LLM-Guided Vine Copula Synthesis for Transporting Treatment Effects from Small-Scale Studies under Covariate Shift

Estimating target-population effects from small source studies is challenging because limited or imbalanced treatment arms produce high variance, while covariate shift creates extrapolation error. We propose VinePrior, a structured causal-augmentation framework that combines regular-vine modeling with large-language-model knowledge. To the best of our knowledge, VinePrior is the first framework to introduce LLM-derived semantic priors into pair-copula family selection for causal data augmentation, combining pretrained knowledge with statistical dependence summaries to stabilize selection in small samples. The framework has two complementary components: (i) source-domain augmentation generates covariates, treatment states, and outcomes in causal order and iteratively expands the training data until the effect-estimation confidence interval stabilizes; and (ii) CondVine incorporates observed target values of effect-relevant covariates and conditionally generates the remaining variables, enabling target-aligned augmentation under weaker overlap. We establish an error bound connecting generator error, outcome-learning error, and source–target overlap to target-ATE error. Across benchmark datasets, VinePrior achieves lower ATE error than ten baselines, with particularly strong gains under small samples, high dimensionality, treatment imbalance, and covariate shift.