## 1 Introduction  
Patients ventilated for a prolonged period often consume a high amount of intensive care unit (ICU) resources [1]. It is estimated that the number of ICU patients needing prolonged mechanical ventilation ranges from 3% to 10%, with these patients utilizing 37-40% of ICU resources [2]. Taiwan's National Health Insurance Administration proposed a four-step Integrated Delivery System (IDS) for the care of ICU patients who receive ventilator treatment for longer than 21 days and require lengthy mechanical ventilation. Under this system, patients are transferred from ICUs to respiratory care centers (RCCs). Patients may also be transferred to an Respiratory Care Ward (RCW) if they stay at an RCC for more than 42 days. Respiratory care wards are chronic care units designed for patients with prolonged respiratory failure [3, 4]. Due to limited medical resources and the rising cost of health care, disease prognosis has become a very important issue for health sciences. The Acute Physiology and Chronic Health Evaluation II (APACHE II) score is a severity-of-illness score that is taken at the time of admission of the patient to the ICU, showing the worst figures during the patient's first 24 h of ICU stay [5]. It has been found that there is a significant association between APACHE II scores and risk of mortality (ROM), i.e., the higher the APACHE II score, the higher the ROM [6]. Clarification of the relationship between APACHE II scores and the medical outcomes of RCC patients can assist in designing more effective medical protocols. The mechanism by which obesity increases the ROM for ICU patients is unclear. [PERSON] et al. [7], for instance, reported that obesity (body mass index (BMI) \(\geq\) 30 kg/m\({}^{2}\)) was not related to crude ICU mortality when compared with patients with a BMI lower than 30 kg/m\({}^{2}\). Conversely, [PERSON] et al. [8] found lesser mortality for obese patients compared with those with normal weight, but [PERSON] et al. [9] stated that obesity is not associated with increased risk for ICU mortality. [PERSON] et al. [10] demonstrated that lower BMI was linked with higher ROM, whereas overweight and obesity were associated with lower mortality. Additionally, the relationship between BMI and patients in the RCC patients weaning rates is much understudied. Well-timed access to appropriate care is imperative for critically ill patients. It has, for example, been found that transported patients have a significantly longer ICU stay and greater estimated ROM compared to non-transported patients [11]. The early transfer of patients has also been found to mitigate the risk of adverse impacts on medical outcomes [12]. The transported source of patients may influence the delivery process when referred to the ICU and thus determine the medical outcome. An exploration of the sociodemographic factors and successful weaning rates' relationship has shown that gender does not affect weaning rates in the Taiwanese context [4]. [PERSON] et al. [13] showed that the successful weaning rates decrease with patients' age. However, other studies have reported that weaning rates have no relationship with age [14]. The critical issues that affect RCC patients' weaning rates have been shown to be the related causes of respiratory failure as well as confounding diseases such as pulmonary disease, cardiovascular disease, cancer, and renal failure [3]. Data mining algorithms have been developed to collect clinical data to aid in the diagnosis of diseases, such as coronary heart disease, Type 2 diabetes, and Parkinson's disease [15; 16; 17]. This is a new scientific area that integrates research from the fields of statistics, machine learning, and computer science (particularly database management). These algorithms facilitate the early detection of diseases, more precise medical treatment, and better use of social medical resources.