应用于随机对照试验中出现的有序尺度数据的协方差分析的稳健性和功效。

Robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials.

作者信息

Sullivan L M, D'Agostino R B

机构信息

Boston University School of Public Health, Department of Biostatistics, 715 Albany Street, Boston, MA 02115, USA.

出版信息

Stat Med. 2003 Apr 30;22(8):1317-34. doi: 10.1002/sim.1433.

Abstract

In clinical trials comparing two treatments, ordinal scales of three, four or five points are often used to assess severity, both prior to and after treatment. Analysis of covariance is an attractive technique, however, the data clearly violate the normality assumption and in the presence of small samples, and large sample theory may not apply. The robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation. Subjects are randomized to one of two competing treatments and the pre-treatment, or baseline, assessment is used as the covariate. We compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t-test on difference scores. Under the null hypothesis of no difference in adjusted treatment means, we estimated actual significance levels by comparing observed test statistics to appropriate critical values from the F- and t-distributions for nominal significance levels of 0.10, 0.05, 0.02 and 0.01. We estimated power by similar comparisons under various alternative hypotheses. The model which assumes homogeneous slopes and the t-test on difference scores were robust in the presence of three, four and five point ordinal scales. The hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non-homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small. The model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated. The t-test on difference scores also produced good power in the presence of small samples.

摘要

在比较两种治疗方法的临床试验中,常使用三分、四分或五分的有序量表在治疗前后评估严重程度。协方差分析是一种有吸引力的技术,然而,数据明显违反了正态性假设,并且在样本量较小的情况下,大样本理论可能不适用。通过计算机模拟研究了应用于有序量表数据小样本的各种参数协方差分析版本的稳健性和功效。受试者被随机分配到两种相互竞争的治疗方法之一,治疗前或基线评估用作协变量。我们比较了两种参数协方差分析检验,它们根据回归斜率的同质性处理而有所不同,以及对差异分数的两独立样本t检验。在调整后的治疗均值无差异的原假设下,我们通过将观察到的检验统计量与F分布和t分布的适当临界值进行比较,来估计名义显著性水平为0.10、0.05、0.02和0.01时的实际显著性水平。我们在各种备择假设下通过类似比较估计功效。假设斜率同质的模型和对差异分数的t检验在三分、四分和五分有序量表的情况下是稳健的。首先检验回归斜率同质性,然后在存在显著非同质性时拟合单独斜率的分层方法产生的显著性水平超过了名义水平,尤其是在样本量较小时。在所有研究的配置中,假设回归斜率同质的模型在竞争检验中产生的功效最高。对差异分数的t检验在样本量较小时也产生了良好的功效。

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