BACKGROUND Longitudinal randomized controlled trials (RCTs) often aim to test and measure the effect of treatment between arms at a single time point. A two-sample χ2 test is a common statistical approach when outcome data are binary. However, only complete outcomes are used in the analysis. Missing responses are common in longitudinal RCTs and by only analyzing complete data, power may be reduced and estimates could be biased. Generalized linear mixed models (GLMM) with a random intercept can be used to test and estimate the treatment effect, which may increase power and reduce bias. METHODS We simulated longitudinal binary RCT data to compare the performance of a complete case χ2 test to a GLMM in terms of power, type I error, relative bias, and coverage under different missing data mechanisms (missing completely at random and missing at random). We considered how the baseline probability of the event, within subject correlation, and dropout rates under various missing mechanisms impacted each performance measure. RESULTS When outcome data were missing completely at random, both χ2 and GLMM produced unbiased estimates; however, the GLMM returned an absolute power gain up to from 12.0% as compared to the χ2 test. When outcome data were missing at random, the GLMM yielded an absolute power gain up to 42.7% and estimates were unbiased or less biased compared to the χ2 test. CONCLUSIONS Investigators wishing to test for a treatment effect between treatment arms in longitudinal RCTs with binary outcome data in the presence of missing data should use a GLMM to gain power and produce minimally unbiased estimates instead of a complete case χ2 test.

中文翻译：

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在存在缺失数据的情况下，χ2 检验与广义线性混合模型的功效差异 - 一项模拟研究。

背景纵向随机对照试验（RCT）通常旨在测试和测量单个时间点各组间治疗的效果。当结果数据为二元数据时，双样本 χ2 检验是一种常见的统计方法。然而，分析中仅使用完整的结果。缺失响应在纵向随机对照试验中很常见，仅分析完整数据可能会降低功效，并且估计可能会出现偏差。具有随机截距的广义线性混合模型 (GLMM) 可用于测试和估计治疗效果，这可能会提高功效并减少偏差。方法 我们模拟纵向二元 RCT 数据，比较完整案例 χ2 检验与 GLMM 在不同缺失数据机制（完全随机缺失和随机缺失）下的功效、I 类误差、相对偏差和覆盖率方面的性能。我们考虑了事件的基线概率、受试者相关性以及各种缺失机制下的辍学率如何影响每个绩效指标。结果 当结果数据完全随机缺失时，χ2 和 GLMM 都会产生无偏估计；然而，与 χ2 检验相比，GLMM 返回的绝对功率增益高达 12.0%。当结果数据随机缺失时，GLMM 产生高达 42.7% 的绝对功效增益，并且与 χ2 检验相比，估计值是无偏或偏倚较小的。结论 在存在缺失数据的情况下，希望在具有二元结果数据的纵向 RCT 中测试治疗组之间的治疗效果的研究人员应使用 GLMM 来获得功效并产生最小无偏估计，而不是完整的病例 χ2 检验。