When assessing the causal effect of an exposure on two or more outcomes in an observational study, a linear combination of outcomes may lessen the sensitivity of a test of the global null hypothesis to potential unmeasured biases. While all linear combinations of scored outcomes can be considered using Scheffe projections or constrained variants thereof, finding the combination that minimizes sensitivity to unmeasured biases requires corrections for multiple testing, which can erode power, especially when many outcomes are of interest. To mitigate this issue, we propose splitting the sample into a planning sample to identify an optimal linear combination and an analysis sample to conduct inference. We provide a novel characterization of the set of linear combinations for which this approach is guaranteed to achieve the same asymptotic power as full-sample alternatives and conduct extensive simulation studies that demonstrate enhanced power in finite samples. Finally, we apply our method to investigate the effects of poverty on the emergence of cardiovascular disease risk factors in children and adolescents. We discover adverse consequences on outcomes related to body composition, physical activity, and tobacco exposure. Although the impact of poverty on elevated tobacco exposure shows some robustness to unmeasured confounding, the other findings remain sensitive to potential biases.

翻译：在观察性研究中评估暴露对两个或以上结局的因果效应时，结局的线性组合可能降低全局零假设检验对潜在未测量偏倚的敏感性。尽管使用Scheffe投影或其约束变体可考虑所有评分结局的线性组合，但寻找最小化未测量偏倚敏感性的组合需进行多重检验校正，这会导致统计功效下降——尤其当关注结局数量较多时。为缓解该问题，本文提出将样本拆分为规划样本（用于识别最优线性组合）与分析样本（用于进行推断）。我们首次刻画了能保证该方法达到与全样本替代方案相同渐近功效的线性组合集，并通过大规模模拟研究证明其在有限样本中具有增强的功效。最后，我们将该方法应用于探究贫困对儿童青少年心血管疾病风险因素涌现的影响，发现与身体成分、体力活动和烟草暴露相关的结局呈现不利后果。尽管贫困对烟草暴露升高的影响对未测量混杂因素表现出一定稳健性，其他发现仍对潜在偏倚敏感。