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Motivation: Discrimination statistics describe the ability of a survival model to assign higher risks to individuals who experience earlier events: examples are Harrell's C-index and Royston and Sauerbrei's D, which we call the D-index. Prognostic covariates whose distributions are controlled by the study design (e.g. age and sex) influence discrimination and can make it difficult to compare model discrimination between studies. Although covariate adjustment is a standard procedure for quantifying disease-risk factor associations, there are no covariate adjustment methods for discrimination statistics in censored survival data. Objective: To develop extensions of the C-index and D-index that describe the prognostic ability of a model adjusted for one or more covariate(s). Method: We define a covariate-adjusted C-index and D-index for censored survival data, propose several estimators, and investigate their performance in simulation studies and in data from a large individual participant data meta-analysis, the Emerging Risk Factors Collaboration. Results: The proposed methods perform well in simulations. In the Emerging Risk Factors Collaboration data, the age-adjusted C-index and D-index were substantially smaller than unadjusted values. The study-specific standard deviation of baseline age was strongly associated with the unadjusted C-index and D-index but not significantly associated with the age-adjusted indices. Conclusions: The proposed estimators improve meta-analysis comparisons, are easy to implement and give a more meaningful clinical interpretation.