The English Longitudinal Study of Ageing (ELSA) is an ongoing prospective and nationally representative cohort of community-dwelling adults aged ≥ 50 years in England. Details concerning objective, design, and method of the study have been published (10). The ELSA was approved by the London Multicentre Research Ethics Committee (MREC/01/2/91), with informed consent obtained for all participants. We used survey data from waves 1 (2002–2003) to 4 (2008–2009) to evaluate physical activity participation, and waves 4 (2008–2009) to 9 (2018–2019) to assess incident DM. Participants were excluded if they had been diagnosed of DM by wave 4. Study timeline was presented in Supplemental Figure 1 .

Biennial evaluation of frequency in participating mild, moderate and vigorous intensity physical activities was performed using three questions, differentiating from work related activities. Answers included 4 categories: 1) hardly ever or never; 2) one to three times per month; 3) once per week; 4) more than once per week. Further details were presented in Supplemental Methods .

A three-stage approach was used to assess physical activity participation. Firstly, we assigned a score of 1, 2, 3 according to frequency of participating in activities of mild, moderate and vigorous intensity, respectively. A score of 1 was assigned for hardly ever or never, 2 assigned for one to three times per month, 3 assigned for at least once per week. Score assignment was the same for the three types of activity (11). Secondly, for each of three types of activity, we calculated standardized Z score by subtracting corresponding mean and dividing by standard deviation (SD) of assigned scores at baseline. An activity Z score of 1 at a certain wave indicated that the particular score of physical activity at the wave was 1 SD higher than the average score of physical activity at baseline. Similar approach can be found for handling cognitive test scores by previous studies (12–14). Thirdly, to account for differences between mild, moderate and vigorous intensity activities, a weighted global activity Z score was summarized. The weights were selected based on metabolic equivalent of tasks (MET) estimates by 2011 Compendium of Physical Activities (15). After calculation, MET weights of 2.3, 4.4, and 7.2 were assigned to mild, moderate, and vigorous intensity activities Z score, respectively. Detailed information for weights calculation was presented in Supplemental Table 1 , which was consistent with previous studies (16).

The ELSA performed physical measurement at regular intervals, with standardized protocols applied, as described in Supplemental Methods. Measurement was conducted by trained nurses for all participants in wave 0, 2, 4, 6, 8 (the year 1998, 2004, 2008, 2012, 2016). We used data in wave 4 to assess obesity, including BMI and waist circumference.

According to the 2014 American Diabetes Association guidelines (ADA), DM was defined as an fasting plasma glucose ≥ 126 mg/dL (7.0 mmol/L) or an HbA1c level ≥ 48 mmol/mol (6.5%), a self-reported physician diagnosis of DM or current use of glucose-lowering therapy (17–19). Among participants without DM, we defined prediabetes as an fasting plasma glucose in the range 100 mg/dL (5.6 mmol/L) to 125 mg/dL (6.9 mmol/L) or an HbA1c level in the range 38.8 to 46.4 mmol/mol (5.7 to 6.4%) (17). The ELSA also collected information about the age being newly diagnosed of DM by physicians since last visit. Time to incident DM was calculated as length between age at wave 4 and age of firstly being diagnosed.

Covariates included demographic and clinical variables assessed at wave 1. Demographic variables included sex, age (years), ethnicity, educational background (high-level education or not), cohabitation status (living alone or not), current smoking (yes or no), alcohol consumption (at least once per week). Clinical variables included overweight status, depressive symptoms, hypertension, prediabetes status, stroke, cardiovascular diseases, cancer, and chronic lung diseases. Considering that elder participants could experience decline in physical activity participation due to deteriorated mobility, we further adjusted for the mobility status.

We defined high-level education as above senior level of high school or 12 or more years of education. Mobility status was defined as whether participants reported any difficulties in daily living activities during waves 1 to 4. These activities included eating, bathing, dressing, getting in/out of bed and walking across a room, which could reflect the general mobility status. Depressive symptoms were defined based on an 8-item version of the Center for Epidemiologic Studies Depression Scale (CESD-8), with scores ≥4 regarded as having depressive symptoms (13, 20). Overweight status was defined by BMI (≥25 or <25 kg/m²) according to World Health Organization (21). Personal history of other diseases was derived from records of self-reported physician diagnoses.

For characteristics description, mean ± SD was used for continuous variables and numbers (percentage) for categorical variables. Overall differences between groups were tested using analysis of variance (ANOVA) or chi-square test.

We used weighted Z score of physical activity over a 6-year span from waves 1 to 4 to evaluate activity trajectories and cumulative participation. For physical activity trajectories, the group-based trajectory modeling (GBTM) was used to identify potential trajectories of participation in global, mild, moderate and vigorous activities, respectively. The GBTM used maximum likelihood estimation to identify participants sharing similar trajectory (22). It can handle data distributions including censored normal, Poisson and Bernoulli, and we used censored normal. Trajectory group of the highest probability was determined for each participant, which was then included in further multivariate analysis. We used SAS Proc Traj to fit GBTM models, with details described in Supplemental Methods (23). For cumulative participation, we used area under the curve (AUC) to calculate cumulative weighted physical activity Z score, based on Trapezoid rule (24). Details for AUC calculation were presented in Figure 1 . Quintiles of cumulative weighted activity Z score were included in analysis as a numerical variable to perform linear trend test and mediation analysis.

Linear regression model was applied to assess associations of physical activity trajectories on subsequent BMI and waist circumference measured at wave 4. Cox regression was utilized to assess association of physical activity on risk of incident DM. Proportional hazard assumption was evaluated using weighted Schoenfeld residuals, with violated covariates included as model terms of interaction with time (25). To address ties in failure time, the method based on exact conditional probability under the proportional hazards assumption was applied (26). Hazard ratios (HR) and 95% Wald’s confidence intervals (CI) were reported. Observations with missing values were excluded from analysis.

Mediation analysis was performed to evaluate the role of obesity in association between cumulative weighted activity Z score quintiles and incident DM. We included two mediators to represent the obesity status, including BMI and waist circumference measured at wave 4. We also assessed the mediating role of change in BMI from waves 0 to 4. As a result, three mediation models were built. Each mediation model comprised of two separate models:

where X represented quintiles of cumulative weighted global physical activity Z score (numerical) and C represented vector of covariates including sex, age, ethnicity, education, cohabitation status, mobility status, current smoking, alcohol consumption, depressive symptoms, hypertension, prediabetes status, stroke, cardiovascular diseases, chronic lung diseases and cancer, as well as BMI in wave 0 (when the mediator was change in BMI). M represented hypothesized mediators. After assessing normality distribution for BMI, change in BMI, and waist circumference, linear regression was used for fitting the mediator model;

where new variable Y represented recorded incident DM from waves 4 to 9, with meaning for X, M and C remaining the same. Considering the incident DM of binary type, binary logistic regression was used for fitting the response model, with exponential transformed coefficient equivalent to odds ratio (OR). Quasi-Bayesian approximation method was used to perform significance test for mediating effects, based on 2000 Monte Carlo replications (27).

Several sensitivity analyses were conducted. Firstly, we respectively identified trajectories of mild, moderate and vigorous activities, as well as calculated cumulative participation Z score. Then we evaluated associations between these sub-domain physical activity participation and outcomes. Secondly, we performed stratified analyses according to sex, age group (≥ 65 or <65 years), and overweight status (BMI < 25 or ≥ 25 kg/m²). Thirdly, we excluded participants suffered any difficulties in activities of daily living during waves 1 to 4, and participants developed incident DM within two years after wave 4, to address reverse causation (28). Finally, we analyzed association between physical activity and incident DM recorded in 2 to 6 years after wave 4, to explore the potential time range of protective tole by physical activity on incident DM.

All statistical analyses were conducted using SAS 9.4 (SAS Institute, Cary, NC), and the package mediation in R language 3.6.2 (R Foundation, Vienna, Austria), with two-tailed alpha of 0.05 referred as statistically significant level.

A total of 9757 diabetes-free participants from the ELSA were included for analysis. Detailed process of participant selection was shown in Supplemental Figure 2 .

Among the included participants, 4243 (43.5%) participants were male, and the mean age was 58.9 ± 10.3 years. Differences were observed in most characteristics between activity trajectories, with details summarized in Table 1 .

As shown in Figure 2 , 5 trajectories of global physical activity were identified, including: 1) persistently low trajectory (N=3037), with constantly low participation; 2) initially low then improving (N=1868), with initially low participation but turned to elevating afterwards; 3) initially high then declining (N=325), with initially high participation but turned to declining afterwards; 4) persistently moderate (N=2489), with constantly intermediate participation; 5) persistently high (N=2038), with highly active participation throughout the span.

As illustrated in Table 2 , significant associations were observed of global physical activity trajectories and cumulative participation on subsequent obesity. Compared with the persistently low trajectory, participants in trajectories of initially low then improving, persistently moderate and high had significantly lower BMI of 1.121 kg/m² (95% CI: 0.777 to 1.465, P <0.001), 0.688 kg/m² (95% CI: 0.345 to 1.031, P < 0.001), and 1.441 kg/m² (95% CI: 1.070 to 1.813, P <0.001), respectively. And those with initially high then declining trajectory showed no significant differences compared with persistently low trajectory. Similar results were observed for waist circumference. Compared with the persistently low trajectory, participants in trajectories of initially low then improving, persistently moderate and high had significantly lower waist circumference of 3.183 cm (95% CI: 2.351 to 4.015, P <0.001), 2.367 cm (95% CI: 1.544 to 3.191, P < 0.001), and 4.740 cm (95% CI: 3.846 to 5.634, P <0.001), respectively.

As for cumulative physical activity participation, it was found that elevated participation was associated with both lower BMI and waist circumference, with each 10 units increment in cumulative weighted global activity Z score associated with decreased BMI of 0.109 kg/m² (95% CI: 0.085 to 0.133, P <0.001) and waist circumference of 0.348 cm (95% CI: 0.291 to 0.406, P <0.001).

During a 10-year span, 670 incident DM cases were reported, with results summarized in Table 3 . Compared with the persistently low trajectory, participants in initially low then improving, persistently moderate and high trajectories had significant lower DM risk, with HR of 0.41 (95% CI: 0.32 to 0.53, P <0.001), 0.70 (95% CI: 0.56 to 0.89, P =0.004) and 0.49 (95% CI: 0.37 to 0.65, P <0.001), respectively. By contrast, DM risk in initially high then declining trajectory showed no significant differences with persistently low trajectory. For cumulative activity participation, elevated cumulative weighted global activity Z score was also associated with lower DM risk, with each quintile and 10 units increment corresponding to HR of 0.76 (95% CI: 0.71 to 0.82, P <0.001) and 0.94 (95% CI: 0.92 to 0.95, P <0.001), respectively.

As shown in Figures 3 – 5 , significant mediation roles by BMI, waist circumference, and change in BMI were identified in association between cumulative weighted global physical activity Z score quintiles and subsequent incident DM, after adjusting for other covariates. The total indirect effect through BMI (βi=-0.03, P <0.001), defined as product of indirect effect 1 (β1) and indirect effect 2 (β2) reached significance level, which mediated 10% (P <0.001) of overall association. Similarly, the total indirect effect through waist circumference (βi=-0.05, P <0.001) and change in BMI (βi=-0.02, P <0.001) were significant, mediating 17% (P <0.001) and 9% (P <0.001) of overall association, respectively.

Similar with global physical activity, 5 trajectories were identified for both mild and moderate activities, as shown in Supplemental Figures 3, 4 , respectively. For vigorous activities, a total of 4 trajectories were identified, shown in Supplemental Figure 5 .

Associations of sub-domain physical activity participation on obesity, and incident DM risk were presented in Supplemental Tables 2, 3 , respectively. For obesity, consistent results with global activity participation were observed for all three mild, moderate and vigorous intensity activities. For incident DM, consistent results were mainly observed for moderate and vigorous intensity activities participation.

Stratified analyses by sex ( Supplemental Tables 4, 5 ), age ( Supplemental Tables 6, 7 ), and overweight status ( Supplemental Tables 8, 9 ) showed that similar results were consistently observed. After further excluding participants with difficulties in daily living activities or developed incident DM within two years after wave 4, our main results preserved, shown in Supplemental Tables 10, 11 . For physical activity trajectories, significant associations with incident DM risk reduction in 2 to 6 years were consistently observed for the persistently moderate group, shown in Supplemental Table 12 . The initially low then improving group was not associated with incident DM risk in 2 years but associated with lower incident DM risk in 4 to 6 years after wave 4, while no significant associations were observed for the initially high then declining and persistently high groups in this span.