When the objective is to administer the best of two treatments to an individual, it is necessary to know his or her individual treatment effects (ITEs) and the correlation between the potential responses (PRs) Y i 1 and Y i 0 under treatments 1 and 0. Data that are generated in a parallel-group design RCT does not allow the ITE to be determined because only two samples from the marginal distributions of these PRs are observed and not the corresponding joint distribution. This is due to the "fundamental problem of causal inference." Here, we present a counterfactual approach for estimating the joint distribution of two normally distributed responses to two treatments. This joint distribution of the PRs Y i 1 and Y i 0 can be estimated by assuming a bivariate normal distribution for the PRs and by using a normally distributed baseline biomarker Z i functionally related to the sum Y i 1 + Y i 0 . Such a functional relationship is plausible since a biomarker Z i and the sum Y i 1 + Y i 0 encode for the same information in an RCT, namely the variation between subjects. The estimation of the joint trivariate distribution is subjected to some constraints. These constraints can be framed in the context of linear regressions with regard to the proportions of variances in the responses explained and with regard to the residual variation. This presents new insights on the presence of treatment-biomarker interactions. We applied our approach to example data on exercise and heart rate and extended the approach to survival data.

中文翻译：

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从平行组 RCT 中的治疗反应和预测性生物标志物估计异质治疗效果的分布：结构模型方法

当目标是对个体进行两种治疗中最好的一种时，有必要了解他或她的个体治疗效果 (ITE) 以及治疗 1 和治疗 1 下潜在反应 (PR) Y i 1 和 Y i 0 之间的相关性。 0. 在平行组设计 RCT 中生成的数据不允许确定 ITE，因为仅观察到来自这些 PR 边缘分布的两个样本，而不是相应的联合分布。这是由于“因果推断的基本问题”所致。在这里，我们提出了一种反事实方法，用于估计对两种治疗的两种正态分布响应的联合分布。PRs Y i 1 和Y i 0 的这种联合分布可以通过假设PRs 的二元正态分布并通过使用与Y i 1 + Y i 0 总和功能相关的正态分布基线生物标志物Z i 来估计。这种函数关系是合理的，因为生物标志物 Z i 和总和 Y i 1 + Y i 0 在 RCT 中编码相同的信息，即受试者之间的变化。联合三变量分布的估计受到一些限制。这些约束可以在线性回归的背景下就所解释的响应中的方差比例和残差变化进行框架化。 188金宝搏官网手机版 188金宝搏官网 。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 这为治疗-生物标志物相互作用的存在提供了新的见解。