Wang Bingkai, Ogburn Elizabeth L, Rosenblum Michael
Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland.
Biometrics. 2019 Dec;75(4):1391-1400. doi: 10.1111/biom.13062. Epub 2019 Jun 3.
"Covariate adjustment" in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables (called "covariates"). The baseline variables could include, for example, age, sex, disease severity, and biomarkers. According to two surveys of clinical trial reports, there is confusion about the statistical properties of covariate adjustment. We focus on the analysis of covariance (ANCOVA) estimator, which involves fitting a linear model for the outcome given the treatment arm and baseline variables, and trials that use simple randomization with equal probability of assignment to treatment and control. We prove the following new (to the best of our knowledge) robustness property of ANCOVA to arbitrary model misspecification: Not only is the ANCOVA point estimate consistent (as proved by Yang and Tsiatis, 2001) but so is its standard error. This implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified, for example, when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity. We also give a simple, robust formula for the variance reduction (equivalently, sample size reduction) from using ANCOVA. By reanalyzing completed randomized trials for mild cognitive impairment, schizophrenia, and depression, we demonstrate how ANCOVA can achieve variance reductions of 4 to 32%.
在随机试验背景下，“协变量调整”指的是对平均治疗效果的一种估计方法，该方法可针对研究组在基线变量（称为“协变量”）方面的随机失衡进行调整。基线变量可包括例如年龄、性别、疾病严重程度和生物标志物等。根据两项对临床试验报告的调查，对于协变量调整的统计特性存在混淆。我们聚焦于协方差分析（ANCOVA）估计量，它涉及为给定治疗组和基线变量的结果拟合一个线性模型，以及使用简单随机化且治疗组和对照组分配概率相等的试验。我们证明了以下（据我们所知）ANCOVA对于任意模型误设的新稳健特性：不仅ANCOVA点估计是一致的（如Yang和Tsiatis在2001年所证明），其标准误也是如此。这意味着即使线性模型被任意误设，例如当基线变量与结果非线性相关或存在治疗效果异质性时，如同线性模型正确时那样进行的置信区间和假设检验在渐近意义上仍然是有效的。我们还给出了一个使用ANCOVA进行方差缩减（等效于样本量缩减）的简单稳健公式。通过重新分析针对轻度认知障碍、精神分裂症和抑郁症的已完成随机试验，我们展示了ANCOVA如何能够实现4%至32%的方差缩减。
