Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators such as the Lasso, or other regularisation approaches. Naϊve use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates grows with sample size, correctly specifying a model for the outcome is non-trivial. In this work, we deal with both of these concerns simultaneously, delivering confidence intervals for conditional treatment effects that are uniformly valid, regardless of whether the outcome model is correct. This is done by incorporating an additional model for the treatment-selection mechanism. When both models are correctly specified, we can weaken the standard conditions on model sparsity. Our procedure extends to multivariate treatment effect parameters and complex longitudinal settings.

中文翻译：

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在潜在错误指定的高维模型中推断治疗效果参数

在观察性研究中消除混淆的影响通常涉及针对协变量调整后的结果拟合模型。通常，当这些协变量是高维的时，这就需要使用稀疏估计量（例如Lasso）或其他正则化方法。单纯使用此类估计器会产生条件治疗效果参数的置信区间，该置信区间不是统一有效的。此外，随着协变量数量随样本数量的增加而增长，正确指定结果模型并不容易。在这项工作中，我们同时处理这两个问题，不管结果模型是否正确，都为统一有效的条件治疗效果提供了置信区间。这是通过合并用于治疗选择机制的其他模型来完成的。正确指定两个模型后，我们可以削弱模型稀疏性的标准条件。我们的程序扩展到多变量治疗效果参数和复杂的纵向设置。