Bayesian inference on the patient population size given list mismatches

Area of Science:

• Epidemiology
• Biostatistics
• Statistical modeling

Background:

• Estimating disease prevalence in closed populations often relies on multiple patient lists.
• Data errors in these lists, such as mistyping or misinformation, present significant challenges.
• Existing capture-recapture methods, like those proposed by Seber et al. (2000), address some of these issues but can be improved.

Purpose of the Study:

• To evaluate novel Bayesian point and interval estimates for population size (N) in epidemiological studies with imperfect lists.
• To compare the frequentist performance (standard errors, MSE, coverage probability) of these Bayesian methods against established frequentist approaches.
• To apply the proposed Bayesian methods to a real-world dataset of gestational diabetics.

Main Methods:

• Simulation study comparing Bayesian estimates (using improper constant and Jeffreys priors) with Seber et al.'s (2000) methods.
• Analysis of frequentist standard errors, Mean Squared Errors (MSEs), and coverage probabilities.
• Application of the developed Bayesian methods to a real dataset.

Main Results:

• Bayesian point estimates demonstrated smaller frequentist standard errors and MSEs compared to Seber et al.'s estimates.
• Bayesian credible intervals exhibited superior frequentist coverage probabilities.
• Some traditional frequentist confidence intervals showed poor coverage performance.

Conclusions:

• The proposed Bayesian methods offer a more accurate and reliable approach for estimating population size and constructing confidence intervals in epidemiological studies with list errors.
• These methods provide a valuable alternative, particularly when dealing with imperfect data.
• The study highlights the advantages of Bayesian inference in addressing complex statistical challenges in public health research.