Analysis of covariance with pre-treatment measurements in randomized trials under the cases that covariances and post-treatment variances differ between groups

Takashi Funatogawa, Ikuko Funatogawa, Yu Shyr

研究成果: Article同行評審

4 引文 斯高帕斯(Scopus)

摘要

When primary endpoints of randomized trials are continuous variables, the analysis of covariance (ANCOVA) with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation.

原文English
頁(從 - 到)512-524
頁數13
期刊Biometrical Journal
53
發行號3
DOIs
出版狀態Published - 2011 五月

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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