Treatment effect estimates are often available from randomized controlled trials as a single average treatment effect for a certain patient population. Estimates of the conditional average treatment effect (CATE) are more useful for individualized treatment decision making, but randomized trials are often too small to estimate the CATE. Examples in medical literature make use of the relative treatment effect (e.g. an odds-ratio) reported by randomized trials to estimate the CATE using large observational datasets. One approach to estimating these CATE models is by using the relative treatment effect as an offset, while estimating the covariate-specific untreated risk. We observe that the odds-ratios reported in randomized controlled trials are not the odds-ratios that are needed in offset models because trials often report the marginal odds-ratio. We introduce a constraint or regularizer to better use marginal odds-ratios from randomized controlled trials and find that under the standard observational causal inference assumptions this approach provides a consistent estimate of the CATE. Next, we show that the offset approach is not valid for CATE estimation in the presence of unobserved confounding. We study if the offset assumption and the marginal constraint lead to better approximations of the CATE relative to the alternative of using the average treatment effect estimate from the randomized trial. We empirically show that when the underlying CATE has sufficient variation, the constraint and offset approaches lead to closer approximations to the CATE.

翻译：处理效应估计通常来源于随机对照试验，以针对特定患者群体的单一平均处理效应形式呈现。条件平均处理效应（CATE）的估计对个体化治疗决策更有价值，但随机试验往往规模过小，难以估算CATE。医学文献中的实例利用随机试验报告的相对处理效应（如比值比），结合大型观察性数据集来估计CATE。一种估计此类CATE模型的方法是将相对处理效应作为偏移量，同时估计协变量特定的未治疗风险。我们观察到，随机对照试验中报告的比值比并非偏移模型中所需的比值比，因为试验通常报告的是边际比值比。我们引入一种约束或正则化项，以更好地利用随机对照试验中的边际比值比，并发现：在标准观察性因果推断假设下，该方法能够提供CATE的一致估计。接下来，我们证明：在存在未观测混杂因素的情况下，偏移方法对CATE估计无效。我们研究了偏移假设与边际约束是否比使用随机试验的平均处理效应估计值更能逼近CATE。实验表明，当潜在CATE具有足够变异时，约束与偏移方法能对CATE实现更精确的近似。