title: Covariate-adjusted measures of discrimination for survival data.
abstract: BACKGROUND
  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).
  
  
  METHODS
  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.
authors.affiliation: MRC Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, UK.
authors.forename: Ian R
authors.initials: IR
authors.lastname: White
authors.affiliation: Farr Institute for Health Informatics Research, Department of Epidemiology and Public Health, University College London Medical School, 222 Euston Road, London WC1E 6BT, UK.
authors.forename: Eleni
authors.initials: E
authors.lastname: Rapsomaniki
mesh_terms: D000704:Analysis of Variance; D001699:Biometry / Q000379:methods*; D002318:Cardiovascular Diseases / Q000453:epidemiology*; D002986:Clinical Trials as Topic; D016002:Discriminant Analysis; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D012307:Risk Factors; D016019:Survival Analysis
keywords: C-index; D-index; Discrimination