Generalized estimating equations for longitudinal zero-truncated negative binomial data: analysis of tuberculosis cases in Central Sulawesi

Abstract

This research employs a ZTNB-GEE framework to examine positive annual tuberculosis counts recorded across 13 districts and cities in Central Sulawesi between 2020 and 2024. The data comprise 65 district/city-year observations and six predictors representing population density, inadequate housing, poverty, drinking-water quality, access to adequate sanitation, and public facilities that meet environmental health standards. The deviance and Pearson dispersion ratios were 106.228 and 111.963, respectively, indicating substantial overdispersion. ZTNB-GEE models were fitted using independence, exchangeable, unstructured, and first-order autoregressive working correlations. The corresponding QIC values were 84.47478, 96.29610, 269.64114, and 95.01389, so the independence structure was selected. Under the preferred correlation specification, only and satisfied the 5% significance criterion, with estimated coefficients of 0.00085832 and 0.02060237, respectively. Both coefficient estimates were positive. With the other covariates held fixed, the fitted mean was multiplied by 1.0008587 for every one-person increase in population density and by 1.0208161 for every additional thousand people living below the poverty line. These ratios are equivalent to changes of approximately 0.08587% and 2.08161%, respectively.