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Covariate-adjusted measures of discrimination for survival data

Published version
Peer-reviewed

Change log

Authors

White, IR 
Rapsomaniki, E 
Emerging Risk Factors Collaboration 

Abstract

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.

Description

Keywords

C-index, D-index, Discrimination, Analysis of Variance, Biometry, Cardiovascular Diseases, Clinical Trials as Topic, Discriminant Analysis, Female, Humans, Male, Middle Aged, Risk Factors, Survival Analysis

Journal Title

Biometrical Journal

Conference Name

Journal ISSN

0323-3847
1521-4036

Volume Title

57

Publisher

John Wiley & Sons Ltd.
Sponsorship
Medical Research Council (G0700463)
Medical Research Council (MR/L003120/1)
Medical Research Council (MR/P02811X/1)
European Commission and European Federation of Pharmaceutical Industries and Associations (EFPIA) FP7 Innovative Medicines Initiative (IMI) (116074)
Cambridge University Hospitals NHS Foundation Trust (CUH) (BRC)
British Heart Foundation (CH/12/2/29428)
Medical Research Council (MR/P013880/1)
Ume� University (unknown)
NHS Blood and Transplant (NHSBT) (WP12-01)
European Commission (279143)
NHS Blood and Transplant (NHSBT) (11-01-GEN)
Cambridge University Hospitals NHS Foundation Trust (CUH) (BRC 2012-2017)
British Heart Foundation (None)
European Commission (279233)
European Research Council (268834)
MRC (MR/J015709/1)
MRC (MR/J006602/1)
MRC (MR/J006599/1)
Medical Research Council (MR/M012816/1)
Cambridge University Hospitals NHS Foundation Trust (CUH) (146281)
Cambridge University Hospitals NHS Foundation Trust (CUH) (146281)
British Heart Foundation (RG/16/4/32218)
Cambridge University Hospitals NHS Foundation Trust (CUH) (3819-1617-25)
Department of Health (via National Institute for Health Research (NIHR)) (NIHR BTRU-2014-10024)
Cambridge University Hospitals NHS Foundation Trust (CUH) (3819-1516-29)
Cambridge University Hospitals NHS Foundation Trust (CUH) (unknown)
British Heart Foundation (None)
Medical Research Council (G0700463/1)
This work was supported by the Medical Research Council Grant G0700463 and Unit Programme U105260558.