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Multiple comparisons of treatments with skewed ordinal responses

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  • Lu, Tong-Yu
  • Poon, Wai-Yin
  • Cheung, Siu Hung

Abstract

In clinical studies, treatment responses are frequently measured with an ordinal scale. To compare the efficacy of these treatments, one could employ either the proportional odds model or the latent normal model. However, these two models are inadequate for comparing treatments with highly skewed ordinal responses, due to the possibility of yielding an inflated type I error rate. To overcome this problem, the latent Weibull model has been suggested for investigating the efficacy difference between two treatments. For more general applications, this model is extended to include clinical trials with more than two treatments. Two testing procedures are derived: one for multiple comparisons with a control and the other for pairwise treatment comparisons. The testing procedures are also demonstrated with two clinical examples.

Suggested Citation

  • Lu, Tong-Yu & Poon, Wai-Yin & Cheung, Siu Hung, 2016. "Multiple comparisons of treatments with skewed ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 223-232.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:223-232
    DOI: 10.1016/j.csda.2016.07.004
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    1. J. A. Anderson & P. R. Philips, 1981. "Regression, Discrimination and Measurement Models for Ordered Categorical Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(1), pages 22-31, March.
    2. L.G. Leon-Novelo & X. Zhou & B. Nebiyou Bekele & P. Müller, 2010. "Assessing Toxicities in a Clinical Trial: Bayesian Inference for Ordinal Data Nested within Categories," Biometrics, The International Biometric Society, vol. 66(3), pages 966-974, September.
    3. Charles W. Dunnett, 1989. "Multivariate Normal Probability Integrals with Product Correlation Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(3), pages 564-579, November.
    4. Liu, W. & Somerville, P. N., 2004. "Stepwise multiple tests for successive comparisons of treatment effects," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 189-199, May.
    5. Tong-Yu Lu & Wai-Yin Poon & Siu Cheung, 2014. "A Unified Framework for the Comparison of Treatments with Ordinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 605-620, October.
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