Analysis of Hospitalization-Recovery Duration for DHF Patients at RSUD Haji, East Java Utilizing the Three-Parameter Log-Logistic Regression

Analytical challenges such as skewness and asymmetry often arise with continuous data, especially when values are strictly positive, rendering traditional models like the Normal distribution ineffective. Addressing these issues, this study introduces the Three-Parameter Log-Logistic Regression (LL3R) model, an advancement of the Three-Parameter Log-Logistic Distribution (LL3D). This research aims to apply the LL3R model to estimate parameters and test hypotheses, specifically analyzing hospitalization duration for Dengue Hemorrhagic Fever patients in 2022 at RSUD Haji, East Java Province. The response variable is the duration of hospitalization until recovery, with 10 predictor variables considered. The model's parameters are estimated using Conjugate Gradient (CG) and Berndt-Hall-Hall-Hausman (BHHH) technique for numerical iteration. Hypothesis testing employs the LRT test. Model effectiveness is gauged via the AICc. Results indicate the BHHH method outperforms CG with a lower AICc of 124,082 compared to CG's 3450,22 so that the best LL3R model is given by numerical iteration of BHHH method. Simultaneously, testing rejects the null hypothesis, and individual tests reveal significant effects of seven variables including body temperature, systolic and diastolic blood pressure, pulse frequency, respiratory rate, gender, and age on the duration of hospitalization until recovery of DHF patients at a 5% significance level.