative of the likelihood is not consistent. The magnitude of overestimation or underestimation is evaluated numerically for specific settings. The precision of the treatment effect estimate under covariate omission or categorization is compared with the precision of the estimate in the correct and not misspecified model. It turns out that correct adjustment does not lead to a higher precision of the treatment effect estimate, but due to the resulting underestimation, covariate omission or categorization lead to loss of power of the test of no treatment effect.