Integrating multiple observational datasets from disparate sources remains fundamentally challenging when validation data are absent. These pooled datasets typically contain incomplete records with substantial missingness, necessitating careful handling to ensure valid causal inference. For estimating average treatment effect (ATE) from such incomplete data, conventional approaches employ a two-step procedure: multiple imputation precedes propensity score estimation. However, a critical methodological limitation is that the imputation often operates independently of causal assumptions, potentially compromising subsequent ATE estimation. Without validation data, the accuracy of imputed values becomes inherently uncertain, resulting in diminished statistical efficiency. Standard imputation methods may inadvertently undermine the very causal structures they aim to preserve, representing a fundamental gap in practice. We propose a one-step framework for estimating the ATE that simultaneously imputes missing data and estimates causal effects by incorporating the propensity score directly into the multiple imputation process. Missing values are thus imputed in alignment with causal inference assumptions required for observational studies. Unlike two-step methods that estimate propensity scores separately for each imputed dataset, our approach updates them iteratively: completed data inform propensity score estimation, which then guides the subsequent imputation cycle. Within this iterative architecture, internal consistency is structurally guaranteed; consequently, the computational burden of second-stage estimation is removed, optimizing statistical power in pooled analyses. Across varied missingness patterns and sample sizes, the proposed method demonstrates superior performance. Its estimates are unbiased, with lower variance and reduced root mean square error relative to conventional two-step procedures. Applied to childhood anemia data from Sierra Leone Demographic and Health Surveys (2008, 2013, 2019), the framework yields efficient causal estimates both individually and when datasets are combined. A consistent finding shows that improved maternal education causally reduces anemia risk among children under five years. By integrating propensity scores into imputation processes, the proposed framework addresses a longstanding gap in causal inference under multiple incomplete observational datasets, without requiring validation data. When applied to Sierra Leone survey, robust evidence of maternal education’s protective effect against childhood anemia is provided. The framework’s implementation requires only standard multiple imputation software, representing a practical advantage for survey analysts conducting causal inference with incomplete data.
Woldemariam et al. (Fri,) studied this question.