The PHREG Procedure

References

  • Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1992), Statistical Models Based on Counting Processes, New York: Springer-Verlag.

  • Andersen, P. K. and Gill, R. D. (1982), “Cox’s Regression Model Counting Process: A Large Sample Study,” Annals of Statistics, 10, 1100–1120.

  • Binder, D. A. (1992), “Fitting Cox’s Proportional Hazards Models from Survey Data,” Biometrika, 79, 139–147.

  • Borgan, Ø. and Liestøl, K. (1990), “A Note on Confidence Interval and Bands for the Survival Curves Based on Transformations,” Scandinavian Journal of Statistics, 18, 35–41.

  • Breslow, N. E. (1972), “Discussion of Professor Cox’s Paper,” Journal of the Royal Statistical Society, Series B, 34, 216–217.

  • Breslow, N. E. (1974), “Covariance Analysis of Censored Survival Data,” Biometrics, 30, 89–99.

  • Breslow, N. E. and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9–25.

  • Bryson, M. C. and Johnson, M. E. (1981), “The Incidence of Monotone Likelihood in the Cox Model,” Technometrics, 23, 381–383.

  • Cain, K. C. and Lange, N. T. (1984), “Approximate Case Influence for the Proportional Hazards Regression Model with Censored Data,” Biometrics, 40, 493–499.

  • Cox, D. R. (1972), “Regression Models and Life Tables,” Journal of the Royal Statistical Society, Series B, 20, 187–220, with discussion.

  • Cox, D. R. (1975), “Partial Likelihood,” Biometrika, 62, 269–276.

  • Crowley, J. and Hu, M. (1977), “Covariance Analysis of Heart Transplant Survival Data,” Journal of the American Statistical Association, 72, 27–36.

  • DeLong, D. M., Guirguis, G. H., and So, Y. C. (1994), “Efficient Computation of Subset Selection Probabilities with Application to Cox Regression,” Biometrika, 81, 607–611.

  • Efron, B. (1977), “The Efficiency of Cox’s Likelihood Function for Censored Data,” Journal of the American Statistical Association, 72, 557–565.

  • Fine, J. P. and Gray, R. J. (1999), “A Proportional Hazards Model for the Subdistribution of a Competing Risk,” Journal of the American Statistical Association, 94, 496–509.

  • Firth, D. (1993), “Bias Reduction of Maximum Likelihood Estimates,” Biometrika, 80, 27–38.

  • Fleming, T. R. and Harrington, D. P. (1984), “Nonparametric Estimation of the Survival Distribution in Censored Data,” Communications in Statistics—Theory and Methods, 13, 2469–2486.

  • Fleming, T. R. and Harrington, D. P. (1991), Counting Processes and Survival Analysis, New York: John Wiley & Sons.

  • Furnival, G. M. and Wilson, R. W. (1974), “Regression by Leaps and Bounds,” Technometrics, 16, 499–511.

  • Gail, M. H. and Byar, D. P. (1986), “Variance Calculations for Direct Adjusted Survival Curves, with Applications to Testing for No Treatment Effect,” Biometrical Journal, 28, 587–599.

  • Gail, M. H., Lubin, J. H., and Rubinstein, L. V. (1981), “Likelihood Calculations for Matched Case-Control Studies and Survival Studies with Tied Death Times,” Biometrika, 68, 703–707.

  • Gilks, W. R., Best, N. G., and Tan, K. K. C. (1995), “Adaptive Rejection Metropolis Sampling within Gibbs Sampling,” Applied Statistics, 44, 455–472.

  • Grambsch, P. M. and Therneau, T. M. (1994), “Proportional Hazards Tests and Diagnostics Based on Weighted Residuals,” Biometrika, 81, 515–526.

  • Gray, R. J. (1992), “Flexible Method for Analyzing Survival Data Using Splines, with Applications to Breast Cancer Prognosis,” Journal of the American Statistical Association, 87, 942–951.

  • Harrell, F. E. (1986), “The PHGLM Procedure,” in SUGI Supplemental Library Guide, Version 5 Edition, Cary, NC: SAS Institute Inc.

  • Heinze, G. (1999), The Application of Firth’s Procedure to Cox and Logistic Regression, Technical Report 10/1999, updated in January 2001, Section of Clinical Biometrics, Department of Medical Computer Sciences, University of Vienna.

  • Heinze, G. and Schemper, M. (2001), “A Solution to the Problem of Monotone Likelihood in Cox Regression,” Biometrics, 51, 114–119.

  • Hosmer, D. W., Jr. and Lemeshow, S. (1989), Applied Logistic Regression, New York: John Wiley & Sons.

  • Ibrahim, J. G., Chen, M.-H., and Sinha, D. (2001), Bayesian Survival Analysis, New York: Springer-Verlag.

  • Kalbfleisch, J. D. and Prentice, R. L. (1980), The Statistical Analysis of Failure Time Data, New York: John Wiley & Sons.

  • Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. M. (1998), “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” American Statistician, 52, 93–100.

  • Klein, J. P. and Moeschberger, M. L. (1997), Survival Analysis: Techniques for Censored and Truncated Data, New York: Springer-Verlag.

  • Klein, J. P. and Moeschberger, M. L. (2003), Survival Analysis: Techniques for Censored and Truncated Data, 2nd Edition, New York: Springer-Verlag.

  • Krall, J. M., Uthoff, V. A., and Harley, J. B. (1975), “A Step-Up Procedure for Selecting Variables Associated with Survival,” Biometrics, 31, 49–57.

  • Lawless, J. F. (2003), Statistical Model and Methods for Lifetime Data, 2nd Edition, New York: John Wiley & Sons.

  • Lawless, J. F. and Nadeau, C. (1995), “Some Simple Robust Methods for the Analysis of Recurrent Events,” Technometrics, 37, 158–168.

  • Lee, E. W., Wei, L. J., and Amato, D. A. (1992), “Cox-Type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations,” in J. P. Klein and P. K. Goel, eds., Survival Analysis: State of the Art, 237–247, Dordrecht, Netherlands: Kluwer Academic.

  • Lin, D. Y. (1994), “Cox Regression Analysis of Multivariate Failure Time Data: The Marginal Approach,” Statistics in Medicine, 13, 2233–2247.

  • Lin, D. Y. and Wei, L. J. (1989), “The Robust Inference for the Proportional Hazards Model,” Journal of the American Statistical Association, 84, 1074–1078.

  • Lin, D. Y., Wei, L. J., Yang, I., and Ying, Z. (2000), “Semiparametric Regression for the Mean and Rate Functions of Recurrent Events,” Journal of the Royal Statistical Society, Series B, 62, 711–730.

  • Lin, D. Y., Wei, L. J., and Ying, Z. (1993), “Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals,” Biometrika, 80, 557–572.

  • Littell, R. C., Freund, R. J., and Spector, P. C. (1991), SAS System for Linear Models, 3rd Edition, Cary, NC: SAS Institute Inc.

  • Makuch, R. W. (1982), “Adjusted Survival Curve Estimation Using Covariates,” Journal of Chronic Diseases, 35, 437–443.

  • Muller, K. E. and Fetterman, B. A. (2002), Regression and ANOVA: An Integrated Approach Using SAS Software, Cary, NC: SAS Institute Inc.

  • Nelson, W. (2002), Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications, ASA-SIAM Series on Statistics and Applied Probability, Philadelphia: Society for Industrial and Applied Mathematics.

  • Neuberger, J., Altman, D. G., Christensen, E., Tygstrup, N., and Williams, R. (1986), “Use of a Prognostic Index in Evaluation of Liver Transplantation for Primary Biliary Cirrhosis,” Transplantation, 41, 713–716.

  • Pepe, M. S. and Cai, J. (1993), “Some Graphical Displays and Marginal Regression Analyses for Recurrent Failure Times and Time Dependent Covariates,” Journal of the American Statistical Association, 88, 811–820.

  • Pettitt, A. N. and Bin Daud, I. (1989), “Case-Weighted Measures of Influence for Proportional Hazards Regression,” Applied Statistics, 38, 313–329.

  • Prentice, R. L., Williams, B. J., and Peterson, A. V. (1981), “On the Regression Analysis of Multivariate Failure Time Data,” Biometrika, 68, 373–379.

  • Reid, N. and Crèpeau, H. (1985), “Influence Functions for Proportional Hazards Regression,” Biometrika, 72, 1–9.

  • Ripatti, S. and Palmgren, J. (2000), “Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood,” Biometrics, 56, 1016–1022.

  • Sargent, D. J. (1998), “A General Framework for Random Effects Survival Analysis in the Cox Proportional Hazards Setting,” Biometrics, 54, 1486–1497.

  • Schemper, M. and Henderson, R. (2000), “Predictive Accuracy and Explained Variation in Cox Regression,” Biometrics, 56, 249–255.

  • Schoenfeld, D. A. (1982), “Partial Residuals for the Proportional Hazards Regression Model,” Biometrika, 69, 239–241.

  • Sinha, D., Ibrahim, J. G., and Chen, M.-H. (2003), “A Bayesian Justification of Cox’s Partial Likelihood,” Biometrika, 90, 629–641.

  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit,” Journal of the Royal Statistical Society, Series B, 64(4), 583–616, with discussion.

  • Spiekerman, C. F. and Lin, D. Y. (1998), “Marginal Regression Models for Multivariate Failure Time Data,” Journal of American Statistical Association, 93, 1164–1175.

  • Therneau, T. M. (1994), A Package for Survival Analysis in S, Technical Report 53, Section of Biostatistics, Mayo Clinic, Rochester, MN.

  • Therneau, T. M. and Grambsch, P. M. (2000), Modeling Survival Data: Extending the Cox Model, New York: Springer-Verlag.

  • Therneau, T. M., Grambsch, P. M., and Fleming, T. R. (1990), “Martingale-Based Residuals and Survival Models,” Biometrika, 77, 147–160.

  • Tsiatis, A. A. (1981), “A Large Sample Study of the Estimates for the Integrated Hazard Function in Cox’s Regression Model for Survival Data,” Annals of Statistics, 9, 93–108.

  • Venzon, D. J. and Moolgavkar, S. H. (1988), “A Method for Computing Profile-Likelihood Based Confidence Intervals,” Applied Statistics, 37, 87–94.

  • Wei, L. J., Lin, D. Y., and Weissfeld, L. (1989), “Regression Analysis of Multivariate Incomplete Failure Time Data by Modeling Marginal Distribution,” Journal of the American Statistical Association, 84, 1065–1073.

  • Zhang, X., Loberiza, F. R., Klein, J. P., and Zhang, M. J. (2007), “A SAS Macro for Estimation of Direct Adjusted Survival Curves Based on a Stratified Cox Regression Model,” Computer Methods and Programs in Biomedicine, 88, 95–111.

  • Zhou, B., Fine, J., Latouche, A., and Labopin, M. (2012), “Competing Risks Regression for Cluster Data,” Biostatistics, 13, 371–383.

  • Zhou, B., Latouche, A., Rocha, V., and Fine, J. (2011), “Competing Risks Regression for Stratified Data,” Biometrics, 67, 661–670.