Studies intended to estimate the effect of a treatment, like randomized trials, may not be sampled from the desired target population. To correct for this discrepancy, estimates can be transported to the 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 when transporting to external populations. 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：旨在估计治疗效果的研究（如随机试验）可能并非从期望的目标总体中抽样。为纠正这种差异，可将估计值迁移至目标总体。总体间迁移的方法通常基于正性假设，即一个总体中的所有相关协变量模式在另一总体中也存在。然而，当向外部总体迁移时，特别是试验中的入组标准可能导致正性假设的违背。为解决非正性问题，可考虑采用统计模型与数学模型的合成方法。该方法整合多源数据（如试验数据、观察性研究数据、药代动力学研究数据），利用数学模型处理正性假设违背问题以估计治疗效果。先前研究已针对单一二值协变量导致的正性假设违背验证了该方法的有效性。本文将该合成方法扩展至连续协变量导致的正性假设违背场景。在估计方面，提出了两种新颖的增强逆概率加权估计量。这两种估计量均与处理非正性问题的其他常用方法进行了对比。通过蒙特卡洛模拟比较了各方法的实证性能。最后，以HIV感染女性患者中双药与单药抗逆转录病毒疗法对CD4 T细胞计数的影响为例，展示了不同方法的实际应用。