Comparison of parametric and semiparametric survival regression models with kernel estimation

References

• Kaplan EI, Meier PV. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53(282):457–481.
   Web of Science ®Google Scholar
• Horová I, Koláček J, Zelinka J. Kernel smoothing in MATLAB: theory and practice of kernel smoothing. Singapore: World Scientific; 2012.
   Google Scholar
• Wand MP, Jones MC. Kernel smoothing. London: Chapman & Hall; 1994.
   Google Scholar
• Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data. New York: John Wiley & Sons; 2002.
   Google Scholar
• Cox DR. Regression models and life-tables. J R Stat Soc Ser B. 1972;34(2):187–220.
   Web of Science ®Google Scholar
• Aalen OO. A linear regression model for the analysis of life times. Stat Med. 1989;8(8):907–925.
   PubMed Web of Science ®Google Scholar
• Kooperberg C, Stone CJ, Truong YK. Hazard regression. J Am Stat Assoc. 1995;90(429):78–94.
   Web of Science ®Google Scholar
• Rosenberg PS. Hazard function estimation using B-splines. Biometrics. 1995;51(3):874–887.
   PubMed Web of Science ®Google Scholar
• Watson GS, Leadbetter MR. Hazard analysis I. Biometrika. 1964;51(1/2):175–184.
   Web of Science ®Google Scholar
• Watson GS, Leadbetter MR. Hazard analysis II. Sank Indian J Stat Ser A. 1964;26(1):101–116.
   Google Scholar
• Uzunoguallari Ü, Wang JL. A comparison of hazard rate estimators for left truncated and right censored data. Biometrika. 1992;79(2):297–310.
   Web of Science ®Google Scholar
• Nielsen JP, Linton OB. Kernel estimation in a nonparametric marker dependent hazard model. Ann Stat. 1995;23(5):1735–1748.
   Web of Science ®Google Scholar
• Spierdijk L. Nonparametric conditional hazard rate estimation: a local linear approach. Comput Stat Data Anal. 2008;52(5):2419–2434.
   Web of Science ®Google Scholar
• Kim C, Oh M, Yang SJ, et al. A local linear estimation of conditional hazard function in censored data. J Kor Stat Soc. 2010;39(3):347–355.
   Web of Science ®Google Scholar
• Tanner MA, Wong WH. The estimation of the hazard function from randomly censored data by the kernel method. Ann Stat. 1983;11(3):989–993.
   Web of Science ®Google Scholar
• Müller HG, Wang JL. Nonparametric analysis of changes in hazard rates for censored survival data: an alternative to change-point models. Biometrika. 1990;77(2):305–314.
   Web of Science ®Google Scholar
• Li G. Optimal rate local smoothing in a multiplicative intensity counting process model. Math Methods Stat. 1997;6(2):224–244.
   Google Scholar
• Van Keilegom I, Veraverbeke N. Hazard rate estimation in nonparametric regression with censored data. Ann Inst Stat Math. 2001;53(4):730–745.
   Web of Science ®Google Scholar
• Linton OB, Nielsen JP, Van de Geer S. Estimating multiplicative and additive hazard functions by kernel methods. Ann Stat. 2003;31(2):464–492.
   Web of Science ®Google Scholar
• Wolter JL. Kernel estimation of hazard functions when observations have dependent and common covariates. J Econom. 2016;193(1):1–16.
   Web of Science ®Google Scholar
• R Core Team. R. A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2015. Available from: http://www.R-project.org/.
   Google Scholar
• Beran R. Nonparametric regression with randomly censored survival data. University of California at Berkeley; 1981. Technical report.
   Google Scholar
• Klein JP, Moeschberger ML. Survival analysis: techniques for censored and truncated data. New York: Springer; 2003.
   Google Scholar
• Selingerová I. Kernel estimates of hazard function (in Czech). [Dissertation]. Brno Masaryk University; 2015.
   Google Scholar
• Gámiz ML, Kulasekera KB, Limnios N, et al. Applied nonparametric statistics in reliability. London: Springer; 2011.
   Google Scholar
• Bagdonavicius V, Nikulin M. Accelerated life models: modeling and statistical analysis. Boca Raton/Florida: CRC Press; 2001.
   Google Scholar
• Wei LJ. The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med. 1992;11(14–15):1871–1879.
   PubMed Web of Science ®Google Scholar
• Therneau TM, Grambsch PM. Modeling survival data: extending the Cox model. New York: Springer; 2000.
   Google Scholar
• Vaida F, Xu R, et al. Proportional hazards model with random effects. Stat Med. 2000;19(24):3309–3324.
   PubMed Web of Science ®Google Scholar
• Schemper M, Wakounig S, Heinze G. The estimation of average hazard ratios by weighted Cox regression. Stat Med. 2009;28(19):2473–2489.
   PubMed Web of Science ®Google Scholar
• Gray RJ. Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. J Am Stat Assoc. 1992;87(420):942–951.
   Web of Science ®Google Scholar
• Valenta Z, Weissfeld L. Estimation of the survival function for Gray's piecewise-constant time-varying coefficients model. Stat Med. 2002;21(5):717–727.
   PubMed Web of Science ®Google Scholar
• Aalen OO. Further results on the non-parametric linear regression model in survival analysis. Stat Med. 1993;12(17):1569–1588.
   PubMed Web of Science ®Google Scholar
• Scheike TH, Zhang MJ. An additive–multiplicative Cox-Aalen regression model. Scand J Stat. 2002;29(1):75–88.
   Web of Science ®Google Scholar
• Scheike TH, Zhang MJ. Extensions and applications of the Cox-Aalen survival model. Biometrics. 2003;59(4):1036–1045.
   PubMed Web of Science ®Google Scholar
• Royston P, Parmar MK. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med. 2002;21(15):2175–2197.
   PubMed Web of Science ®Google Scholar
• Lambert PC, Royston P. Further development of flexible parametric models for survival analysis. Stat J. 2009;9(2):265–290.
   Web of Science ®Google Scholar
• Talamakrouni M, Van Keilegom I, El Ghouch A. Parametrically guided nonparametric density and hazard estimation with censored data. Comput Stat Data Anal. 2016;93:308–323.
   Web of Science ®Google Scholar
• Oueslati A, Lopez O. A proportional hazards regression model with change-points in the baseline function. Lifetime Data Anal. 2013;19:59–78.
   PubMed Web of Science ®Google Scholar
• Svoboda M, Navrátil J, Fabian P, et al. Triple-negative breast cancer: analysis of patients diagnosed and/or treated at the Masaryk Memorial Cancer Institute between 2004 and 2009 (in czech). Klin Onkol. 2012;25(3):188–198.
   PubMedGoogle Scholar
• Wan F. Simulating survival data with predefined censoring rates for proportional hazards models. Stat Med. 2017;36(5):838–854.
   PubMed Web of Science ®Google Scholar
• Hutton J, Monaghan P. Choice of parametric accelerated life and proportional hazards models for survival data: asymptotic results. Lifetime Data Anal. 2002;8(4):375–393.
   PubMed Web of Science ®Google Scholar
• Sun J. The statistical analysis of interval-censored failure time data. New York (NY): Springer New York; 2006. Statistics for Biology and Health.
   Google Scholar
• Jackson D, White IR, Seaman S, et al. Relaxing the independent censoring assumption in the Cox proportional hazards model using multiple imputation. Stat Med. 2014;33(27):4681–4694.
   PubMed Web of Science ®Google Scholar
• Betensky RA, Lindsey JC, Ryan LM, et al. Local EM estimation of the hazard function for interval-censored data. Biometrics. 1999;55(1):238–245.
   PubMed Web of Science ®Google Scholar
• Rabhi Y, Asgharian M. Inference under biased sampling and right censoring for a change point in the hazard function. Bernoulli. 2017;23(4A):2720–2745.
   Web of Science ®Google Scholar
• Scharfstein DO, Robins JM. Estimation of the failure time distribution in the presence of informative censoring. Biometrika. 2002;89(3):617–634.
   Web of Science ®Google Scholar
• Müller HG, Wang JL. Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics. 1994;50(1):61–76.
   PubMed Web of Science ®Google Scholar
• Chen SX. Probability density function estimation using gamma kernels. Ann Inst Stat Math. 2000;52(3):471–480.
   Web of Science ®Google Scholar
• Bouezmarni T, El Ghouch A, Mesfioui M. Gamma kernel estimators for density and hazard rate of right-censored data. J Probab Stat. 2011;2011: 937574.
   Google Scholar