Logistic regression for dichotomized counts

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Dichotomizing count data (zero vs. positive) can lead to information loss and reduced statistical efficiency.
• Ordinary logistic regression may be suboptimal when applied to such dichotomized count data, especially with a high prevalence of zero counts.

Purpose of the Study:

• To investigate a shared-parameter hurdle model for more efficient estimation of regression parameters in dichotomized count data.
• To evaluate the asymptotic efficiency of the hurdle model compared to ordinary logistic regression.
• To assess the performance of the hurdle model in terms of statistical power and Type I error rates.

Main Methods:

• A shared-parameter hurdle model was developed, comprising a logistic regression for the dichotomous outcome and an ancillary model for the count process (Poisson or negative binomial).
• Asymptotic efficiency of the hurdle model's logistic component was compared to ordinary logistic regression.
• Monte Carlo simulations were conducted to evaluate power and Type I error under various model specifications.

Main Results:

• The shared-parameter hurdle model demonstrated potential for more efficient estimation of regression parameters compared to ordinary logistic regression.
• Simulation results provided insights into the power and Type I error characteristics of the proposed model.
• The model was successfully applied to analyze dental caries data from a randomized clinical trial.

Conclusions:

• The shared-parameter hurdle model offers an efficient approach for analyzing dichotomized count data with excess zeros.
• This methodology provides a robust framework for estimating covariate effects in such scenarios.
• The application to dental caries data highlights the practical utility of the model in public health research.