Coarse Structural Nested Mean Models (SNMMs, Robins (2000)) and G-estimation can be used to estimate the causal effect of a time-varying treatment from longitudinal observational studies. However, they rely on an untestable assumption of no unmeasured confounding. In the presence of unmeasured confounders, the unobserved potential outcomes are not missing at random, and standard G-estimation leads to biased effect estimates. To remedy this, we investigate the sensitivity of G-estimators of coarse SNMMs to unmeasured confounding, assuming a nonidentifiable bias function which quantifies the impact of unmeasured confounding on the average potential outcome. We present adjusted G-estimators of coarse SNMM parameters and prove their consistency, under the bias modeling for unmeasured confounding. We apply this to a sensitivity analysis for the effect of the ART initiation time on the mean CD4 count at year 2 after infection in HIV-positive patients, based on the prospective Acute and Early Disease Research Program.

中文翻译：

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粗结构嵌套平均模型中未测量混杂的敏感性分析

粗结构嵌套平均模型 (SNMMs, Robins (2000)) 和 G 估计可用于估计纵向观察研究中随时间变化的处理的因果效应。然而，他们依赖于一个不可测试的假设，即没有不可测量的混杂因素。在存在未测量的混杂因素的情况下，未观察到的潜在结果不会随机丢失，并且标准 G 估计会导致效应估计有偏差。为了解决这个问题，我们研究了粗 SNMM 的 G 估计量对未测量混杂的敏感性，假设有一个不可识别的偏差函数，它量化了未测量混杂对平均潜在结果的影响。我们提出了粗 SNMM 参数的调整 G 估计量，并在未测量混杂的偏差建模下证明了它们的一致性。