Minimal inference from incomplete 2x2-tables

TL;DR

This paper introduces a minimal inference framework for incomplete 2x2 tables, using corroboration to measure evidence without likelihoods, enabling robust interval-based inference when data is missing or incomplete.

Contribution

It develops the concept of corroboration for inference from incomplete tables, providing a likelihood-free approach to handle data incompleteness in 2x2 frequency tables.

Findings

Corroboration identifies the most robust parameter values against refutation.

The approach allows inference without relying on additional assumptions or likelihoods.

Provides a foundation for sharper inference with external beliefs.

Abstract

Estimates based on 2x2 tables of frequencies are widely used in statistical applications. However, in many cases these tables are incomplete in the sense that the data required to compute the frequencies for a subset of the cells defining the table are unavailable. Minimal inference addresses those situations where this incompleteness leads to target parameters for these tables that are interval, rather than point, identifiable. In particular, we develop the concept of corroboration as a measure of the statistical evidence in the observed data that is not based on likelihoods. The corroboration function identifies the parameter values that are the hardest to refute, i.e., those values which, under repeated sampling, remain interval identified. This enables us to develop a general approach to inference from incomplete 2x2 tables when the additional assumptions required to support a likelihood-based approach cannot be sustained based on the data available. This minimal inference approach then provides a foundation for further analysis that aims at making sharper inference supported by plausible external beliefs.