By exploiting the theory of skew-symmetric distributions, we generalise existing results in sensitivity analysis by providing the analytic expression of the bias induced by marginalization over an unobserved continuous confounder in a logistic regression model. The expression is approximated and mimics Cochran's formula under some simplifying assumptions. Other link functions and error distributions are also considered. A simulation study is performed to assess its properties. The derivations can also be applied in causal mediation analysis, thereby enlarging the number of circumstances where simple parametric formulations can be used to evaluate causal direct and indirect effects. Standard errors of the causal effect estimators are provided via the first-order Delta method. Simulations show that our proposed estimators perform equally well as others based on numerical methods and that the additional interpretability of the explicit formulas does not compromise their precision. The new estimator has been applied to measure the effect of humidity on upper airways diseases mediated by the presence of common aeroallergens in the air.

翻译：利用偏斜对称分布理论，我们通过提供逻辑回归模型中因未观测连续混杂变量边缘化所导致的偏差解析表达式，推广了敏感性分析的现有结果。该表达式为近似形式，并在某些简化假设下模仿了科克伦公式。同时考虑了其他连接函数和误差分布。通过模拟研究评估其性质。该推导也可应用于因果中介分析，从而扩大了使用简单参数公式评估因果直接和间接效应的情景范围。通过一阶德尔塔方法给出因果效应估计量的标准误。模拟表明，我们提出的估计量与基于数值方法的其他估计量表现同样良好，且显式公式的额外可解释性并未降低其精度。新估计量已应用于测量湿度经由空气中常见气传变应原存在介导的上呼吸道疾病效应。