Confidence Regions for Multiple Outcomes, Effect Modifiers, and Other Multiple Comparisons

2025-10-08

AI Summary

In epidemiology, standard confidence intervals fail to guarantee joint coverage probability when simultaneously inferring multiple parameters—such as multiple causal effects, effect modification, or dose–response relationships—leading to systematic underestimation of random error uncertainty. To address this, we propose a sup-t-based simultaneous confidence band method for multiparameter inference, which rigorously controls the family-wise error rate while maintaining high statistical power and computational feasibility. The approach is theoretically sound, easily implementable in standard statistical software (SAS, R, Python), and supports intuitive visual interpretation. Evaluated across multiple real-world epidemiological datasets, the framework substantially improves the statistical reliability and reproducibility of multiparameter inference. It provides a robust, transparent, and practical tool for causal inference and exposure–risk modeling.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

In epidemiology, some have argued that multiple comparison corrections are not necessary as there is rarely interest in the universal null hypothesis. From a parameter estimation perspective, epidemiologists may still be interested in multiple parameters. In this context, standard confidence intervals are not guaranteed to provide simultaneous coverage of more than one parameter. In other words, use of confidence intervals in these cases will understate the uncertainty due to random error. To address this challenge, one can use confidence bands, an extension of confidence intervals to parameter vectors. We illustrate the use of confidence bands in three case studies: estimation of multiple causal effects, effect measure modification by a binary variable, and effect measure modification by a continuous variable. Each example uses publicly available data is accompanied by SAS, R, and Python code. The type of confidence region reported by epidemiologists should depend on whether scientific interest is in a single parameter or a set of parameters. For sets of parameters, like in cases where multiple actions or outcomes, effect measure modification, dose-response, or other functions are of interest, sup-t confidence bands are preferred due to their statistical properties, computational simplicity, and ease of presentation.

Problem

• Addressing simultaneous coverage issues for multiple parameters in epidemiology
• Extending confidence intervals to parameter vectors using confidence bands
• Demonstrating confidence bands for multiple outcomes and effect modifiers

Innovation

• Extends confidence intervals to parameter vectors
• Uses sup-t confidence bands for multiple parameters
• Provides code for SAS, R, and Python implementation