Abstract

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally precludes the nonparametric identification of causal effects. Nonparametric bounds can provide a way to narrow the range of possible values for a nonidentifiable causal effect without making additional untestable assumptions. The nonparametric bounds literature has almost exclusively focused on settings with random sampling, and the bounds have often been derived with a particular linear programming method. We derive novel bounds for the causal risk difference, often referred to as the average treatment effect, in six settings with outcome-dependent sampling and unmeasured confounding for a binary outcome and exposure. Our derivations of the bounds illustrate two approaches that may be applicable in other settings where the bounding problem cannot be directly stated as a system of linear constraints. We illustrate our derived bounds in a real data example involving the effect of vitamin D concentration on mortality. Supplementary materials for this article are available online.

摘要

结果相关抽样设计在许多不同的科学领域都很常见，包括流行病学、生态学和经济学。与所有观察性研究一样，此类设计通常会受到无法测量的混杂因素的影响，这通常会排除因果效应的非参数识别。非参数界限可以提供一种方法来缩小不可识别的因果效应的可能值范围，而无需做出额外的不可检验的假设。非参数界限文献几乎只关注随机抽样的设置，并且界限通常是通过特定的线性规划方法得出的。我们得出因果风险差异的新界限，通常称为平均治疗效果，在六种环境中，结果依赖抽样和二元结果和暴露的未测量混杂。我们对边界的推导说明了两种可能适用于其他环境的方法，在这些环境中，边界问题不能直接描述为线性约束系统。我们在一个涉及维生素 D 浓度对死亡率影响的真实数据示例中说明了我们得出的界限。本文的补充材料可在线获取。