Covariate-adjusted measures of discrimination for survival data
White, Ian R.; Rapsomaniki, Eleni; Wannamethee, S. G.; Morris, R. W.; Willeit, J.; Willeit, P.; Santer, P.; Kiechl, S.; Wald, N.; Ebrahim, S.; Lawlor, D. A.; Gallacher, J.; Yarnell, J. W G; Ben-Shlomo, Y.; Casiglia, E.; Tikhonoff, V.; Sutherland, S. E.; Nietert, P. J.; Keil, J. E.; Bachman, D. L.; Psaty, B. M.; Cushman, M.; Nordestgaard, B. G.; Tybjærg-Hansen, A.; Frikke-Schmidt, R.; Giampaoli, S.; Palmieri, L.; Panico, S.; Pilotto, L.; Vanuzzo, D.; Simons, L. A.; Friedlander, Y.; McCallum, J.; Price, J. F.; McLachlan, S.; Taylor, J. O.; Guralnik, J. M.; Wallace, R. B.; Kohout, F. J.; Cornoni-Huntley, J. C.; Guralnik, J. M.; Blazer, D. G.; Guralnik, J. M.; Phillips, C. L.; Phillips, C. L.; Guralnik, J. M.; Wareham, N. J.; Khaw, K. T.; Brenner, H.; Schöttker, B.; Müller, H. T.; Rothenbacher, D.; Nissinen, A.; Donfrancesco, C.; Giampaoli, S.; Harald, K.; Jousilahti, P. R.; Vartiainen, E.; Salomaa, V.; D'Agostino, R. B.; Wolf, P. A.; Vasan, R. S.; Daimon, M.; Oizumi, T.; Kayama, T.; Kato, T.; Chetrit, A.; Dankner, R.; Lubin, F.; Welin, L.; Svärdsudd, K.; Eriksson, H.; Lappas, G.; Lissner, L.; Mehlig, K.; Björkelund, C.; Nagel, D.; Kiyohara, Y.; Arima, H.; Ninomiya, T.; Hata, J.; Rodriguez, B.; Dekker, J. M.; Nijpels, G.; Stehouwer, C. D A; Iso, H.; Kitamura, A.; Yamagishi, K.; Noda, H.; Goldbourt, U.; Kauhanen, J.; Salonen, J. T.; Tuomainen, T. P.; Meade, T. W.; DeStavola, B. L.; Blokstra, A.; Verschuren, W. M M; Cushman, M.; de Boer, I. H.; Folsom, A. R.; Psaty, B. M.; Koenig, W.; Meisinger, C.; Peters, A.; Verschuren, W. M M; Bueno-de-Mesquita, H. B.; Blokstra, A.; Rosengren, A.; Wilhelmsen, L.; Lappas, G.; Kuller, L. H.; Grandits, G.; Cooper, J. A.; Bauer, K. A.; Davidson, K. W.; Kirkland, S.; Shaffer, J. A.; Shimbo, D.; Kitamura, A.; Iso, H.; Sato, S.; Dullaart, R. P F; Bakker, S. J L; Gansevoort, R. T.; Ducimetiere, P.; Amouyel, P.; Arveiler, D.; Evans, A.; Ferrières, J.; Schulte, H.; Assmann, G.; Jukema, J. W.; Westendorp, R. G J; Sattar, N.; Cantin, B.; Lamarche, B.; Després, J. P.; E.Barrett-Connor; Wingard, D. L.; Daniels, L. B.; Gudnason, V.; Aspelund, T.; Trevisan, M.; Hofman, A.; Franco, O. H.; Tunstall-Pedoe, H.; Tavendale, R.; Lowe, G. D O; Woodward, M.; Howard, W. J.; Howard, B. V.; Zhang, Y.; Best, L. G.; Umans, J.; Ben-Shlomo, Y.; Davey-Smith, G.; Onat, A.; Nakagawa, H.; Sakurai, M.; Nakamura, K.; Morikawa, Y.; Njølstad, I.; Mathiesen, E. B.; Wilsgaard, T.; Sundström, J.; Gaziano, J. M.; Ridker, P. M.; Marmot, M.; Clarke, R.; Collins, R.; Fletcher, A.; Brunner, E.; Shipley, M.; Kivimaki, M.; Ridker, P. M.; Buring, J.; Rifai, N.; Cook, N.; Ford, I.; Robertson, M.; Marín Ibañez, A.; Feskens, E. J M; Geleijnse, J. M.
(2015) Biometrical Journal, volume 57, issue 4, pp. 592 - 613
(Article)
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
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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.
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Keywords: C-index, D-index, Discrimination, Statistics and Probability, General Medicine, Statistics, Probability and Uncertainty
ISSN: 0323-3847
Publisher: Wiley-VCH Verlag
(Peer reviewed)