BAYESIAN ESTIMATION OF THE SCALE PARAMETER OF THE WEIBULL DISTRIBUTION USING THE LINEX AND ITS APPLICATION TO STROKE PATIENT DATA

Abstrak

Survival analysis is used to study the timing of an event, such as recovery or death, in the context of medical data. One of the diseases that many people suffer from is stroke. Based on the survey results, the number of stroke sufferers in Indonesia reached 8.3% of 1000 people in Indonesia continues to increase every year, especially among the elderly. The research conducted aims to model the estimation of the type III censored Weibull distribution parameters with the Bayesian Linear Exponential Loss Function (LINEX) method. This study uses secondary data on stroke patients in the period January-November 2024 with a sample of 62 patients at the Haji Surabaya Regional General Hospital. Weibull distribution model with Bayesian approach using Linear Exponential Loss Function (LINEX) was applied to estimate the distribution parameters and survival function. The estimation results show that the parameter α is 6.32342 with an average hospitalization time of 5.9151646 days. MSE value is 0.000270555, which indicates that the estimation model is more accurate in predicting data for the length of hospitalization for stroke patients at the Haji Surabaya Regional General Hospital. The probability value of the survival function of stroke patients who have been hospitalized on the 5th day shows a probability of 82.4% so that no further hospitalization is needed, which indicates that the patient's health condition is improving. In addition, the hazard function analysis shows that the longer a patient is hospitalized, the greater the risk of the patient not recovering.