The PHREG Procedure

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.

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.