Behaviour of higher-order approximations of the tests in the single parameter Cox proportional hazards model

Aneta Andrášiková; Eva Fišerová

Applications of Mathematics (2020)

  • Volume: 65, Issue: 3, page 229-244
  • ISSN: 0862-7940

Abstract

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Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations based on Barndorff-Nielsen and Lugannani-Rice formulas are used for more accurate approximations. In this paper, comparison of these tests' size and power for small sample sizes is performed on simulated datasets with various proportions of right-censored data, distributions of baseline hazard functions and different types of covariate---continuous or discrete.

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Andrášiková, Aneta, and Fišerová, Eva. "Behaviour of higher-order approximations of the tests in the single parameter Cox proportional hazards model." Applications of Mathematics 65.3 (2020): 229-244. <http://eudml.org/doc/297385>.

@article{Andrášiková2020,
abstract = {Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations based on Barndorff-Nielsen and Lugannani-Rice formulas are used for more accurate approximations. In this paper, comparison of these tests' size and power for small sample sizes is performed on simulated datasets with various proportions of right-censored data, distributions of baseline hazard functions and different types of covariate---continuous or discrete.},
author = {Andrášiková, Aneta, Fišerová, Eva},
journal = {Applications of Mathematics},
keywords = {survival analysis; likelihood ratio test; wald test; score test; statistical power; adjusted power; higher-order approximation; confidence band},
language = {eng},
number = {3},
pages = {229-244},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Behaviour of higher-order approximations of the tests in the single parameter Cox proportional hazards model},
url = {http://eudml.org/doc/297385},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Andrášiková, Aneta
AU - Fišerová, Eva
TI - Behaviour of higher-order approximations of the tests in the single parameter Cox proportional hazards model
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 229
EP - 244
AB - Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations based on Barndorff-Nielsen and Lugannani-Rice formulas are used for more accurate approximations. In this paper, comparison of these tests' size and power for small sample sizes is performed on simulated datasets with various proportions of right-censored data, distributions of baseline hazard functions and different types of covariate---continuous or discrete.
LA - eng
KW - survival analysis; likelihood ratio test; wald test; score test; statistical power; adjusted power; higher-order approximation; confidence band
UR - http://eudml.org/doc/297385
ER -

References

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  1. Adujemo, A. O., Ahmadu, A. O., A study of the slope of Cox proportional hazard and Weibull models: Simulated and real life data approach, Science World Journal 11 (2016), 31-35. (2016) 
  2. Agresti, A., Coull, B. A., 10.2307/2685469, Am. Stat. 52 (1998), 119-126. (1998) MR1628435DOI10.2307/2685469
  3. Barndorff-Nielsen, O., Cox, D. R., 10.1111/j.2517-6161.1979.tb01085.x, J. R. Stat. Soc., Ser. B 41 (1979), 279-312. (1979) Zbl0424.62010MR0557595DOI10.1111/j.2517-6161.1979.tb01085.x
  4. Bělašková, S., Fišerová, E., 10.2298/FIL1718591B, Filomat 31 (2017), 5591-5601. (2017) MR3744163DOI10.2298/FIL1718591B
  5. Bender, R., Augustin, T., Blettner, M., 10.1002/sim.2059, Stat. Med. 24 (2005), 1713-1723. (2005) MR2137646DOI10.1002/sim.2059
  6. Brazzale, A. R., Valentina, M., Likelihood asymptotics in nonregular settings: A review with emphasis on the likelihood ratio, Working Paper Series 4 (2018), 45 pages Available at http://paduaresearch.cab.unipd.it/11306/. (2018) 
  7. Breslow, N., Discussion of Professor Cox's paper, J. R. Stat. Soc., Ser. B 34 (1972), 216-217. (1972) Zbl0243.62041MR0341758
  8. Brown, L. D., Cai, T. T., DasGupta, A., 10.1214/ss/1009213286, Stat. Sci. 16 (2001), 101-133. (2001) Zbl1059.62533MR1861069DOI10.1214/ss/1009213286
  9. Buse, A., 10.2307/2683166, Am. Stat. 36 (1982), 153-157. (1982) DOI10.2307/2683166
  10. Chandra, T. K., Joshi, S. N., Comparison of likelihood ratio, Rao's and Wald's tests and a conjecture of C. R. Rao, Sankhy, Ser. A 45 (1983), 226-246. (1983) Zbl0563.62018MR0748461
  11. Cox, D. R., Oakes, D., 10.1201/9781315137438, Monographs on Statistics and Applied Probability. Chapman & Hall, London (1984). (1984) MR0751780DOI10.1201/9781315137438
  12. Crumer, A. M., Comparison Between Weibull and Cox Proportional Hazards Models, Kansas State University, Manhattan (2011), Available at https://core.ac.uk/download/pdf/5172563.pdf. (2011) 
  13. Efron, B., 10.2307/2286217, J. Am. Stat. Assoc. 72 (1977), 557-565. (1977) Zbl0373.62020MR0451514DOI10.2307/2286217
  14. Fišerová, E., Chvosteková, M., Bělašková, S., Bumbálek, M., Joska, Z., 10.1155/2015/189703, Adv. Mater. Sci. Engineer. 2015 (2015), Article ID 189703, 6 pages. (2015) DOI10.1155/2015/189703
  15. Fraser, D. A. S., Wu, J., Wong, A. C. M., 10.1080/03610919808813480, Commun. Stat., Simulation Comput. 27 (1998), 275-287. (1998) Zbl0929.62011MR1625949DOI10.1080/03610919808813480
  16. Gudicha, D. W., Schmittmann, V. D., Vermunt, J. K., 10.3758/s13428-016-0825-y, Behavior Research Methods 49 (2017), 1824-1837. (2017) DOI10.3758/s13428-016-0825-y
  17. D. W. Hosmer, Jr., S. Lemeshow, 10.1002/9780470258019, Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York (1999). (1999) Zbl0966.62071MR1674644DOI10.1002/9780470258019
  18. Ihwah, A., 10.1016/j.aaspro.2015.01.017, Agriculture and Agricultural Science Procedia 3 (2015), 78-83. (2015) DOI10.1016/j.aaspro.2015.01.017
  19. Lawless, J. F., 10.1002/9781118033005, Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken (2003). (2003) Zbl1015.62093MR1940115DOI10.1002/9781118033005
  20. Lee, E. T., Go, O. T., 10.1146/annurev.publhealth.18.1.105, Annu. Rev. Public Health 18 (1997), 105-134. (1997) DOI10.1146/annurev.publhealth.18.1.105
  21. Lugannani, R., Rice, S., 10.2307/1426607, Adv. Appl. Probab. 12 (1980), 475-490. (1980) Zbl0425.60042MR0569438DOI10.2307/1426607
  22. Pierce, D. A., Bellio, R., 10.3150/13-BEJ572, Bernoulli 21 (2015), 401-419. (2015) Zbl1388.62051MR3322324DOI10.3150/13-BEJ572
  23. Qian, J., Li, B., Chen, P., 10.1109/ICIC.2010.294, Third International Conference on Information and Computing IEEE, Los Alamitos (2010), 93-96. (2010) DOI10.1109/ICIC.2010.294
  24. Schemper, M., 10.2307/2349009, J. R. Stat. Soc., Ser. D 41 (1992), 455-465. (1992) DOI10.2307/2349009
  25. Sen, P. K., Singer, J. M., 10.1201/9780203711606, Chapman & Hall, New York (1993). (1993) Zbl0867.62003MR1293125DOI10.1201/9780203711606
  26. Skovgaard, I. M., 10.2307/3318548, Bernoulli 2 (1996), 145-165. (1996) Zbl1066.62508MR1410135DOI10.2307/3318548
  27. Skovgaard, I. M., 10.1111/1467-9469.00223, Scand. J. Stat. 28 (2001), 3-32. (2001) Zbl0965.62014MR1844348DOI10.1111/1467-9469.00223
  28. Wan, F., 10.1002/sim.7178, Stat. Med. 36 (2017), 838-854. (2017) MR3597660DOI10.1002/sim.7178
  29. Yi, Y., Wang, X., Comparison of Wald, score, and likelihood ratio tests for response adaptive designs, J. Stat. Theory Appl. 10 (2011), 553-569. (2011) MR2907394
  30. Zhang, J., Boos, D. D., 10.1080/03610919408813162, Commun. Stat., Simulation Comput. 23 (1994), 165-173. (1994) Zbl0825.62018DOI10.1080/03610919408813162
  31. Zhang, J., Kolassa, J. E., 10.1214/074921707000000193, Complex Datasets and Inverse Problems: Tomography, Networks and Beyond IMS Lecture Notes Monograph Series 54, Institute of Mathematical Statistics, Beachwood (2007), 250-259. (2007) MR2459193DOI10.1214/074921707000000193

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