Studies intended to estimate the effect of a treatment, like randomized trials, often consist of a biased sample of the desired target population. To correct for this bias, estimates can be transported to the desired target population. Methods for transporting between populations are often premised on a positivity assumption, such that all relevant covariate patterns in one population are also present in the other. However, eligibility criteria, particularly in the case of trials, can result in violations of positivity. To address nonpositivity, a synthesis of statistical and mathematical models can be considered. This approach integrates multiple data sources (e.g. trials, observational, pharmacokinetic studies) to estimate treatment effects, leveraging mathematical models to handle positivity violations. This approach was previously demonstrated for positivity violations by a single binary covariate. Here, we extend the synthesis approach for positivity violations with a continuous covariate. For estimation, two novel augmented inverse probability weighting estimators are proposed. Both estimators are contrasted with other common approaches for addressing nonpositivity. Empirical performance is compared via Monte Carlo simulation. Finally, the competing approaches are illustrated with an example in the context of two-drug versus one-drug antiretroviral therapy on CD4 T cell counts among women with HIV.

翻译：旨在评估治疗效果的研究（如随机试验）常常包含目标人群的偏倚样本。为校正该偏倚，可将估计值外推至目标人群。跨人群外推方法通常基于阳性假设，即一个人群中的所有相关协变量模式在另一个人群中同样存在。然而，尤其是在临床试验中，纳入标准可能导致阳性假设的违反。为应对非阳性问题，可考虑统计模型与数学模型的合成方法。该方法整合多源数据（如试验、观察性研究、药代动力学研究）以估计治疗效果，并借助数学模型处理阳性违反问题。先前研究已证实在单一二元协变量导致的阳性违反中该方法的有效性。本文将此合成方法扩展至连续协变量导致的阳性违反场景。我们提出两种新型增广逆概率加权估计量，并与处理非阳性问题的其他常用方法进行对比。通过蒙特卡洛模拟比较经验性能。最后，以HIV感染者女性中两种药物对比一种药物抗逆转录病毒治疗对CD4 T细胞计数的疗效为例，展示各竞争方法的应用。