Health satisfaction is a critical indicator for measuring individual health levels and health-related quality of life (HRQoL) and assessing the impact of national healthcare policies. Health satisfaction is considered a major predictor of HRQoL [1]. HRQoL is generally understood as the level of satisfaction individuals feel in multiple dimensions, including health, social connections, personal fulfilment, and environmental conditions [2]. In recent years, an increasing amount of research has focused on the concept of subjective well-being (SWB) in decision-making, where health is one of the most influential factors in SWB [3]. The measurement of health satisfaction has also been widely used to assess SWB [4], [5]. This highlights the importance of understanding and addressing health satisfaction to improve HRQoL and overall well-being.

Improving the health satisfaction of middle-aged and elderly adults in China is of great significance for alleviating their severe disease burden and improving their HRQoL. China, the country with the largest elderly population in the world, is facing a serious issue of population ageing, with the proportion of middle-aged and elderly adults continuously rising [6]. According to the "2023 National Ageing Development Bulletin" released by the National Health Commission of China, by the end of 2023, the population aged 60 and above reached 296.97 million, accounting for 21.1 % of the total population. Additionally, the elderly population aged 65 and above was 216.76 million, representing 15.4 % of the total population. Concurrently, 81.1 % of elderly citizens suffer from chronic non-communicable diseases (NCDs), creating a dual burden of ageing and disease that severely impacts HRQoL[7], [8]. In this context, understanding the factors that influence their health satisfaction and enhancing the health satisfaction of middle-aged and elderly adults are not only concerns for their individual well-being but also effective means to address the challenges of an ageing society and alleviate pressure on the healthcare system.

While research on health satisfaction and its influencing factors has made certain progress, research that comprehensively considers both social and biological determinants, as well as evidence on the Chinese middle-aged and elderly population, remains relatively limited. Research conducted in various countries and regions has unveiled a close link between health satisfaction and social factors. For instance, studies in Iran have indicated that age, marital status, HRQoL, and chronic illnesses significantly influence adults' health satisfaction [3], [9]. In South Korea, research has found a positive correlation between monthly income, mobility, self-management, daily living status, pain/discomfort, anxiety/depression, and health satisfaction. In contrast, the number of chronic illnesses and types of health insurance are negatively correlated with it [10]. Studies in Brazil, focusing on the elderly, have shown an association between poor oral health and health satisfaction [4]. Meanwhile, research in Italy, targeting patients with CVD (Cardiovascular Disease), has revealed a relationship between disease severity, depressive moods, and health satisfaction, mediated by illness perceptions and self-efficacy beliefs [11], [12]. However, despite the extensive research on social factors, the role of biological factors in health satisfaction has not been adequately explored. Studies have confirmed that BMI significantly impacts adults' health satisfaction [3]. Furthermore, biological factors such as various physical examination indicators and blood biomarkers are directly related to individuals' physiological functions and health risks [13], serving as crucial determinants of HRQoL and population health. Yet, the association between these factors and health satisfaction remains unclear. More importantly, research on satisfaction in China has predominantly focused on areas such as life satisfaction [14], job satisfaction [15], [16], patient satisfaction [17], and health system satisfaction [18], yet there is a lack of representative evidence regarding the determinants of health satisfaction, particularly among middle-aged and elderly populations. Given the importance of this evidence for policy formulation, this study aims to comprehensively investigate the social and biological determinants of health satisfaction among middle-aged and elderly Chinese individuals. By delving into the relationships between these factors and health satisfaction, our findings will provide valuable insights for policymakers to design effective interventions, modify risk factors, and ultimately enhance the population's health satisfaction and quality of life. One of the core objectives of this study is to explore the spatial distribution of health satisfaction, aiming to reveal regional disparities and potential influencing factors. Previous studies on health satisfaction have primarily focused on individual-level factors and have overlooked the importance of spatial distribution. These studies have limitations in comprehensively understanding the regional differences in health satisfaction. In contrast, this study not only considers individual and environmental factors but also delves deep into the spatial distribution of health satisfaction, which fills the research gap and provides a more comprehensive perspective for improving public health policies.

Currently, research on health satisfaction among individuals aged 45 and above in China has not been deeply explored, especially in the utilisation of advanced technologies for data analysis and prediction. This study aims to fill this gap by employing machine learning algorithms to conduct an in-depth analysis of nationwide cross-sectional data. Machine-learning techniques, as a powerful data-driven tool, have been widely utilised to develop prediction models (e.g., Random Forest, XGBoost, and Gradient Boosting Machines) and have demonstrated great potential in the healthcare domain [19]. In particular, machine-learning models can be instrumental in implementing targeted preventive interventions [20]. They can quickly perform intelligent calculations and have strong capabilities in processing large amounts of data [21]. Additionally, machine learning could identify rare health outcomes [22], which is important for enhancing the accuracy of health satisfaction predictions. Machine learning techniques exhibit superior capabilities in handling complex big data, non-linear relationships, and rare health outcomes. They hold significant promise for developing personalised predictive models focusing on health satisfaction and implementing targeted preventive interventions.

Given the lack of integrated, data-driven evidence on how social and biological factors jointly shape health satisfaction among middle-aged and elderly adults in China, as well as the geographical disparities of this satisfaction across the country, our aimed to utilise machine learning algorithms to conduct a national cross-sectional study of health satisfaction among middle-aged and elderly adults in China, examining the diverse factors influencing their SWB. By comprehensively understanding these factors, we aim to provide valuable insights for formulating policies and interventions that can enhance the HRQoL of China's ageing population.