[See paper for full abstract] Meta-analysis is a crucial tool for answering scientific questions. It is usually conducted on a relatively small amount of ``trusted'' data -- ideally from randomized, controlled trials -- which allow causal effects to be reliably estimated with minimal assumptions. We show how to answer causal questions much more precisely by making two changes. First, we incorporate untrusted data drawn from large observational databases, related scientific literature and practical experience -- without sacrificing rigor or introducing strong assumptions. Second, we train richer models capable of handling heterogeneous trials, addressing a long-standing challenge in meta-analysis. Our approach is based on conformal prediction, which fundamentally produces rigorous prediction intervals, but doesn't handle indirect observations: in meta-analysis, we observe only noisy effects due to the limited number of participants in each trial. To handle noise, we develop a simple, efficient version of fully-conformal kernel ridge regression, based on a novel condition called idiocentricity. We introduce noise-correcting terms in the residuals and analyze their interaction with a ``variance shaving'' technique. In multiple experiments on healthcare datasets, our algorithms deliver tighter, sounder intervals than traditional ones. This paper charts a new course for meta-analysis and evidence-based medicine, where heterogeneity and untrusted data are embraced for more nuanced and precise predictions.

采用即席预测的元分析方法结合大规模观测数据以及相关的科学文献和实际经验来回答因果问题，通过训练能处理异质试验的更丰富模型，以处理元分析中的噪声效应，该论文开创了元分析和循证医学的新领域，以接纳异质性和不可信数据以实现更细致和精确的预测。

元分析与不可信数据