Measures to assess the prognostic ability of the stratified Cox proportional hazards model

Lisa Pennells; I. R. White; A. M. Wood; S. Kaptoge; N. Sarwar; J. B. Kostis; A. C. Wilson; A. R. Folsom; L. Chambless; M. Benderly; U. Goldbourt; J. Willeit; S. Kiechl; J. W.G. Yarnell; P. M. Sweetnam; M. Cushman; B. M. Psaty; R. P. Tracy; A. Tybjærg-Hansen; F. Haverkate; M. P.M. de Maat; S. G. Thompson; F. G.R. Fowkes; A. J. Lee; F. B. Smith; V. Salomaa; K. Harald; E. Vahtera; P. Jousilahti; J. Pekkanen; R. D'Agostino; W. B. Kannel; P. W.F. Wilson; G. Tofler; D. Levy; R. Marchioli; F. Valagussa; A. Rosengren; L. Wilhelmsen; G. Lappas; H. Eriksson; P. Cremer; D. Nagel; J. D. Curb; B. Rodriguez; K. Yano; J. T. Salonen; K. Nyyssönen; T. P. Tuomainen; B. Hedblad; G. Engstrom; G. Berglund; H. Loewel; W. Koenig; H. W. Hense; T. W. Meade; J. W. Cooper; B. De Stavola; C. Knottenbelt; G. J. Miller; J. A. Copper; K. A. Bauer; R. D. Rosenberg; S. Sato; A. Kitamura; Y. Naito; H. Iso; V. Rasi; T. Palosuo; P. Ducimetiere; P. Amouyel; D. Arveiler; A. E. Evans; J. Ferrieres; I. Juhan-Vague; A. Bingham; H. Schulte; G. Assmann; B. Cantin; B. Lamarche; J. P. Després; G. R. Dagenais; H. Tunstall-Pedoe; G. D.O. Lowe; M. Woodward; Y. Ben-Shlomo; G. Davey Smith; V. Palmieri; J. L. Yeh; P. Brennan; A. Rudnicka; J. A. Cooper; P. Ridker; F. Rodeghiero; A. Tosetto; J. Shepherd; I. Ford; M. Robertson; E. Brunner; M. Shipley; E. J.M. Feskens; D. Kromhout; J. Danesh; E. Di Angelantonio; S. Lewington; M. Walker

doi:10.1002/sim.3378

Measures to assess the prognostic ability of the stratified Cox proportional hazards model

Lisa Pennells^*, I. R. White, A. M. Wood, S. Kaptoge, N. Sarwar, J. B. Kostis, A. C. Wilson, A. R. Folsom, L. Chambless, M. Benderly, U. Goldbourt, J. Willeit, S. Kiechl, J. W.G. Yarnell, P. M. Sweetnam, M. Cushman, B. M. Psaty, R. P. Tracy, A. Tybjærg-Hansen, F. HaverkateM. P.M. de Maat, S. G. Thompson, F. G.R. Fowkes, A. J. Lee, F. B. Smith, V. Salomaa, K. Harald, E. Vahtera, P. Jousilahti, J. Pekkanen, R. D'Agostino, W. B. Kannel, P. W.F. Wilson, G. Tofler, D. Levy, R. Marchioli, F. Valagussa, A. Rosengren, L. Wilhelmsen, G. Lappas, H. Eriksson, P. Cremer, D. Nagel, J. D. Curb, B. Rodriguez, K. Yano, J. T. Salonen, K. Nyyssönen, T. P. Tuomainen, B. Hedblad, G. Engstrom, G. Berglund, H. Loewel, W. Koenig, H. W. Hense, T. W. Meade, J. W. Cooper, B. De Stavola, C. Knottenbelt, G. J. Miller, J. A. Copper, K. A. Bauer, R. D. Rosenberg, S. Sato, A. Kitamura, Y. Naito, H. Iso, V. Rasi, T. Palosuo, P. Ducimetiere, P. Amouyel, D. Arveiler, A. E. Evans, J. Ferrieres, I. Juhan-Vague, A. Bingham, H. Schulte, G. Assmann, B. Cantin, B. Lamarche, J. P. Després, G. R. Dagenais, H. Tunstall-Pedoe, G. D.O. Lowe, M. Woodward, Y. Ben-Shlomo, G. Davey Smith, V. Palmieri, J. L. Yeh, P. Brennan, A. Rudnicka, J. A. Cooper, P. Ridker, F. Rodeghiero, A. Tosetto, J. Shepherd, I. Ford, M. Robertson, E. Brunner, M. Shipley, E. J.M. Feskens, D. Kromhout, J. Danesh, E. Di Angelantonio, S. Lewington, M. Walker

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

Many measures have been proposed to summarize the prognostic ability of the Cox proportional hazards (CPH) survival model, although none is universally accepted for general use. By contrast, little work has been done to summarize the prognostic ability of the stratified CPH model; such measures would be useful in analyses of individual participant data from multiple studies, data from multi-centre studies, and in single study analysis where stratification is used to avoid making assumptions of proportional hazards. We have chosen three measures developed for the unstratified CPH model (Schemper and Henderson's V, Harrell's C-index and Royston and Sauerbrei's D), adapted them for use with the stratified CPH model and demonstrated how their values can be represented over time. Although each of these measures is promising in principle, we found the measure of explained variation V very difficult to apply when data are combined from several studies with differing durations of participant follow-up. The two other measures considered, D and the C-index, were more applicable under such circumstances. We illustrate the methods using individual participant data from several prospective epidemiological studies of chronic disease outcomes.

Original language	English
Pages (from-to)	389-411
Number of pages	23
Journal	Statistics in Medicine
Volume	28
Issue number	3
DOIs	https://doi.org/10.1002/sim.3378
State	Published - 10 Feb 2009

Funding

Funders	Funder number
Medical Research Council	MC_U105260558, G0701619
Economic and Social Research Council	ES/G007438/1

Keywords

Concordance
Discrimination
Explained variation
Prediction
Stratified survival analysis

Access to Document

10.1002/sim.3378

Cite this

Pennells, L., White, I. R., Wood, A. M., Kaptoge, S., Sarwar, N., Kostis, J. B., Wilson, A. C., Folsom, A. R., Chambless, L., Benderly, M., Goldbourt, U., Willeit, J., Kiechl, S., Yarnell, J. W. G., Sweetnam, P. M., Cushman, M., Psaty, B. M., Tracy, R. P., Tybjærg-Hansen, A., ... Walker, M. (2009). Measures to assess the prognostic ability of the stratified Cox proportional hazards model. Statistics in Medicine, 28(3), 389-411. https://doi.org/10.1002/sim.3378

@article{59c74ccc431a4aa9a1284947e2254287,

title = "Measures to assess the prognostic ability of the stratified Cox proportional hazards model",

abstract = "Many measures have been proposed to summarize the prognostic ability of the Cox proportional hazards (CPH) survival model, although none is universally accepted for general use. By contrast, little work has been done to summarize the prognostic ability of the stratified CPH model; such measures would be useful in analyses of individual participant data from multiple studies, data from multi-centre studies, and in single study analysis where stratification is used to avoid making assumptions of proportional hazards. We have chosen three measures developed for the unstratified CPH model (Schemper and Henderson's V, Harrell's C-index and Royston and Sauerbrei's D), adapted them for use with the stratified CPH model and demonstrated how their values can be represented over time. Although each of these measures is promising in principle, we found the measure of explained variation V very difficult to apply when data are combined from several studies with differing durations of participant follow-up. The two other measures considered, D and the C-index, were more applicable under such circumstances. We illustrate the methods using individual participant data from several prospective epidemiological studies of chronic disease outcomes.",

keywords = "Concordance, Discrimination, Explained variation, Prediction, Stratified survival analysis",

author = "Lisa Pennells and White, {I. R.} and Wood, {A. M.} and S. Kaptoge and N. Sarwar and Kostis, {J. B.} and Wilson, {A. C.} and Folsom, {A. R.} and L. Chambless and M. Benderly and U. Goldbourt and J. Willeit and S. Kiechl and Yarnell, {J. W.G.} and Sweetnam, {P. M.} and M. Cushman and Psaty, {B. M.} and Tracy, {R. P.} and A. Tybj{\ae}rg-Hansen and F. Haverkate and {de Maat}, {M. P.M.} and Thompson, {S. G.} and Fowkes, {F. G.R.} and Lee, {A. J.} and Smith, {F. B.} and V. Salomaa and K. Harald and E. Vahtera and P. Jousilahti and J. Pekkanen and R. D'Agostino and Kannel, {W. B.} and Wilson, {P. W.F.} and G. Tofler and D. Levy and R. Marchioli and F. Valagussa and A. Rosengren and L. Wilhelmsen and G. Lappas and H. Eriksson and P. Cremer and D. Nagel and Curb, {J. D.} and B. Rodriguez and K. Yano and Salonen, {J. T.} and K. Nyyss{\"o}nen and Tuomainen, {T. P.} and B. Hedblad and G. Engstrom and G. Berglund and H. Loewel and W. Koenig and Hense, {H. W.} and Meade, {T. W.} and Cooper, {J. W.} and {De Stavola}, B. and C. Knottenbelt and Miller, {G. J.} and Copper, {J. A.} and Bauer, {K. A.} and Rosenberg, {R. D.} and S. Sato and A. Kitamura and Y. Naito and H. Iso and V. Rasi and T. Palosuo and P. Ducimetiere and P. Amouyel and D. Arveiler and Evans, {A. E.} and J. Ferrieres and I. Juhan-Vague and A. Bingham and H. Schulte and G. Assmann and B. Cantin and B. Lamarche and Despr{\'e}s, {J. P.} and Dagenais, {G. R.} and H. Tunstall-Pedoe and Lowe, {G. D.O.} and M. Woodward and Y. Ben-Shlomo and Smith, {G. Davey} and V. Palmieri and Yeh, {J. L.} and P. Brennan and A. Rudnicka and Cooper, {J. A.} and P. Ridker and F. Rodeghiero and A. Tosetto and J. Shepherd and I. Ford and M. Robertson and E. Brunner and M. Shipley and Feskens, {E. J.M.} and D. Kromhout and J. Danesh and {Di Angelantonio}, E. and S. Lewington and M. Walker",

year = "2009",

month = feb,

day = "10",

doi = "10.1002/sim.3378",

language = "אנגלית",

volume = "28",

pages = "389--411",

journal = "Statistics in Medicine",

issn = "0277-6715",

publisher = "John Wiley and Sons Ltd",

number = "3",

}

Pennells, L, White, IR, Wood, AM, Kaptoge, S, Sarwar, N, Kostis, JB, Wilson, AC, Folsom, AR, Chambless, L, Benderly, M , Goldbourt, U, Willeit, J, Kiechl, S, Yarnell, JWG, Sweetnam, PM, Cushman, M, Psaty, BM, Tracy, RP, Tybjærg-Hansen, A, Haverkate, F, de Maat, MPM, Thompson, SG, Fowkes, FGR, Lee, AJ, Smith, FB, Salomaa, V, Harald, K, Vahtera, E, Jousilahti, P, Pekkanen, J, D'Agostino, R, Kannel, WB, Wilson, PWF, Tofler, G, Levy, D, Marchioli, R, Valagussa, F, Rosengren, A, Wilhelmsen, L, Lappas, G, Eriksson, H, Cremer, P, Nagel, D, Curb, JD, Rodriguez, B, Yano, K, Salonen, JT, Nyyssönen, K, Tuomainen, TP, Hedblad, B, Engstrom, G, Berglund, G, Loewel, H, Koenig, W, Hense, HW, Meade, TW, Cooper, JW, De Stavola, B, Knottenbelt, C, Miller, GJ, Copper, JA, Bauer, KA, Rosenberg, RD, Sato, S, Kitamura, A, Naito, Y, Iso, H, Rasi, V, Palosuo, T, Ducimetiere, P, Amouyel, P, Arveiler, D, Evans, AE, Ferrieres, J, Juhan-Vague, I, Bingham, A, Schulte, H, Assmann, G, Cantin, B, Lamarche, B, Després, JP, Dagenais, GR, Tunstall-Pedoe, H, Lowe, GDO, Woodward, M, Ben-Shlomo, Y, Smith, GD, Palmieri, V, Yeh, JL, Brennan, P, Rudnicka, A, Cooper, JA, Ridker, P, Rodeghiero, F, Tosetto, A, Shepherd, J, Ford, I, Robertson, M, Brunner, E, Shipley, M, Feskens, EJM, Kromhout, D, Danesh, J, Di Angelantonio, E, Lewington, S & Walker, M 2009, 'Measures to assess the prognostic ability of the stratified Cox proportional hazards model', Statistics in Medicine, vol. 28, no. 3, pp. 389-411. https://doi.org/10.1002/sim.3378

TY - JOUR

T1 - Measures to assess the prognostic ability of the stratified Cox proportional hazards model

AU - Pennells, Lisa

AU - White, I. R.

AU - Wood, A. M.

AU - Kaptoge, S.

AU - Sarwar, N.

AU - Kostis, J. B.

AU - Wilson, A. C.

AU - Folsom, A. R.

AU - Chambless, L.

AU - Benderly, M.

AU - Goldbourt, U.

AU - Willeit, J.

AU - Kiechl, S.

AU - Yarnell, J. W.G.

AU - Sweetnam, P. M.

AU - Cushman, M.

AU - Psaty, B. M.

AU - Tracy, R. P.

AU - Tybjærg-Hansen, A.

AU - Haverkate, F.

AU - de Maat, M. P.M.

AU - Thompson, S. G.

AU - Fowkes, F. G.R.

AU - Lee, A. J.

AU - Smith, F. B.

AU - Salomaa, V.

AU - Harald, K.

AU - Vahtera, E.

AU - Jousilahti, P.

AU - Pekkanen, J.

AU - D'Agostino, R.

AU - Kannel, W. B.

AU - Wilson, P. W.F.

AU - Tofler, G.

AU - Levy, D.

AU - Marchioli, R.

AU - Valagussa, F.

AU - Rosengren, A.

AU - Wilhelmsen, L.

AU - Lappas, G.

AU - Eriksson, H.

AU - Cremer, P.

AU - Nagel, D.

AU - Curb, J. D.

AU - Rodriguez, B.

AU - Yano, K.

AU - Salonen, J. T.

AU - Nyyssönen, K.

AU - Tuomainen, T. P.

AU - Hedblad, B.

AU - Engstrom, G.

AU - Berglund, G.

AU - Loewel, H.

AU - Koenig, W.

AU - Hense, H. W.

AU - Meade, T. W.

AU - Cooper, J. W.

AU - De Stavola, B.

AU - Knottenbelt, C.

AU - Miller, G. J.

AU - Copper, J. A.

AU - Bauer, K. A.

AU - Rosenberg, R. D.

AU - Sato, S.

AU - Kitamura, A.

AU - Naito, Y.

AU - Iso, H.

AU - Rasi, V.

AU - Palosuo, T.

AU - Ducimetiere, P.

AU - Amouyel, P.

AU - Arveiler, D.

AU - Evans, A. E.

AU - Ferrieres, J.

AU - Juhan-Vague, I.

AU - Bingham, A.

AU - Schulte, H.

AU - Assmann, G.

AU - Cantin, B.

AU - Lamarche, B.

AU - Després, J. P.

AU - Dagenais, G. R.

AU - Tunstall-Pedoe, H.

AU - Lowe, G. D.O.

AU - Woodward, M.

AU - Ben-Shlomo, Y.

AU - Smith, G. Davey

AU - Palmieri, V.

AU - Yeh, J. L.

AU - Brennan, P.

AU - Rudnicka, A.

AU - Cooper, J. A.

AU - Ridker, P.

AU - Rodeghiero, F.

AU - Tosetto, A.

AU - Shepherd, J.

AU - Ford, I.

AU - Robertson, M.

AU - Brunner, E.

AU - Shipley, M.

AU - Feskens, E. J.M.

AU - Kromhout, D.

AU - Danesh, J.

AU - Di Angelantonio, E.

AU - Lewington, S.

AU - Walker, M.

PY - 2009/2/10

Y1 - 2009/2/10

N2 - Many measures have been proposed to summarize the prognostic ability of the Cox proportional hazards (CPH) survival model, although none is universally accepted for general use. By contrast, little work has been done to summarize the prognostic ability of the stratified CPH model; such measures would be useful in analyses of individual participant data from multiple studies, data from multi-centre studies, and in single study analysis where stratification is used to avoid making assumptions of proportional hazards. We have chosen three measures developed for the unstratified CPH model (Schemper and Henderson's V, Harrell's C-index and Royston and Sauerbrei's D), adapted them for use with the stratified CPH model and demonstrated how their values can be represented over time. Although each of these measures is promising in principle, we found the measure of explained variation V very difficult to apply when data are combined from several studies with differing durations of participant follow-up. The two other measures considered, D and the C-index, were more applicable under such circumstances. We illustrate the methods using individual participant data from several prospective epidemiological studies of chronic disease outcomes.

AB - Many measures have been proposed to summarize the prognostic ability of the Cox proportional hazards (CPH) survival model, although none is universally accepted for general use. By contrast, little work has been done to summarize the prognostic ability of the stratified CPH model; such measures would be useful in analyses of individual participant data from multiple studies, data from multi-centre studies, and in single study analysis where stratification is used to avoid making assumptions of proportional hazards. We have chosen three measures developed for the unstratified CPH model (Schemper and Henderson's V, Harrell's C-index and Royston and Sauerbrei's D), adapted them for use with the stratified CPH model and demonstrated how their values can be represented over time. Although each of these measures is promising in principle, we found the measure of explained variation V very difficult to apply when data are combined from several studies with differing durations of participant follow-up. The two other measures considered, D and the C-index, were more applicable under such circumstances. We illustrate the methods using individual participant data from several prospective epidemiological studies of chronic disease outcomes.

KW - Concordance

KW - Discrimination

KW - Explained variation

KW - Prediction

KW - Stratified survival analysis

UR - http://www.scopus.com/inward/record.url?scp=63049122495&partnerID=8YFLogxK

U2 - 10.1002/sim.3378

DO - 10.1002/sim.3378

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:63049122495

SN - 0277-6715

VL - 28

SP - 389

EP - 411

JO - Statistics in Medicine

JF - Statistics in Medicine

IS - 3

ER -

Measures to assess the prognostic ability of the stratified Cox proportional hazards model

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this