Point and interval estimation of the population size using a zero-truncated negative binomial regression model.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Estimating population size from a single registration file is challenging.
• Existing models like zero-truncated Poisson regression may not adequately handle overdispersed data common in capture-recapture studies.
• Unobserved heterogeneity can lead to data overdispersion, biasing population estimates.

Purpose of the Study:

• To present and evaluate the zero-truncated negative binomial regression model as an alternative for population size estimation.
• To derive Horvitz-Thompson estimators for population size using this new model.
• To compare the performance of the new model against the zero-truncated Poisson model.

Main Methods:

• Development of the zero-truncated negative binomial regression model for single-recapture data.
• Derivation of point and interval estimators for population size based on the model.
• Conducting a simulation study to assess the performance of the proposed estimators.
• Application of the model to estimate the opiate user population in Rotterdam.

Main Results:

• The zero-truncated negative binomial regression model provides a better fit to the Rotterdam opiate user data compared to the zero-truncated Poisson model.
• The new model yielded a substantially higher population size estimate for opiate users.
• Simulation results indicated favorable performance of the derived Horvitz-Thompson estimators.

Conclusions:

• The zero-truncated negative binomial regression model is a valuable tool for population size estimation, particularly when dealing with overdispersed single-recapture data.
• This model can provide more accurate and robust estimates, accounting for unobserved heterogeneity.
• The findings suggest a potentially larger population of opiate users in Rotterdam than previously estimated by Poisson-based models.