A Note on Analysis of Ratio of Two Correlated Normal Variables

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  • 相関をもつ二つの変数の比に対する解析
  • ソウカン オ モツ フタツ ノ ヘンスウ ノ ヒ ニ タイスル カイセキ

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Abstract

Analysis of the ratio of two variables is common in many areas, with an assumption that the two variables are approximately bivariate-normally distributed. In medical science, many investigators prefer to evaluate the effect of treatments by comparing ``pre-treatment" with ``post-treatment", i.e., using the ratio of baseline and post-treatment values or the percent change of post-treatment values from baseline. For example, in clinical trials of patients with osteoporosis, percent changes in bone mineral density are frequently used to measure the efficacy of treatments. Some authors recommend the use of log-transformed ratio to stabilize the variance and induce normality. We numerically evaluate the distribution of ratio and log-transformed ratio and then show that the means of ratio and log-transformed ratio are biased. We perform a simulation study to determine how much such biases affect the size and power of tests used in one-sample and two-sample problems.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 40 (1), 53-71, 2011

    Japanese Society of Applied Statistics

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