Inverse probability weighting for causal inference in hierarchical data.

Objective: The aim of this study was to explore the impact of model misspecification, balance, and extreme weights on average treatment effect (ATE) estimation in hierarchical data with unmeasured cluster-level confounders using the multilevel propensity score model and inverse probability weight (IPW).

Methods: We simulated 48 hierarchical data scenarios with unmeasured cluster-level confounders, fitting nine ATE estimation strategies. These strategies were combined with IPW, which used both marginal stabilized weights and cluster-mean stabilized weights. Extreme weights were handled by truncation. Moreover, these models were applied to data from patients co-infected with Human Immunodeficiency Virus (HIV) and Tuberculosis (TB) in Liangshan Prefecture, Sichuan, China, to estimate the ATE of TB treatment delay on treatment outcomes.

Results: The simulation study revealed that FEM-Marginal tended to generate the most extreme weights, whereas BART-FE-Marginal considerably reduced the extreme weights in a large number of small clusters. When the data satisfied the positivity assumption, the marginal stabilized weight strategy had the largest absolute percentage bias and RMSE, whereas the cluster-mean stabilized weight strategy had the smallest. Case studies applying different ATE strategies have shown that among HIV-TB co-infected patients, TB treatment delay was a risk factor for treatment outcome.

Conclusions: To better control unmeasured cluster-level confounders, it was more important to consider cluster characteristics when estimating ATE. The use of Bayesian additive regression trees (BART) for constructing multilevel propensity score models, or of cluster-mean stabilized weights is recommended. However, if marginal stabilized weights are used, extreme weight handling methods are necessary to improve effect estimation. In hierarchical data with unmeasured cluster-level confounders, reducing extreme weights, weight variability, and model misspecification while enhancing balance effectively minimizes estimation bias. The case study revealed that TB treatment delay remained associated with treatment outcomes even after accounting for unmeasured cluster-level confounders.