Dementia affects more than 50 million individuals globally, with Alzheimer's disease being the most prevalent subtype (60-70 %), followed by vascular dementia (25 %) (Patterson, 2018). With one new case diagnosed every 3.2 seconds, it is projected that the number of people living with dementia will reach 152 million in 2050 (Patterson, 2018; Prince et al., 2015). There is no medication available for the treatment of dementia, and six drugs approved by the U.S. Food and Drug Administration (FDA) only manage symptoms and have severe side effects such as stroke and death (Gaugler et al., 2022). However, The Lancet Commission reported that the number of dementia could be potentially reduced by 40 % by addressing twelve modifiable risk factors (Livingston et al., 2020). Therefore, targeting these modifiable risk factors is an effective strategy for dementia prevention and management.

Among the twelve modifiable risk factors, physical activity is considered one of the most important modifiable risk factors for dementia. Strong evidence from meta-analyses (Groot et al., 2016; Hersi et al., 2017), longitudinal studies (Najar et al., 2019; Zhu et al., 2022), and genetic studies (Zhu et al., 2022) generally supports the causal relationship between physical activity and dementia, despite a few exceptions reporting null associations (Sabia et al., 2017; Young et al., 2015). The reasons for the null association could be due to underdiagnosed dementia cases (Sabia et al., 2017) and the dose-response relationship between physical activity and incident dementia (Young et al., 2015). A recent systematic review (Erickson et al., 2022) has shown that physical activity could be conducive to cognitive function through cellular and molecular changes such as angiogenesis and neurogenesis, structural and functional brain changes such as volume and thickness and elasticity, and behavioral and socioemotional changes such as strengthening and reducing fatigue.

Previous studies (Groot et al., 2016; Hu et al., 2022; Shao et al., 2022) have primarily concentrated on the overall effect of physical activity on cognitive function or the effects of individual types of physical activities on cognition through subgroup analyses. Several studies (Hu et al., 2022; Shao et al., 2022) have focused on the effect of different types (light, moderate, and vigorous) of physical activity on incident dementia. However, as multiple types of physical activity are correlated and might interact with each other (i.e., persons doing moderate physical activity tend to have high levels of other types of physical activity), there are two research gaps. First, the mixture effect of three types of physical activity has not been examined. Second, the relative contribution of each type of physical activity to dementia risk remains unknown.

Due to high correlations between individual types of physical activity and the presence of coexistence, the traditional Cox proportional hazards model may underestimate the true effects of each physical activity on demntia and be biased or underpowered in estimating these effects. Recent advancements in statistical analysis, such as the weighted quantile sum (WQS) regression, have become increasingly popular in studies of chemical mixtures. For example, the WQS method effectively transfer correlated components, categorized as ordinal variables, into quantiles. These quantiles are then combined into an index for analyzing the mixture's collective effect (Czarnota et al., 2015). By constraining the weights to sum to 1 (with values ranging from 0 to 1), the WQS regression simplifies the data structure and mitigates the challenges posed by collinearity among correlated variables (Czarnota et al., 2015). These advanced models provide the tools necessary for investigating the joint effects of different types of physical activity on the risk of incident dementia. This study aims to estimate the mixture effect of three types of physical activity and their relative contribution to incident dementia using WQS regression.