Exponential vs Log-Normal AFT Models for Predicting Hospital Length of Stay in Hepatitis B Patients

Hospital length of stay (LOS) is a key indicator of healthcare efficiency and resource utilization, particularly for chronic infectious diseases such as hepatitis B virus (HBV) infection.  Prolonged hospitalization increases costs and strains limited hospital capacity in low-resource settings.  Accurate statistical modelling of LOS is therefore essential for planning bed utilization and improving patient management.  This study compares Exponential and Log-Normal accelerated failure time (AFT) survival regression models for predicting LOS among patients living with HBV in Maiduguri, Nigeria.  A retrospective cohort of 60 HBV admissions at a tertiary hospital in Maiduguri was analyzed.  LOS (days) was defined as the time from admission to discharge, with deaths and transfers treated as non-discharge outcomes in sensitivity analyses.  Covariates included age, gender, marital status, diagnostic method, disease stage, comorbidity, antiviral treatment, and admission type.  Exponential and Log-Normal AFT models were fitted and compared using log-likelihood, Akaike and Bayesian information criteria (AIC, BIC), likelihood ratio tests, graphical diagnostics (Q–Q and residual plots), and prediction accuracy metrics (mean absolute error (MAE) and root mean squared error (RMSE)).  Of the 60 patients, 38 were discharged alive, 6 died, and 16 were transferred.  LOS was positively skewed.  The Log-Normal AFT model outperformed the Exponential model with higher log-likelihood (−139.56 vs −194.48), lower AIC (161.87 vs 402.97) and BIC (178.62 vs 417.63), and substantially improved prediction accuracy (MAE = 3.66 vs 12.97 days; RMSE = 8.50 vs 28.20 days).  In the Log-Normal model, age significantly prolonged LOS (TR ≈ 1.06 per year), implying about a 5–6% increase in expected stay per additional year of age.  Antiviral treatment markedly reduced hospitalization time (TR ≈ 0.55), resulting in a roughly 45% shorter LOS.  Gender, disease stage, and comorbidity also showed significant associations with LOS.  Diagnostic plots indicated better conformity to Log-Normal assumptions than to the Exponential specification.  The log-normal AFT model offers better fit, prediction, and interpretability than the exponential model for HBV-related LOS.  Effects on time ratios may be translated to indicate that timely use of antiviral therapy may save 4–5 bed-days per patient, whereas older age alone significantly increases demand for bed types.  These results justify the application of Log-Normal AFT models to predict LOS and hospital resource planning in resource-constrained environments.