Inference about the ratio of age-standardized rates between two overlapping populations

Area of Science:

• Biostatistics
• Epidemiology
• Public Health

Background:

• Comparing age-standardized rates (ASR) between subpopulations and the general population is crucial for epidemiological studies.
• Existing methods often rely on the proportional age-distribution (PAD) assumption, which may not hold true in real-world scenarios.
• Bias correction is necessary when using sample-based population estimates for ASR calculations.

Purpose of the Study:

• To develop a robust bias-corrected method for estimating the ratio of age-standardized rates (RASR).
• To compare ASR between subpopulations and the whole population without the restrictive PAD assumption.
• To address bias arising from sampling errors in population denominators.

Main Methods:

• Development of a bias-corrected estimator for the ratio of age-standardized rates (RASR).
• Derivation of associated variance estimator and confidence intervals.
• Empirical evaluation of the proposed RASR estimator against existing methods.

Main Results:

• The proposed RASR estimator significantly reduces bias compared to existing methods, especially when the PAD assumption is violated.
• Bias reduction is achieved without a substantial increase in variance.
• The method performs comparably to existing approaches when the PAD assumption is valid.
• The proposed method demonstrates desirable performance with sample-based population estimates and robust variance estimation.

Conclusions:

• The developed bias-corrected RASR method offers a more reliable approach for comparing ASR between subpopulations and the general population.
• This method enhances the applicability of epidemiological studies, particularly in cancer risk factor research.
• The proposed technique provides accurate inference even when population age distributions differ or denominators involve sampling errors.