The paper entitled “Precision and Power in Randomized Trials for COVID-19 Treatments Using Covariate Adjustment, for Binary, Ordinal, and Time-to-Event Outcomes” is a welcome addition to the literature on covariate adjustment in clinical trials conducted for medical research. The authors’ work has the potential to make a substantial impact on drug development through increased use of an extremely underutilized tool for improving precision in clinical trials, thereby reducing the number of studies that fail due to insufficient power. And the timeliness of this research could not be better, with the number of clinical trials currently being planned or already in the field to combat COVID-19. Both the urgency with which safe and effective treatments are needed in a pandemic and the competition that inherently follows multiple trials launched at the same time, for the same purpose (i.e., finding those safe and effective treatments), result in an unusually high need for accurately sized trials optimized to reach their goals.

The advantages of covariate adjustment in the much simpler linear model context have been known for a while, and the method is popular with clinical trialists for its ability to improve the precision of treatment effect estimates with minimal assumptions. I have written before (LaVange 2014, 2019) of my quandary, after arriving at FDA in 2011, about the lack of a covariate adjustment guidance document, only to find that one had been drafted in the early 2000s but never published. The guidance was apparently shelved because, although noncontroversial for linear models, regulators were concerned that covariate adjustment would be misused in nonlinear models without appropriate guidance for that more complicated setting. As Biostatistics Office Director in the Center for Drug Evaluation and Research, I was able to prioritize an update of this guidance, which was completed soon after I left and issued in 2019 (FDA, 2019).

An examination of the delay in FDA's issuance of a covariate adjustment guidance helps to explain the importance of the Benkeser et al. paper to the drug development enterprise. The International Council on Harmonisation (ICH) published the guideline, E9 Statistical Principles for Clinical Trials (ICH, 1999), calling for the adjustment of covariates, measured before randomization, that were correlated with the primary trial outcomes. Purposes of this adjustment were twofold, to improve precision and adjust for imbalances between treatment groups. The European Medicines Agency (EMA) followed with a Points to Consider document in 2003 and a guidance document in 2015, both providing similar advice on covariate adjustment for trials regulated in the European Union (EU) region. The FDA guidance followed much later—20 years after ICH E9—and the primary reason was the inability to endorse a simple analytical tool like analysis of covariance when the analysis model was nonlinear. As the FDA guidance makes clear, prespecification of any covariate adjustments is required to ensure that the chance of making an erroneous conclusion about drug effects is not increased due to experimenting with different model adjustments after the trial concludes. The guidance also makes clear that even if the analysis model is inaccurate, the advantages of covariate adjustment in the linear model setting still apply, and the resulting treatment effect estimates are valid to support inference about the drug. Such a statement could not be made in the nonlinear setting, or at least not with respect to an approach that was widely accepted in the early 2000s, and that was, in large part, the source of the delay in issuing the guidance.

Noteworthy is the fact that the FDA guidance remains silent on the use of covariate adjustments to correct for imbalances between treatment groups for purposes of producing unbiased estimates of the drug's effects. Any differences between treatment groups are a random occurrence, provided only prerandomization covariates are used for adjustment. Although adjusting for such imbalances has the potential to substantially improve the precision of estimates and the power of hypothesis tests about those estimates, the unadjusted estimates are still valid for the true drug effects. The advantage lies in the improvement of precision (Permutt, 2009). This point is often missed, but importantly, a misunderstanding about the purpose of covariate adjustment has over time led to its use primarily in small clinical trials, where investigators worry that treatment group imbalances can bias the study results. With large clinical trials, covariate adjustments are more often viewed as a nice-to-have but not essential component of the trial design, thinking random imbalances tend to decrease as sample sizes increase. Senn (1989), however, noted for the bivariate normal case, “covariate imbalance is as much of a concern in larges studies as in small ones” due to the fact that, although absolute differences in baseline covariates (absolute imbalance) may decrease as sample sizes increase, standardized differences do not, and standardized differences are the ones impacting precision. Senn goes on to advocate for analysis of covariance with prespecified covariates as best practice for studies of all sizes, regardless of any random imbalances that may be observed in the study.

Around the same time, Gary Koch and colleagues were exploring randomization-based methods of covariate adjustment in both linear and nonlinear model settings, resulting in a series of publications for a variety of endpoints (see, e.g., Tangen and Koch, 1999; Saville and Koch, 2013). These randomization- based methods have a particular advantage in large, confirmatory clinical trials conducted for regulatory approval, where the primary objective relates to hypothesis testing, as minimal assumptions are required for their use. The emphasis by Benkeser et al. on the utility of covariate adjustment in large trials follows this earlier work by Senn and Koch with a consistent message. By expanding the analytical tools available for ordinal outcomes and, in addition, providing performance results of covariate adjusted estimators for binary and time-to-event outcomes, the use of covariate adjustments in large clinical trials, where endpoints are more often of those categories, should see a dramatic increase. In my opinion, this is the major contribution of the paper and one that makes me very excited to see it in publication!

The authors give the results of extensive simulations for a variety of estimands of interest when primary clinical outcomes correspond to the occurrence of, or time to, an event or an ordinal scale. The control arm distributions were based on real-world data from two highly relevant sources, and sizable power gains or relative efficiencies are reported for all estimands examined. Looking across the National Institutes of Health Accelerating Covid-19 Therapeutic Interventions and Vaccines (ACTIV) master protocols launched during this past year, an array of outcomes is specified, including disease severity assessed by seven-point or eight-point ordinal scales, symptom counts, time on ventilation or in the intensive care unit, time to recovery, and mortality. With the authors’ proposed methods, covariate adjustments could be prespecified in planning the analyses of all primary and key secondary endpoints in these trials, thereby increasing the power of tests and improving the precision of estimates to characterize every important dimension of the pandemic's toll.

Enough cannot be said about the advantage of producing valid estimates of drug effects even in the presence of model misspecification. Prespecification of a clinical trials’ statistical analysis plan provides the foundation for FDA's assurance that sponsors are not presenting the most promising set from a range of exploratory results in their regulatory submissions. If model misspecification cannot be determined until after treatment codes are known and preliminary analyses are conducted, then such prespecification is not possible. The authors provide a framework to drug developers for optimizing their planned analyses without requiring post hoc model fitting. With publication of this paper, there really should be no remaining barriers to the use of covariate adjustment when analyzing the endpoints relevant to the health and well-being of patients. In the time of a pandemic, realizing the advantages of covariate adjustment to reduce sample sizes and get answers about promising therapies sooner is invaluable. The authors’ contributions in this regard are to be commended.

这篇题为“使用协变量调整进行随机试验的 COVID-19 治疗的二元、序数和事件时间结果的精确度和功效”的论文是对医学研究临床试验中协变量调整文献的欢迎补充。作者的工作有可能对药物开发产生重大影响，通过增加使用一种极其未充分利用的工具来提高临床试验的精确度，从而减少因能力不足而失败的研究数量。这项研究的及时性再好不过了，目前正在计划或已经在现场进行大量抗击 COVID-19 的临床试验。在大流行中需要安全有效的治疗方法的紧迫性，以及出于同一目的（即寻找那些安全有效的治疗方法）同时启动多项试验所固有的竞争，导致对药物的需求异常高。精确规模的试验经过优化以实现其目标。

协变量调整在更简单的线性模型背景下的优点已经众所周知，并且该方法因其能够以最少的假设提高治疗效果估计的精度而受到临床试验人员的欢迎。我之前曾写过（LaVange 2014、2019 ），讲述了我在2011年到达 FDA 后的困境，关于缺乏协变量调整指导文件，却发现一份在 2000 年代初期就已起草但从未发表。该指南显然被搁置，因为尽管对于线性模型没有争议，但监管机构担心如果没有针对更复杂的设置的适当指南，协变量调整可能会在非线性模型中被滥用。作为药物评价与研究中心生物统计办公室主任，我能够优先更新本指南，该指南在我离开后不久就完成并于 2019 年发布（FDA， 2019 ）。

对 FDA 延迟发布协变量调整指南的检查有助于解释 Benkeser等人的重要性。论文给药品研发企业。国际协调委员会 (ICH) 发布了指南《E9 临床试验统计原则》 （ICH， 1999 ），要求调整随机化前测量的与主要试验结果相关的协变量。这种调整的目的是双重的，即提高精度并调整治疗组之间的不平衡。欧洲药品管理局 (EMA) 随后于 2003 年发布了一份考虑要点文件，并于 2015 年发布了一份指导文件，两者都为欧盟 (EU) 地区监管的试验的协变量调整提供了类似的建议。 FDA 的指南发布得很晚——在 ICH E9 20 年后——主要原因是当分析模型是非线性时，无法认可协方差分析等简单的分析工具。正如 FDA 指南明确指出的那样，需要预先指定任何协变量调整，以确保不会因在试验结束后进行不同的模型调整而进行实验而增加对药物效应做出错误结论的机会。该指南还明确指出，即使分析模型不准确，线性模型设置中协变量调整的优势仍然适用，并且由此产生的治疗效果估计可有效支持有关药物的推论。在非线性环境中无法做出这样的声明，或者至少对于 2000 年代初期被广泛接受的方法来说不能做出这样的声明，而这在很大程度上是延迟发布指南的根源。

值得注意的是，FDA 指南并未提及使用协变量调整来纠正治疗组之间的不平衡，以对药物效果进行公正的估计。只要仅使用随机化前的协变量进行调整，治疗组之间的任何差异都是随机发生的。尽管对这种不平衡进行调整有可能大大提高估计的精确度和对这些估计的假设检验的能力，但未经调整的估计对于真实的药物作用仍然有效。优点在于精度的提高（Permutt，2009）。这一点经常被忽视，但重要的是，随着时间的推移，对协变量调整目的的误解导致其主要用于小型临床试验，研究人员担心治疗组不平衡可能会使研究结果产生偏差。在大型临床试验中，协变量调整通常被视为试验设计的一个不错的组成部分，但不是必不可少的组成部分，认为随着样本量的增加，随机不平衡往往会减少。然而，Senn（ 1989 ）指出，对于双变量正态情况，“协变量不平衡在大型研究中和小型研究中一样受到关注”，因为尽管基线协变量的绝对差异（绝对不平衡）可能会随着样本量增加，标准化差异没有增加，标准化差异会影响精度。 Senn 继续提倡使用预先指定的协变量进行协方差分析，作为各种规模研究的最佳实践，无论研究中可能观察到任何随机不平衡。

大约在同一时间，Gary Koch 及其同事正在线性和非线性模型设置中探索基于随机化的协变量调整方法，从而发表了一系列针对各种终点的出版物（例如，参见 Tangen 和 Koch， 1999 年；Saville 和科赫， 2013 ）。这些基于随机化的方法在为监管批准而进行的大型验证性临床试验中具有特别的优势，其中主要目标与假设检验有关，因为它们的使用需要最少的假设。 Benkeser等人的强调。关于协变量调整在大型试验中的效用，遵循 Senn 和 Koch 的早期工作，传达了一致的信息。通过扩展可用于序数结果的分析工具，此外，提供二元和事件时间结果的协变量调整估计量的性能结果，在大型临床试验中使用协变量调整，其中终点通常属于这些类别，应该会看到急剧的增长。在我看来，这是这篇论文的主要贡献，并且让我非常高兴看到它的发表！

当主要临床结果对应于事件或序数尺度的发生或时间时，作者给出了对各种感兴趣的估计值进行广泛模拟的结果。控制臂分布基于来自两个高度相关来源的真实数据，并且针对所有检查的估计值报告了相当大的功率增益或相对效率。纵观美国国立卫生研究院去年推出的加速 Covid-19 治疗干预措施和疫苗 (ACTIV) 主方案，明确了一系列结果，包括按七点或八点顺序量表评估的疾病严重程度、症状计数、通气时间或在重症监护室的时间、恢复时间和死亡率。利用作者提出的方法，可以在规划这些试验中所有主要和关键次要终点的分析时预先指定协变量调整，从而增加测试的力量并提高估计的精度，以描述大流行造成的每个重要维度的特征。

即使在存在模型错误指定的情况下，也能对药物效果进行有效估计，其优势不言而喻。临床试验统计分析计划的预先规定为 FDA 保证申办者不会在其监管提交中提供一系列探索性结果中最有希望的一组奠定了基础。如果在已知处理代码并进行初步分析之后才能确定模型错误指定，那么这种预先指定是不可能的。作者为药物开发人员提供了一个框架，用于优化他们的计划分析，而无需事后模型拟合。随着本文的发表，在分析与患者健康和福祉相关的终点时，使用协变量调整确实应该不存在任何障碍。在大流行期间，认识到协变量调整的优势以减少样本量并更快地获得有希望的治疗方法的答案是非常宝贵的。作者在这方面的贡献值得赞扬。