Karrison Theodore, Kocherginsky Masha
1 Department of Public Health Sciences, The University of Chicago, Chicago, IL, USA.
2 Department of Preventive Medicine, Northwestern University, Chicago, IL, USA.
Clin Trials. 2018 Apr;15(2):178-188. doi: 10.1177/1740774518759281. Epub 2018 Mar 4.
Restricted mean survival time is a measure of average survival time up to a specified time point. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves.
This article addresses the question of whether covariate adjustment in randomized clinical trials that compare restricted mean survival times improves precision of the estimated treatment effect (difference in restricted mean survival times between treatment arms). Although precision generally increases in linear models when prognostic covariates are added, this is not necessarily the case in non-linear models. For example, in logistic and Cox regression, the standard error of the estimated treatment effect does not decrease when prognostic covariates are added, although the situation is complicated in those settings because the estimand changes as well. Because estimation of restricted mean survival time in the manner described in this article is also based on a model that is non-linear in the covariates, we investigate whether the comparison of restricted mean survival times with adjustment for covariates leads to a reduction in the standard error of the estimated treatment effect relative to the unadjusted estimator or whether covariate adjustment provides no improvement in precision. Chen and Tsiatis suggest that precision will increase if covariates are chosen judiciously. We present results of simulation studies that compare unadjusted versus adjusted comparisons of restricted mean survival time between treatment arms in randomized clinical trials.
We find that for comparison of restricted means in a randomized clinical trial, adjusting for covariates that are associated with survival increases precision and therefore statistical power, relative to the unadjusted estimator. Omitting important covariates results in less precision but estimates remain unbiased.
When comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.
受限平均生存时间是衡量直至特定时间点的平均生存时间的指标。在随机临床试验中，使用受限平均生存时间来比较治疗组的情况越来越受到关注，因为此类比较不依赖于比例风险或关于生存曲线之间关系性质的其他假设。
本文探讨了在比较受限平均生存时间的随机临床试验中进行协变量调整是否能提高估计治疗效果（治疗组之间受限平均生存时间的差异）的精度这一问题。虽然在添加预后协变量时线性模型中的精度通常会提高，但在非线性模型中情况未必如此。例如，在逻辑回归和Cox回归中，添加预后协变量时估计治疗效果的标准误并不会降低，尽管在这些情况下情况较为复杂，因为估计量也会发生变化。由于本文所述方式估计受限平均生存时间也是基于协变量非线性的模型，我们研究在对协变量进行调整的情况下比较受限平均生存时间是否会使估计治疗效果的标准误相对于未调整估计量有所降低，或者协变量调整是否不会提高精度。Chen和Tsiatis认为如果明智地选择协变量，精度将会提高。我们展示了模拟研究的结果，该研究比较了随机临床试验中治疗组之间受限平均生存时间的未调整与调整后的比较。
我们发现，对于随机临床试验中受限均值的比较，相对于未调整估计量，对与生存相关的协变量进行调整可提高精度，从而提高统计功效。遗漏重要协变量会导致精度降低，但估计仍保持无偏性。
在随机临床试验中比较受限均值时，对预后协变量进行调整可提高精度并增加功效。
