NHMRC Clinical Trials Centre, University of Sydney, Locked bag 77, Camperdown, NSW, 1450, Australia.
BMC Med Res Methodol. 2022 Feb 27;22(1):56. doi: 10.1186/s12874-022-01534-8.
The classical linear model is widely used in the analysis of clinical trials with continuous outcomes. However, required model assumptions are frequently not met, resulting in estimates of treatment effect that can be inefficient and biased. In addition, traditional models assess treatment effect only on the mean response, and not on other aspects of the response, such as the variance. Distributional regression modelling overcomes these limitations. The purpose of this paper is to demonstrate its usefulness for the analysis of clinical trials, and superior performance to that of traditional models.
Distributional regression models are demonstrated, and contrasted with normal linear models, on data from the LIPID randomized controlled trial, which compared the effects of pravastatin with placebo in patients with coronary heart disease. Systolic blood pressure (SBP) and the biomarker midregional pro-adrenomedullin (MR-proADM) were analysed. Treatment effect was estimated in models that used response distributions more appropriate than the normal (Box-Cox-t and Johnson's S for MR-proADM and SBP, respectively), applied censoring below the detection limit of MR-proADM, estimated treatment effect on distributional parameters other than the mean, and included random effects for longitudinal observations. A simulation study was conducted to compare the performance of distributional regression models with normal linear regression, under conditions mimicking the LIPID study. The R package gamlss (Generalized Additive Models for Location, Scale and Shape), which implements maximum likelihood estimation for distributional regression modelling, was used throughout.
In all cases the distributional regression models fit the data well, in contrast to poor fits obtained for traditional models; for MR-proADM a small but significant treatment effect on the mean was detected by the distributional regression model and not the normal model; and for SBP a beneficial treatment effect on the variance was demonstrated. In the simulation study distributional models strongly outperformed normal models when the response variable was non-normal and heterogeneous; and there was no disadvantage introduced by the use of distributional regression modelling when the response satisfied the normal linear model assumptions.
Distributional regression models are a rich framework, largely untapped in the clinical trials world. We have demonstrated a sample of the capabilities of these models for the analysis of trials. If interest lies in accurate estimation of treatment effect on the mean, or other distributional features such as variance, the use of distributional regression modelling will yield superior estimates to traditional normal models, and is strongly recommended.
The LIPID trial was retrospectively registered on ANZCTR on 27/04/2016, registration number ACTRN12616000535471 .
经典线性模型广泛应用于连续结局的临床试验分析。然而，所需的模型假设经常得不到满足，导致治疗效果的估计效率低下且有偏差。此外，传统模型仅评估平均响应的治疗效果，而不评估响应的其他方面，如方差。分布回归模型克服了这些限制。本文旨在展示其在临床试验分析中的有用性，并展示其优于传统模型的性能。
展示了分布回归模型，并与来自 LIPID 随机对照试验的数据进行了对比，该试验比较了普伐他汀与安慰剂在冠心病患者中的效果。分析了收缩压（SBP）和生物标志物中区域前肾上腺髓质素（MR-proADM）。在使用比正态分布更合适的反应分布（分别为 MR-proADM 和 SBP 的 Box-Cox-t 和 Johnson's S）的模型中估计治疗效果，应用截断低于 MR-proADM 的检测限，估计除平均值以外的分布参数的治疗效果，以及包括纵向观察的随机效应。进行了一项模拟研究，以比较分布回归模型与正态线性回归在模拟 LIPID 研究条件下的性能。整个过程都使用了实现分布回归建模最大似然估计的 R 包 gamlss（位置、比例和形状的广义加性模型）。
在所有情况下，分布回归模型都很好地拟合了数据，而传统模型则拟合不佳；对于 MR-proADM，分布回归模型检测到均值上的治疗效果很小但有统计学意义，而传统模型则没有；对于 SBP，证明了治疗效果有益方差。在模拟研究中，当响应变量是非正态且异质时，分布模型的表现明显优于正态模型；并且当响应满足正态线性模型假设时，使用分布回归建模不会带来劣势。
分布回归模型是一个丰富的框架，在临床试验领域尚未得到充分利用。我们已经展示了这些模型用于分析试验的部分能力。如果对治疗效果的平均值或其他分布特征（如方差）的准确估计感兴趣，那么使用分布回归建模将产生优于传统正态模型的估计值，强烈推荐使用。
LIPID 试验于 2016 年 4 月 27 日在 ANZCTR 上进行了回顾性注册，注册号为 ACTRN12616000535471。
