Marginal structural models (MSMs) with inverse probability weighted estimators (IPWEs) are widely used to estimate causal effects of treatment sequences on longitudinal outcomes in the presence of time-varying confounding and dependent censoring. However, IPWEs for MSMs can be inefficient and unstable if weights are estimated by maximum likelihood. To improve the performance of IPWEs, covariate balancing weight (CBW) methods have been proposed and recently extended to MSMs. However, existing CBW methods for MSMs are inflexible for practical use because they often do not handle dependent censoring, nonbinary treatments, and longitudinal outcomes (instead of eventual outcomes at a study end). In this paper, we propose a joint calibration approach to CBW estimation for MSMs that can accommodate (1) both time-varying confounding and dependent censoring, (2) binary and nonbinary treatments, (3) eventual outcomes and longitudinal outcomes. We develop novel calibration restrictions by jointly eliminating covariate associations with both treatment assignment and censoring processes after weighting the observed data sample (i.e., to optimize covariate balance in finite samples). Two different methods are proposed to implement the calibration. Simulations show that IPWEs with calibrated weights perform better than IPWEs with weights from maximum likelihood and the “Covariate Balancing Propensity Score” method. We apply our method to a natural history study of HIV for estimating the effects of highly active antiretroviral therapy on CD4 cell counts over time.

中文翻译：

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边缘结构模型的治疗逆概率和审查权重的联合校准估计

具有逆概率加权估计量 (IPWE) 的边际结构模型 (MSM) 被广泛用于在存在时变混杂和依赖审查的情况下估计治疗序列对纵向结果的因果影响。但是，如果权重是通过最大似然估计的，则 MSM 的 IPWE 可能效率低下且不稳定。为了提高 IPWE 的性能，已经提出了协变量平衡权重 (CBW) 方法，并且最近扩展到了 MSM。然而，现有的 MSM 的 CBW 方法在实际使用中不灵活，因为它们通常不处理依赖审查、非二元处理和纵向结果（而不是研究结束时的最终结果）。在本文中，我们提出了一种联合校准方法来估计 MSM 的 CBW，它可以适应 (1) 时变混杂和依赖审查，(2) 二元和非二元处理，(3) 最终结果和纵向结果。我们通过以下方式开发新的校准限制在对观察到的数据样本进行加权后，联合消除与治疗分配和审查过程的协变量关联（即，优化有限样本中的协变量平衡）。提出了两种不同的方法来实现校准。模拟表明，具有校准权重的 IPWE 比具有最大似然权重和“协变量平衡倾向得分”方法的 IPWE 表现更好。我们将我们的方法应用于 HIV 的自然史研究，以评估高效抗逆转录病毒疗法对 CD4 细胞计数的影响。