##
**Study of bootstrap estimates in Cox regression model with delayed entry.**
*(English)*
Zbl 1302.62208

Summary: In most clinical studies, patients are observed for extended time periods to evaluate influences in treatment such as drug treatment, approaches to surgery, etc. The primary event in these studies is death, relapse, adverse drug reaction, or development of a new disease. The follow-up time may range from few weeks to many years. Although these studies are long term, the number of observed events is small. Longitudinal studies have increased the importance of statistical methods for time-to event data that can incorporate time-dependent covariates. The Cox proportional regression model is a widely used method. It is a statistical technique for exploring the relationship between the survival of a patient and several explanatory variables. We apply Cox regression models when right censoring and delayed entry survival data are considered. Y.-R. Su and J.-L. Wang [Ann. Stat. 40, No. 3, 1465–1488 (2012; Zbl 1257.62114)] stated that delayed entry produced biased sample. In the paper we present how re-sampling together with effect of delayed entry affect estimated parameters. The possibilities as well as limitations of this approach are demonstrated through the retrospective study of mitral valve replacement in children under 18 years.

### MSC:

62N01 | Censored data models |

62N02 | Estimation in survival analysis and censored data |

62G09 | Nonparametric statistical resampling methods |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

### Keywords:

Cox proportional regression model; Breslow method; delayed entry; observation study; mitral valve### Citations:

Zbl 1257.62114
PDFBibTeX
XMLCite

\textit{S. Bělašková} et al., Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 52, No. 2, 21--30 (2013; Zbl 1302.62208)

Full Text:
Link

### References:

[1] | Allison, P. D., SAS Institute: Survival Analysis Using the Sas System: A Practical Guide. SAS Institute Inc., Cary, NC, 1995 |

[2] | Breslow, N. E.: Discussion of Professor Cox’s paper. J. Royal Stat. Soc. B 34 (1972), 216-217. |

[3] | Breslow, N. E.: Covariance analysis of censored survival data. Biometrics 30 (1974), 89-99. |

[4] | Cassell, D. L.: Don’t Be Loopy: Re-Sampling and Simulation the SAS Way. Proceedings of the 2007 SAS Global Forum, SAS Institute Inc., Cary, NC, 2007. |

[5] | Cary, N. C., SAS Institute Inc.: User’s Guide. SAS Institute Inc. SAS/STAT 9.2, Cary, NC, 2008. |

[6] | Collett, D.: Modeling Survival Data in Medical Research. Chapman & Hall, London, 1994. |

[7] | Cox, D. R.: Regression models and life tables. Journal of the Royal Statistical Society, Series B 20 (1972), 187-220. · Zbl 0243.62041 |

[8] | Cox, D. R., Oakes, D.: Analysis of Survival Data. Chapman & Hall, London, 1984. |

[9] | Edgington, E. S.: Randomization Tests. M. Dekker, New York, 1995. · Zbl 0893.62036 |

[10] | Efron, B., Tibshirani, R. J.: An Introduction to the Bootstrap. Chapman & Hall, New York, 1993. · Zbl 0835.62038 |

[11] | Jun Qian, Bin Li, Ping-yan Chen: Generating Survival Data in the Simulation Studies of Cox Model. Information and Computing (ICIC) Third International Conference on, 4 (2010), 93-96. |

[12] | Kaplan, E. L., Meier, P.: Non-parametric estimation from incomplete observations. J. Am. Stat. Assoc. 53 (1958), 457-481. · Zbl 0089.14801 |

[13] | Klein, J. P., Moeschberger, M. L.: Survival Analysis: Techniques for Censored and Truncated Data. Springer, New York, 1997. · Zbl 0871.62091 |

[14] | Kleinbaum, D. G., Klien, M.: Survival Analysis: A Self-Learning Text. Second Edition, Springer, New York, 2005. |

[15] | Kongerud, J., Samuelsen, S. O.: A longitudinal study of respiratory symptoms in aluminum potroom workers. American Review of Respiratory Diseases 144 (1991), 10-16. |

[16] | Li Ji: Cox Model Analysis with the Dependently Left Truncated Data. Mathematics Theses, Paper 88, Georgia State University, Atlanta, GA, 2010. |

[17] | Su Y. R., Wang J. L.: Modeling left-truncated and right-censored survival data with longitudinal covariates. The Annals of Statistics 40, 3 (2012), 1465-1488. · Zbl 1257.62114 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.