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Theory and Methods

Survival Regression Models With Dependent Bayesian Nonparametric Priors

, ORCID Icon & ORCID Icon
Pages 1530-1539 | Received 04 Sep 2019, Accepted 22 Nov 2020, Published online: 10 Feb 2021

References

  • Andersen, P. K., and Gill, R. D. (1982), “Cox’s Regression Model for Counting Processes: A Large Sample Study,” The Annals of Statistics, 10, 1100–1120. DOI: 10.1214/aos/1176345976.
  • Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (2012), Statistical Models Based on Counting Processes, New York: Springer-Verlag.
  • Buckley, J., and James, I. (1979), “Linear Regression With Censored Data,” Biometrika, 66, 429–436. DOI: 10.1093/biomet/66.3.429.
  • Camerlenghi, F., Dunson, D. B., Lijoi, A., Prünster, I., and Rodríguez, A. (2019), “Latent Nested Nonparametric Priors” (with discussion), Bayesian Analysis, 14, 1303–1356. DOI: 10.1214/19-BA1169.
  • Camerlenghi, F., Lijoi, A., Orbanz, P., and Prünster, I. (2019), “Distribution Theory for Hierarchical Processes,” The Annals of Statistics, 47, 67–92. DOI: 10.1214/17-AOS1678.
  • Cheng, S. C., Wei, L. J., and Ying, Z. (1995), “Analysis of Transformation Models With Censored Data,” Biometrika, 82, 835–845. DOI: 10.1093/biomet/82.4.835.
  • Christensen, R., and Johnson, W. (1988), “Modelling Accelerated Failure Time With a Dirichlet Process,” Biometrika, 75, 693–704. DOI: 10.1093/biomet/75.4.693.
  • Cox, D. R. (1972), “Regression Models and Life-Tables,” Journal of the Royal Statistical Society, Series B, 34, 187–220. DOI: 10.1111/j.2517-6161.1972.tb00899.x.
  • Cox, D. R. (1975), “Partial Likelihood,” Biometrika, 62, 269–276.
  • De Iorio, M., Johnson, W. O., Mueller, P., and Rosner, G. L. (2009), “Bayesian Nonparametric Nonproportional Hazards Survival Modeling,” Biometrics, 65, 762–771. DOI: 10.1111/j.1541-0420.2008.01166.x.
  • Denison, D. G., Holmes, C. C., Mallick, B. K., and Smith, A. F. (2002), Bayesian Methods for Nonlinear Classification and Regression (Vol. 386), New York: Wiley.
  • Di Benedetto, G., Caron, F., and Teh, Y.-W. (2017), “Non-Exchangeable Random Partition Models for Microclustering,” arXiv no. 1711.07287.
  • Doksum, K. (1974), “Tailfree and Neutral Random Probabilities and Their Posterior Distributions,” The Annals of Probability, 2, 183–201. DOI: 10.1214/aop/1176996703.
  • Doss, H. (1994), “Bayesian Nonparametric Estimation for Incomplete Data via Successive Substitution Sampling,” The Annals of Statistics, 22, 1763–1786. DOI: 10.1214/aos/1176325756.
  • Dykstra, R. L., and Laud, P. (1981), “A Bayesian Nonparametric Approach to Reliability,” The Annals of Statistics, 9, 356–367. DOI: 10.1214/aos/1176345401.
  • Epifani, I., and Lijoi, A. (2010), “Nonparametric Priors for Vectors of Survival Functions,” Statistica Sinica, 20, 1455–1484.
  • Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209–230. DOI: 10.1214/aos/1176342360.
  • Ferguson, T. S. (1974), “Prior Distributions on Spaces of Probability Measures,” The Annals of Statistics, 2, 615–629.
  • Ferguson, T. S., and Phadia, E. G. (1979), “Bayesian Nonparametric Estimation Based on Censored Data,” The Annals of Statistics, 7, 163–186. DOI: 10.1214/aos/1176344562.
  • Fernández, T., Rivera, N., and Teh, Y. W. (2016), “Gaussian Processes for Survival Analysis,” in Advances in Neural Information Processing Systems (Vol. 29), eds. D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett, pp. 5021–5029.
  • Friedberg, S. H., Insel, A. J., and Spence, L. E. (2013), Linear Algebra: Pearson New International Edition, Harlow, UK: Pearson Higher Ed.
  • Griffin, J., and Leisen, F. (2017), “Compound Random Measures and Their Use in Bayesian Nonparametrics,” Journal of the Royal Statistical Society, Series B, 79, 525–545. DOI: 10.1111/rssb.12176.
  • Hjort, N. L. (1990), “Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data,” The Annals of Statistics, 18, 1259–1294. DOI: 10.1214/aos/1176347749.
  • Hjort, N. L., Holmes, C., Müller, P., and Walker, S. G., eds. (2010), Bayesian Nonparametrics, Cambridge: Cambridge University Press.
  • Hanson, T. E., and Jara A. (2013), “Surviving Fully Bayesian Nonparametric Regression Models,” in Bayesian Theory and Applications, eds. P. Damien, P. Dellaportas, N. Polson, and D. Stephens, Oxford: Oxford University Press, pp. 593–615.
  • Jara, A., and Hanson, T. E. (2011), “A Class of Mixtures of Dependent Tail-Free Processes,” Biometrika, 98, 553–566. DOI: 10.1093/biomet/asq082.
  • Jara, A., Hanson, T. E., Quintana, F. A., Müller, P., and Rosner, G. L. (2011), “DPpackage: Bayesian Semi- and Nonparametric Modeling in R,” Journal of Statistical Software, 40, 1–30. DOI: 10.18637/jss.v040.i05.
  • Kalbfleisch, J. D., and Prentice, R. L. (2011), The Statistical Analysis of Failure Time Data, New York: Wiley.
  • Kim, Y., and Lee, J. (2001), “On Posterior Consistency of Survival Models,” The Annals of Statistics, 29, 666–686. DOI: 10.1214/aos/1009210685.
  • Kim, Y., and Lee, J. (2003), “Bayesian Analysis of Proportional Hazard Models,” The Annals of Statistics, 31, 493–511.
  • Kim, Y., and Lee, J. (2004), “A Bernstein-von Mises Theorem in the Nonparametric Right-Censoring Model,” The Annals of Statistics, 32, 1492–1512.
  • Kingman, J. (1967), “Completely Random Measures,” Pacific Journal of Mathematics, 21, 59–78. DOI: 10.2140/pjm.1967.21.59.
  • Klein, J. P., and Moeschberger, M. L. (2006), Survival Analysis: Techniques for Censored and Truncated Data, New York: Springer-Verlag.
  • Lijoi, A., Nipoti, B., and Prünster, I. (2014), “Bayesian Inference With Dependent Normalized Completely Random Measures,” Bernoulli, 20, 1260–1291. DOI: 10.3150/13-BEJ521.
  • MacEachern, S. N. (1999), “Dependent Nonparametric Processes,” in ASA Proceedings of the Section on Bayesian Statistical Science, American Statistical Association, Alexandria, VA.
  • Masoero, L., Camerlenghi, F., Favaro, S., and Broderick, T. (2019), “More for Less: Predicting and Maximizing Genetic Variant Discovery via Bayesian Nonparametrics,” arXiv no. 1912.05516.
  • Mogensen, P. K., and Riseth, A. N. (2018), “Optim: A Mathematical Optimization Package for Julia,” Journal of Open Source Software, 3, 615.
  • Muliere, P., and Walker, S. G. (1997), “Beta-Stacy Processes and a Generalization of the Pólya-Urn Scheme,” The Annals of Statistics, 25, 1762–1780. DOI: 10.1214/aos/1031594741.
  • Murphy, S. A., Rossini, A. J., and Van der Vaart, A. W. (1997), “Maximum Likelihood Estimation in the Proportional Odds Model,” Journal of the American Statistical Association, 92, 968–976. DOI: 10.1080/01621459.1997.10474051.
  • Nieto-Barajas, L. E. (2014), “Bayesian Semiparametric Analysis of Short- and Long-Term Hazard Ratios With Covariates,” Computational Statistics & Data Analysis, 71, 477–490.
  • Nipoti, B., Jara, A., and Guindani, M. (2018), “A Bayesian Semiparametric Partially PH Model for Clustered Time-to-Event Data,” Scandinavian Journal of Statistics, 45, 1016–1035. DOI: 10.1111/sjos.12332.
  • Petrone, S., Rizzelli, S., Rousseau, J., and Scricciolo, C. (2014), “Empirical Bayes Methods in Classical and Bayesian Inference,” Metron, 72, 201–215. DOI: 10.1007/s40300-014-0044-1.
  • Phadia, E. G. (2015), Prior Processes and Their Applications, New York: Springer.
  • Prentice, R. L., Kalbrleisch, J. D., Peterson, A. V., Jr., Flournoy, N., Farewell, V. T., and Breslow, N. E. (1978), “The Analysis of Failure Times in the Presence of Competing Risks,” Biometrics, 34, 541–554. DOI: 10.2307/2530374.
  • Riva-Palacio, A., and Leisen, F. (2018), “Bayesian Nonparametric Estimation of Survival Functions With Multiple-Samples Information,” Electronic Journal of Statistics, 12, 1330–1357. DOI: 10.1214/18-EJS1420.
  • Riva-Palacio, A., and Leisen, F. (2019), “Compound Vectors of Subordinators and Their Associated Positive Lévy Copulas,” arXiv no. 1909.12112.
  • Ryan, T., and Woodall, W. (2005), “The Most Cited Statistical Papers,” Journal of Applied Statistics, 32, 461–474. DOI: 10.1080/02664760500079373.
  • Therneau, T. M., and Grambsch, P. M. (2000), Modeling Survival Data: Extending the Cox Model, New York: Springer-Verlag.
  • Original by Klein, J. P. and Moeschberger, M. L. and modifications by Yan, J. (2012), “KMsurv: Data sets from Klein and Moeschberger (1997), Survival Analysis,” R Package Version 0.1-5, available at https://CRAN.R-project.org/package=KMsurv.
  • Yang, S., and Prentice, R. L. (1999), “Semiparametric Inference in the Proportional Odds Regression Model,” Journal of the American Statistical Association, 94, 125–136. DOI: 10.1080/01621459.1999.10473829.

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