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Goodness-of-fit and diagnostics for proportional hazards regression models

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Recent Advances in Clinical Trial Design and Analysis

Part of the book series: Cancer Treatment and Research ((CTAR,volume 75))

Abstract

A common clinical study design follows patients over time, recording end-point events as they occur for each individual. In a cancer clinical trial with death as the endpoint, there can be at most one event per patient. In other cases, multiple events are possible — for example, studies of recurrent infections in bone marrow transplantation recipients. The study goal is to model the event rate as a function of covariates measured at baseline. In a clinical trial, these would typically include the treatment group, measures of disease severity, patient age, and other sociodemographic variables. The proportional hazards regression model is a popular tool.

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References

  1. Fleming TR, Harrington DP (1991). Counting Processes and Survival Analysis. New York: J. Wiley Sons.

    Google Scholar 

  2. Andersen PK, Borgan O, Gill RD, Keiding N (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.

    Book  Google Scholar 

  3. Kay R (1984) Goodness-of-fit methods for the proportional hazards model: a review. Rev Epidemiol Santé Publ 32:185–198.

    CAS  Google Scholar 

  4. Lin DY, Wei LJ (1991). Goodness-of-fit tests for the general Cox regression model. Stat Sinica 1:1–17.

    Google Scholar 

  5. Cox DR (1972). Regression models and life-tables (with discussion). J R Stat Soc B 34: 187–220.

    Google Scholar 

  6. Andersen PK, Gill RD (1982). Cox’s regression model for counting processes: a large sample study. Ann Stat 10:1100–1120.

    Article  Google Scholar 

  7. Breslow NE (1974). Covariance analysis of censored survival data. Biometrics 30:89–99.

    Article  PubMed  CAS  Google Scholar 

  8. Barlow WE, Prentice R (1988). Residuals for relative risk regression. Biometrika 75:65–74.

    Article  Google Scholar 

  9. Schoenfeld D (1982). Partial residuals for the proportional hazards regression model. Biometrika 69:239–241.

    Article  Google Scholar 

  10. O’Quigley J, Pessione F (1989). Score tests for homogeneity of regression effects in the proportional hazards model. Biometrics 45:135–144.

    Article  PubMed  Google Scholar 

  11. Schoenfeld D (1980). Chi-square goodness of fit tests for the proportional hazards model. Biometrika 67:145–153.

    Article  Google Scholar 

  12. Moreau T, O’Quigley J, Mesbah M (1985). A global goodness-of-fit statistic for the proportional hazards model. Appl Stat 34:212–218.

    Article  Google Scholar 

  13. Harrell F (1986). The PHGLM procedure. SAS Supplemental Library User’s Guide, Version 5. Cary, NC: SAS Institute Inc.

    Google Scholar 

  14. Lin DY (1991). Goodness-of-fit analysis for the Cox regression model based on a class of parameter estimators. J Am Stat Assoc 86:725–728.

    Article  Google Scholar 

  15. Nagelkerke NJD, Oosting J, Hart AAM (1984). A simple test for goodness of fit of Cox’s proportional hazards model. Biometrics 40:483–486.

    Article  Google Scholar 

  16. Jones MP, Crowley J (1989). A general class of nonparametric tests for survival analysis. Biometrics 45:157–170.

    Article  PubMed  CAS  Google Scholar 

  17. Jones MP, Crowley J (1990). Asymptotic properties of a general class of nonparametric tests for survival analysis. Ann Stat 18:1203–1220.

    Article  Google Scholar 

  18. Harrington DP, Fleming TR (1982). A class of rank test procedures for censored survival data. Biometrika 69:533–546.

    Article  Google Scholar 

  19. Tarone RE, Ware J (1977). On distribution-free test for equality of survival distributions. Biometrika 64:156–160.

    Article  Google Scholar 

  20. O’Brien PC (1978). A nonparametric test for association with censored data. Biometrics 34:243–250.

    Article  PubMed  Google Scholar 

  21. Pettitt AN, Bin Daud I (1990). Investigating time dependence in Cox’s proportional hazards model. Appl Stat 39:313–329.

    Article  Google Scholar 

  22. Cleveland WS, Devlin SJ (1988). Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc 83:596–610.

    Article  Google Scholar 

  23. Cleveland WS, Devlin SJ, Grosse E (1988). Regression by local fitting: mothods, properties, and computational algorithms. J Econometr 37:87–114.

    Article  Google Scholar 

  24. Cleveland WS, Grosse E, Shyu WM (1992). Local regression models. In Statistical Models in S, JM Chambers, JJ Hastie (eds.). Pacific Grove, CA: Wadsworth and Brooks, 309–376.

    Google Scholar 

  25. Cleveland WS (1979). Robust locally-weighted regression and smoothing scatterplots. J Am Stat Assoc 74:829–836.

    Article  Google Scholar 

  26. Hastie TJ, Tibshirani RJ (1990). Generalized Additive Models. London: Chapman and Hall.

    Google Scholar 

  27. Stablein DM, Carter WH Jr, Novak J (1981). Analysis of survival data with nonproportional hazard functions. Controlled Clin Trials 2:149–159.

    Article  PubMed  CAS  Google Scholar 

  28. Chang IS, Hsiung CA (1990). Finite sample optimality of maximum partial likelihood estimation in Cox’s model for counting processes. J Stat Planning Infer 25:35–42.

    Article  Google Scholar 

  29. Therneau T (1993). A package of survival functions for S, available from StatLib.

    Google Scholar 

  30. Becker RA, Chambers JM, Wilks AR (1988). The New S Language, Pacific Grove, Califormia: Wadsworth & Brooks/Cole.

    Google Scholar 

  31. Statistical Sciences, Inc. (1993). S-Plus Training Manual: Introductory/Advanced, Version 3.1 for Unix. Seattle, WA: Statistical Sciences, Inc.

    Google Scholar 

  32. Fleming TR, O’Fallon JR, O’Brien PC, Harrington DP (1980). Modified Kolmogorov-Smirnov test procedures with applications to arbitrarily censored data. Biometrics 36: 607–625.

    Article  Google Scholar 

  33. Gill R, Schumacher M (1987). A simple test of the proportional hazards assumption. Biometrika 74:289–300.

    Article  Google Scholar 

  34. Grambsch PM, Therneau TM (in press). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika.

    Google Scholar 

  35. Therneau TM, Grambsch PM, Fleming TR (1990). Martingale-based residuals for survival models. Biometrika 77:147–160.

    Article  Google Scholar 

  36. McCullagh P, Nelder JA (1989). Generalized Linear Models, 2nd edition. New York: J. Wiley and Sons.

    Google Scholar 

  37. Grambsch PM, Therneau TM, Fleming TR (1994). Diagnostic plots to reveal functional form for covariates in multiplicative intensity models. Research Report 94-005, University of Minnesota Division of Biostatistics Research Report Series, Minneapolis, MN.

    Google Scholar 

  38. Hastie T, Tibshirani R (1993). Varying-coefficient models (with discussion). J R Stat B 55:757–796.

    Google Scholar 

  39. Gentleman R, Crowley J (1991). Local full likelihood estimation for the proportional hazards model. Biometrics 47:1283–1296.

    Article  PubMed  CAS  Google Scholar 

  40. Gray RJ (1992). Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. J Am Stat Assoc 87:942–951.

    Article  Google Scholar 

  41. Gray RJ (1990). Some diagnostic methods for Cox regression models through hazard smoothing. Biometrics 46:93–102.

    Article  PubMed  CAS  Google Scholar 

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Authors
  1. Patricia M. Grambsch
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Editors and Affiliations

  1. Department of Biomathematics, The University of Texas M.D. Anderson Cancer Center, 1515 Holcombe Boulevard, Box 237, Houston, Texas, 77030, USA

    Peter F. Thall Ph.D.

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© 1995 Springer Science+Business Media New York

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Grambsch, P.M. (1995). Goodness-of-fit and diagnostics for proportional hazards regression models. In: Thall, P.F. (eds) Recent Advances in Clinical Trial Design and Analysis. Cancer Treatment and Research, vol 75. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2009-2_5

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  • DOI: https://doi.org/10.1007/978-1-4615-2009-2_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5830-5

  • Online ISBN: 978-1-4615-2009-2

  • eBook Packages: Springer Book Archive

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