Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is typically needed to assess a causal conclusion's sensitivity to unmeasured confounding. Sensitivity analysis frameworks for binary exposures have been well-established for various matching designs and are commonly used in various studies. However, unlike the binary exposure case, there still lacks valid and general sensitivity analysis methods for continuous exposures, except in some special cases such as pair matching. To fill this gap in the binary outcome case, we develop a sensitivity analysis framework for general matching designs with continuous exposures and binary outcomes. First, we use probabilistic lattice theory to show our sensitivity analysis approach is finite-population-exact under Fisher's sharp null. Second, we prove a novel design sensitivity formula as a powerful tool for asymptotically evaluating the performance of our sensitivity analysis approach. Third, to allow effect heterogeneity with binary outcomes, we introduce a framework for conducting asymptotically exact inference and sensitivity analysis on generalized attributable effects with binary outcomes via mixed-integer programming. Fourth, for the continuous outcomes case, we show that conducting an asymptotically exact sensitivity analysis in matched observational studies when both the exposures and outcomes are continuous is generally NP-hard, except in some special cases such as pair matching. As a real data application, we apply our new methods to study the effect of early-life lead exposure on juvenile delinquency. We also develop a publicly available R package for implementation of the methods in this work.

翻译：匹配是观察性研究中调整已知混杂因素最广泛使用的设计之一。然而，未测量的混杂因素可能存在且无法通过匹配消除，因此通常需要进行敏感性分析以评估因果结论对未测量混杂因素的敏感程度。针对二元暴露的敏感性分析框架已在多种匹配设计中建立完善，并广泛应用于各类研究。但与二元暴露情形不同，除配对匹配等特殊情况外，连续暴露领域仍缺乏有效且通用的敏感性分析方法。为填补二元结局情形下的这一空白，我们针对连续暴露与二元结局的一般性匹配设计开发了敏感性分析框架。首先，利用概率格理论证明我们提出的敏感性分析方法在Fisher精确零假设下具有有限总体精确性。其次，推导出新颖的设计敏感性公式，作为渐进评估该敏感性分析方法性能的有效工具。第三，为处理二元结局的效应异质性，引入基于混合整数规划的方法框架，对二元结局的广义归因效应进行渐进精确推断和敏感性分析。第四，针对连续结局情形，证明当暴露与结局均为连续变量时，在匹配观察性研究中开展渐进精确敏感性分析通常属于NP难问题（除配对匹配等特殊情况外）。在真实数据应用中，我们采用新方法研究了早期铅暴露对青少年犯罪的影响，并开发了公开可用的R语言软件包以实现本文提出的方法。