An Approximate Likelihood Ratio Test for Comparing Several Treatments to a Control
比较多个处理与对照的近似似然比检验AI 解读 ↓
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比较多个处理与对照的近似似然比检验
- 研究问题
- 比较多个处理与共同对照时，如何构造兼顾计算简便和检验功效的统计量，并支持样本量规划及成对比较？
- 方法与思路
- 作者用基于正交关系的简单统计量近似似然比统计量，给出临界值与样本量计算方法，并结合闭合检验进行模拟比较。
- 材料陈述的贡献
- 摘要称，新检验具有接近似然比检验的功效函数，其零假设分布对各组样本量的依赖仅通过总样本量体现。
- 阅读关注点
- 应核对参数模型和备择假设、近似误差及功效最优性的比较范围，并查看不等组样本量和闭合检验的具体实现。
- 阅读边界
- 材料为 OpenAlex 索引摘要，稿件版本未注明；摘要未列出模型条件，关于功效最优性的陈述不能解释为对所有检验普遍最优。
原文摘要
Some parametric tests for comparing several treatments to a control are examined. Those tests developed earlier tend to rest on a single principle: Simplicity or power; those developed later attempt to fill the gap. We propose a new test that represents another such attempt. The basic idea is to find a simple statistic that is a good approximation to the likelihood ratio statistic. This leads to a power function similar to that of the likelihood ratio test, which is optimal among the available competitors. Like the orthogonal contrast test, the new test is built on an orthogonal relationship, resulting in a relatively simple null distribution that depends on the sample sizes only through their total. Thus critical values can be easily computed and a detailed listing results in only a moderately large table. Computing the statistic is elementary when the sample sizes of the new treatments are equal; otherwise, some matrix operations are needed. A simple procedure is given to estimate the sample size required to achieve a given power level. To compete with Dunnett's test in terms of pairwise comparison, the new test (or any of the other tests) can be applied according to the closed testing procedure. In this setting the new test is compared to Dunnett's test by simulation.