Abstract
Statistical simulations in medical and biological research are usually conducted with normal random numbers. However, in many cases, the distributions of real data in medical fields are usually right skewed. The conclusions led by simulations with the misspecified model might be misleading because of a gap between real data’s distribution and theoretical one. In this paper, we provide the simulation procedure for right skewed data based on reparameterized, easily interpretable parameters of the Box–Cox transformation model which includes multivariate distributions and regression models. We also show that the provided procedure is widely applicable to real world based on laboratory data, and then we provide parameter vector sets obtained by reparameterized parameter estimates that would cover almost all situations in which the distributions of data were right skewed and unimodal.
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References
Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc B 26:211–246
Bickel P, Doksum K (1981) An analysis of transformations revisited. J Am Stat Assoc 76:296–311
Ceyhan E, Goad CL (2009) A comparison of analysis of covariate-adjusted residuals and analysis of covariance. Commun Stat-Simul Comput 38:2019–2038
Doksum KA, Wong CW (1983) Statistical tests based on transformed data. J Am Stat Assoc 78:411–417
Fitzmaurice GM, Laird NM, Ware JH (2011) Applied longitudinal analysis, 2nd edn. Wiley, New York
Freeman J, Modarres R (2006) Inverse Box–Cox: the power-normal distribution. Stat Prob Lett 76:764–772
Goto M, Hamasaki T (2002) The bivariate power-normal distribution. Bull Inform Cybermet 34:29–49
Goto M, Matsubara M, Tsuchiya Y (1983) Power-normal distribution and its applications. Rep Stat Appl Res JUSE 30:8–28
Goto M, Uesaka H, Inoue T (1979) Some linear models for power transformed data. Invited paper at the 10th international biometric conference, Res Rep no. 93, Res Instit Fund Infor Sc, Kyusyu University, pp 6–10
Gurka MJ, Edwards LJ, Muller KE, Kupper LL (2006) Extending the Box–Cox transformation to the linear mixed model. J R Stat Soc A 40:273–288
Henry K, Erice A, Tierney C, Balfour HH Jr, Fischl MA, Kmack A, Liou SH, Kenton A, Hirsch MS, Phair J, Martinez A, Kahn JO for the AIDS Clinical Trial Group 193A Study Team (1998) A randomized, controlled, double-blind study comparing the survival benefit of four different reverse transcriptase inhibitor therapies (three-drug, two-drug, and alternating drug) for the treatment of advanced AIDS. J Acquir Immune Defic Syndr Hum Retrovirol 19:339–349
Joe H (2005) Asymptotic efficiency of the two-stage estimation method for copula-based model. J Multivar Anal 94:401–419
Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions. Wiley, New York
Lipsitz SR, Ibrahim J, Molenberghs G (2000) Using a Box–Cox transformation in the analysis of longitudinal data with incomplete responses. Appl Stat 49:287–296
Maruo K, Goto M (2013) Percentile estimation based on the power-normal distribution. Comput Stat 28:341–356
Maruo K, Isogawa N, Gosho M (2015) Inference of median difference based on the Box–Cox model in randomized clinical trials. Stat Med 34:1634–1644
Maruo K, Shirahata S, Goto M (2011) Underlying assumptions of the power-normal distribution. Behaviormetrika 38:85–95
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Maruo, K., Yamabe, T. & Yamaguchi, Y. Statistical simulation based on right skewed distributions. Comput Stat 32, 889–907 (2017). https://doi.org/10.1007/s00180-016-0664-4
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DOI: https://doi.org/10.1007/s00180-016-0664-4