Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference
Organizations: Bonn Center for Mathematical Life Sciences, University of Bonn, Bonn, Germany · Life & Medical Sciences Institute, University of Bonn, Bonn, Germany · Epidemiology and Modeling of Antibiotic Evasion Unit, Institut Pasteur, Paris, France · Université de Versailles Saint-Quentin-en-Yvelines, Université Paris Saclay, Inserm U1018, Team Infectious Diseases, Interactions and Antimicrobial Resistance, Paris, France · Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany · Freiburg Center for Data Analysis, Modeling and AI, University of Freiburg, Freiburg, Germany · Institute of Infectious Diseases and Tropical Medicine, LMU University Hospital, Munich, Germany · German Center for Infection Research, Partner Site Munich, Munich, Germany · Fraunhofer Institute ITMP, Immunology, Infection and Pandemic Research, Munich, Germany · Max von Pettenkofer Institute, LMU Munich, Munich, Germany · Unit Global Health, Helmholtz Zentrum München, German Research Center for Environmental Health (HMGU), Neuherberg, Germany · Centre de Référence Maladies Rares, Mucoviscidose et Maladies Apparentées, Site Constitutif Pédiatrique, Hôpital Necker Enfants Malades, Paris, France · Université de Paris, CNRS, INSERM, Institut Necker-Enfants Malades, Paris, France · European Rare Disease Network–Lung, Frankfurt, Germany · Institute of General Practice/Family Medicine, Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany
Abstract
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in epidemiological or survey settings, individuals with certain outcomes may be more likely to be included, resulting in biased prevalence estimates with potentially substantial downstream impact. Classical corrections, such as inverse-probability weighting or explicit likelihood-based models of the selection process, rely on tractable likelihoods, which limits their applicability in complex stochastic models with latent dynamics or high-dimensional structure. Simulation-based inference enables Bayesian analysis without tractable likelihoods but typically assumes missingness at random and thus fails when selection depends on unobserved outcomes or covariates. Here, we develop a bias-aware simulation-based inference framework that explicitly incorporates selection into neural posterior estimation. By embedding the selection mechanism directly into the generative simulator, the approach enables amortized Bayesian inference without requiring tractable likelihoods. This recasting of selection bias as part of the simulation process allows us to both obtain debiased estimates and explicitly test for the presence of bias. The framework integrates diagnostics to detect discrepancies between simulated and observed data and to assess posterior calibration. The method recovers well-calibrated posterior distributions across three statistical applications with diverse selection mechanisms, including settings in which likelihood-based approaches yield biased estimates. These results recast the correction of selection bias as a simulation problem and establish simulation-based inference as a practical and testable strategy for parameter estimation under selection bias.