Estimating exposure-specific disease rates from case-control studies using Bayes' theorem

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Case-control studies are crucial for investigating disease etiology.
• Different subject selection methods can influence the interpretation of exposure-odds ratios.

Purpose of the Study:

• To differentiate three types of case-control studies based on subject selection.
• To clarify the relationship between exposure-odds ratios and rate ratios in each study type.
• To present methods for calculating exposure-specific rates without the rare disease assumption.

Main Methods:

• Categorization of case-control studies into three types based on case and non-case selection.
• Analysis of the mathematical equivalence between exposure-odds ratios and rate ratios under different study designs.
• Application of Bayes' theorem for rate estimation.

Main Results:

• Study type 1 (incident cases vs. representative non-cases) yields an exposure-odds ratio equivalent to the incidence density ratio without a rare disease assumption.
• Study types 2 and 3 (incident cases vs. residual non-cases; prevalent cases vs. non-cases) yield exposure-odds ratios equivalent to cumulative incidence-odds ratios and prevalence odds ratios, respectively.
• Exposure-specific rates can be estimated using Bayes' theorem, even without the rare disease assumption, when the overall disease rate is known.

Conclusions:

• The choice of case-control study design significantly impacts the interpretation of exposure-odds ratios.
• Accurate estimation of disease rates is achievable across different study designs, mitigating the need for the rare disease assumption.
• Methods are provided for calculating approximate confidence limits for exposure-specific rates.