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Keywords:
survival analysis; likelihood ratio test; wald test; score test; statistical power; adjusted power; higher-order approximation; confidence band
Summary:
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.
References:
[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.
[2] Agresti, A., Coull, B. A.: Approximate is better than ``exact'' for interval estimation of binomial proportions. Am. Stat. 52 (1998), 119-126. DOI 10.2307/2685469 | MR 1628435
[3] Barndorff-Nielsen, O., Cox, D. R.: Edgeworth and saddle-point approximations with statistical applications. J. R. Stat. Soc., Ser. B 41 (1979), 279-312. DOI 10.1111/j.2517-6161.1979.tb01085.x | MR 0557595 | Zbl 0424.62010
[4] Bělašková, S., Fišerová, E.: Improvement of the accuracy in testing the effect in the Cox proportional hazards model using higher order approximations. Filomat 31 (2017), 5591-5601. DOI 10.2298/FIL1718591B | MR 3744163
[5] Bender, R., Augustin, T., Blettner, M.: Generating survival times to simulate Cox proportional hazards models. Stat. Med. 24 (2005), 1713-1723. DOI 10.1002/sim.2059 | MR 2137646
[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/\kern0pt
[7] Breslow, N.: Discussion of Professor Cox's paper. J. R. Stat. Soc., Ser. B 34 (1972), 216-217. MR 0341758 | Zbl 0243.62041
[8] Brown, L. D., Cai, T. T., DasGupta, A.: Interval estimation for a binomial proportion. Stat. Sci. 16 (2001), 101-133. DOI 10.1214/ss/1009213286 | MR 1861069 | Zbl 1059.62533
[9] Buse, A.: The likelihood ratio, Wald, and Lagrange multiplier tests: An expository note. Am. Stat. 36 (1982), 153-157. DOI 10.2307/2683166
[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$\bar a$, Ser. A 45 (1983), 226-246. MR 0748461 | Zbl 0563.62018
[11] Cox, D. R., Oakes, D.: Analysis of Survival Data. Monographs on Statistics and Applied Probability. Chapman & Hall, London (1984). DOI 10.1201/9781315137438 | MR 0751780
[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\kern0pt
[13] Efron, B.: The efficiency of Cox's likelihood function for censored data. J. Am. Stat. Assoc. 72 (1977), 557-565. DOI 10.2307/2286217 | MR 0451514 | Zbl 0373.62020
[14] Fišerová, E., Chvosteková, M., Bělašková, S., Bumbálek, M., Joska, Z.: Survival analysis of factors influencing cyclic fatigue of nickel-titanium endodontic instruments. Adv. Mater. Sci. Engineer. 2015 (2015), Article ID 189703, 6 pages. DOI 10.1155/2015/189703
[15] Fraser, D. A. S., Wu, J., Wong, A. C. M.: An approximation for noncentral chi-squared distribution. Commun. Stat., Simulation Comput. 27 (1998), 275-287. DOI 10.1080/03610919808813480 | MR 1625949 | Zbl 0929.62011
[16] Gudicha, D. W., Schmittmann, V. D., Vermunt, J. K.: Statistical power of likelihood ratio and Wald test in latent class models with covariates. Behavior Research Methods 49 (2017), 1824-1837. DOI 10.3758/s13428-016-0825-y
[17] D. W. Hosmer, Jr., S. Lemeshow: Applied Survival Analysis: Regression Modeling of Time to Event Data. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York (1999). DOI 10.1002/9780470258019 | MR 1674644 | Zbl 0966.62071
[18] Ihwah, A.: The use of Cox regression model to analyze the factors that influence consumer purchase decision on a product. Agriculture and Agricultural Science Procedia 3 (2015), 78-83. DOI 10.1016/j.aaspro.2015.01.017
[19] Lawless, J. F.: Statistical Models and Methods for Lifetime Data. Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken (2003). DOI 10.1002/9781118033005 | MR 1940115 | Zbl 1015.62093
[20] Lee, E. T., Go, O. T.: Survival analysis in public health research. Annu. Rev. Public Health 18 (1997), 105-134. DOI 10.1146/annurev.publhealth.18.1.105
[21] Lugannani, R., Rice, S.: Saddle point approximation for the distribution of the sum of independent random variables. Adv. Appl. Probab. 12 (1980), 475-490. DOI 10.2307/1426607 | MR 0569438 | Zbl 0425.60042
[22] Pierce, D. A., Bellio, R.: Beyond first-order asymptotics for Cox regression. Bernoulli 21 (2015), 401-419. DOI 10.3150/13-BEJ572 | MR 3322324 | Zbl 1388.62051
[23] Qian, J., Li, B., Chen, P.: Generating survival data in the simulation studies of Cox model. Third International Conference on Information and Computing IEEE, Los Alamitos (2010), 93-96. DOI 10.1109/ICIC.2010.294
[24] Schemper, M.: Cox analysis of survival data with non-proportional hazard functions. J. R. Stat. Soc., Ser. D 41 (1992), 455-465. DOI 10.2307/2349009
[25] Sen, P. K., Singer, J. M.: Large Sample Methods in Statistics: An Introduction With Applications. Chapman & Hall, New York (1993). DOI 10.1201/9780203711606 | MR 1293125 | Zbl 0867.62003
[26] Skovgaard, I. M.: An explicit large-deviation approximation to one-parameter tests. Bernoulli 2 (1996), 145-165. DOI 10.2307/3318548 | MR 1410135 | Zbl 1066.62508
[27] Skovgaard, I. M.: Likelihood asymptotics. Scand. J. Stat. 28 (2001), 3-32. DOI 10.1111/1467-9469.00223 | MR 1844348 | Zbl 0965.62014
[28] Wan, F.: Simulating survival data with predefined censoring rates for proportional hazards models. Stat. Med. 36 (2017), 838-854. DOI 10.1002/sim.7178 | MR 3597660
[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. MR 2907394
[30] Zhang, J., Boos, D. D.: Adjusted power estimates in Monte Carlo experiments. Commun. Stat., Simulation Comput. 23 (1994), 165-173. DOI 10.1080/03610919408813162 | Zbl 0825.62018
[31] Zhang, J., Kolassa, J. E.: A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations. Complex Datasets and Inverse Problems: Tomography, Networks and Beyond IMS Lecture Notes Monograph Series 54, Institute of Mathematical Statistics, Beachwood (2007), 250-259. DOI 10.1214/074921707000000193 | MR 2459193
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