Binary Regression Analysis Using Three Link Function in Modeling Pulmonary Tuberculosis

Abstract

Pulmonary tuberculosis (PTB) remains a substantial public health challenge, particularly in sub-Saharan Africa. Understanding demographic patterns in PTB occurrence and selecting appropriate statistical models can inform epidemiological analysis and intervention planning. This study examined associations between selected demographic and temporal characteristics and PTB status, comparing binary regression models with logit, probit, and complementary log-log link functions. A retrospective analysis was conducted using secondary data comprising 4,167 patient records from Haruna Tsokwa General Hospital, Takum, Nigeria. PTB status was specified as the binary response variable, while age, sex, and year of diagnosis were included as explanatory variables. Model parameters were estimated using maximum likelihood. Goodness-of-fit was assessed using deviance, Pearson chi-square, and Hosmer–Lemeshow tests, while model selection was informed by the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Age and sex were statistically significant predictors across all three models, with male sex and older age associated with a higher modeled probability of PTB. The consistency of these findings across link functions supports the relevance of these demographic characteristics within the analyzed dataset. The logit model produced the lowest AIC and BIC values and was therefore preferred among the three candidate models. This preference concerns relative model fit within the study context and does not establish predictive performance in other populations. The findings provide hospital-based evidence that may inform the planning of targeted tuberculosis interventions and demonstrate the value of comparing alternative link functions when analyzing binary health outcomes. Further research should evaluate the preferred model using independent datasets and examine additional clinical and contextual variables. The study concludes that logit regression offers the most suitable specification among the models assessed for these hospital records.