Vansteelandt Stijn, VanderWeele Tyler J, Robins James M
Department of Applied Mathematics and Computer Sciences Ghent University, 281 (S9) Krijgslaan, 9000 Ghent, Belgium.
Departments of Biostatistics and Epidemiology Harvard School of Public Health, Boston, MA 02115, U.S.A.
J R Stat Soc Series B Stat Methodol. 2012 Mar;74(2):223-244. doi: 10.1111/j.1467-9868.2011.01011.x.
A sufficient cause interaction between two exposures signals the presence of individuals for whom the outcome would occur only under certain values of the two exposures. When the outcome is dichotomous and all exposures are categorical, then under certain no confounding assumptions, empirical conditions for sufficient cause interactions can be constructed based on the sign of linear contrasts of conditional outcome probabilities between differently exposed subgroups, given confounders. It is argued that logistic regression models are unsatisfactory for evaluating such contrasts, and that Bernoulli regression models with linear link are prone to misspecification. We therefore develop semiparametric tests for sufficient cause interactions under models which postulate probability contrasts in terms of a finite-dimensional parameter, but which are otherwise unspecified. Estimation is often not feasible in these models because it would require nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. We therefore develop 'multiply robust tests' under a union model that assumes at least one of several working submodels holds. In the special case of a randomized experiment or a family-based genetic study in which the joint exposure distribution is known by design or Mendelian inheritance, the procedure leads to asymptotically distribution-free tests of the null hypothesis of no sufficient cause interaction.
两种暴露之间的充分病因相互作用表明，存在这样一些个体，其结局仅在两种暴露的特定取值组合下才会出现。当结局为二分类且所有暴露均为分类变量时，在某些无混杂假设下，可根据给定混杂因素时不同暴露亚组之间条件结局概率的线性对比符号，构建充分病因相互作用的经验条件。有人认为，逻辑回归模型对于评估此类对比并不理想，而具有线性连接函数的伯努利回归模型容易出现模型设定错误。因此，我们在假设概率对比由有限维参数表示、但其他方面未作具体设定的模型下，开发了用于充分病因相互作用的半参数检验。在这些模型中，估计通常不可行，因为这需要对给定高维变量的辅助条件期望进行非参数估计。因此，我们在联合模型下开发了“多重稳健检验”，该联合模型假设几个工作子模型中至少有一个成立。在随机试验或基于家系的基因研究的特殊情况下，联合暴露分布通过设计或孟德尔遗传已知，该程序可得到关于无充分病因相互作用零假设的渐近无分布检验。
