<p>Adjustment for prognostic baseline covariates is routinely used to increase power in randomized controlled trials. Yet, time-to-event outcomes are commonly analyzed using the log-rank test or Cox regression with no covariates besides treatment. Covariate adjustment in non-linear models is more complex than in linear models: effect measures such as hazard ratios are non-collapsible, risk scores may be weakly prognostic, and misspecification can inflate type I error. Nine cardiovascular outcome trials were re-analyzed with adjustment for existing risk scores and known prognostic factors. We also assessed whether adjustment for these covariates would be outperformed by adjustment for predictions from newly created models (so-called ‘super covariates’). In addition to conditional Cox model analyses, marginal treatment effects were compared. We evaluated the strength of prognostic covariates required for adjustment to be worthwhile using simulations. Adjustment for existing risk scores and known prognostic factors had minimal impact on treatment effect estimates. Adjusting for newly developed model-based predictions on average improved conditional test statistics, but not consistently across studies or cross-validation folds. While the model-based predictions were stronger prognostic factors, variability of the gain in test statistic also increased. Efficiency gains for marginal estimates were consistent but modest. The simulations suggest that stronger prognostic covariates than the existing or our newly developed risk scores are required for greater efficiency gains. For cardiovascular outcome trials, covariate adjustment should be used more often, but one should assess the potential benefits carefully to avoid unrealistic expectations or unwarranted reductions in the target number of patients with an event.</p>