“…To control for selection bias with regard to baseline characteristics of patients between groups, we performed generalized propensity score analysis to estimate the dose-response function for each year. The propensity score method has been widely used in observational studies to deal with possible biases [21,22]. We used a multinomial logistic regression model with logit as the link function to obtain generalized propensity scores using the data of patient characteristics, such as type of hemorrhagic peptic ulcer, age, sex, chronic comorbid conditions, use of ambulance transportation and intensive care units, and other treatments of peptic ulcer.…”