Re-interpreting conventional interval estimates taking into account bias and extra-variation

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Randomized clinical trials offer the least bias for causal inference but are often infeasible in epidemiology.
• Epidemiologic studies face challenges in properly modeling bias and accounting for random and systematic variation.
• Confidence interval exclusion of a target parameter value may indicate incompatibility due to bias or extra-variation.

Purpose of the Study:

• To propose a method for re-interpreting conventional statistical results, particularly confidence intervals.
• To provide a framework for assessing the impact of bias and extra-variation on the compatibility of focal values with study data.
• To stimulate further research into bias-adjusted results and the re-interpretation of confidence intervals.

Main Methods:

• Calculate the difference between a specified focal value and the nearest confidence interval boundary.
• Determine the maximum bias and extra-variation correction that would still render the focal value incompatible with the data.
• Illustrate the approach with a meta-analysis example on newborn resuscitation treatments.

Main Results:

• The proposed method quantifies the maximum allowable bias and extra-variation for a focal value to remain statistically incompatible with the data.
• Provides guidelines for assessing the probability that the required correction for bias and extra-variation exceeds this maximum.
• Demonstrates application in a meta-analysis, highlighting the need for bias consideration.

Conclusions:

• The approach offers a novel way to reinterpret confidence intervals but requires further development into a formal method.
• Encourages more comprehensive studies on the effects of various biases on statistical results.
• Aims to improve the understanding and reporting of bias-adjusted findings in scientific literature.