The Integrated Care for Older People (ICOPE) screening tool was used to assess intrinsic capacity and has demonstrated good reliability among Chinese older adults [19]. ICOPE is a framework developed by the WHO that provides corresponding assessment tools based on each dimension of IC, offering recommendations and guidelines for its measurement from the perspective of both screening and in-depth assessment [20, 21]. Referring to previous study and the ICOPE, the following variables were selected for assessing IC: cognition (memory ability and mental status), locomotion: (sit-to-stand test), vitality (BMI), sensory (hearing and vision), and psychological (depression) [22]. The IC score ranged from 0 to 6, with a higher score representative of better IC [23].

Cognition: The Telephone Interview of Cognitive Status (TICS), which assesses memory and mental status, was used to measure cognition. The total score was 11 points, with the cut-off value determined by subtracting one standard deviation from the average. Cognitive function was assigned one point if neither memory nor mental status fell below the cut-off point; otherwise, it was scored as 0 [24]. Memory was evaluated by immediate and delayed recall of 10 unrelated words. Respondents were asked to recall the words after approximately 2 and 4 min. A total of 20 points were scored when the respondents answered 20 words correctly. To evaluate mental status, respondents got five points for correct orientation (day, month, year, day of the week, and season), five points for their ability to calculate accurately (100–7 for five times in a row), and one point for vision construction (reproducing a picture of two five-pointed stars shown by the interviewers).

Locomotion: Locomotion was assessed by having respondents independently complete five sit-to-stand tests. A completion time of 14 s or less was assigned 1 point, indicating normal mobility and lower fall risk, while a time exceeding 14 s was assigned 0 points, suggesting mobility limitations [25].

Vitality: Vitality was represented by BMI and the cutoff value for BMI was set at 18.5 kg/m²: individuals with a BMI ≤ 18.5 kg/m² were assigned 0 points indicating lower vitality and potential nutritional concerns, while those with a BMI > 18.5 kg/m² received 1 point, indicating normal vitality [26].

Hearing: Respondents were asked, “How is your hearing (with a hearing aid if you normally use it)?” If they responded “poor” they were assigned 0 points. If they responded “fair”, “good”, “very good”, or “excellent” they were assigned 1 point.

Vision: Respondents were asked, “how well do you see distant things (with glasses or corrective lenses if you wear them)?” and “how well do you see near things (with glasses or corrective lenses if you wear them)?” If their responses to both questions were fair”, “good”, “very good” or “excellent” they were assigned 1 point. If either response was “poor” they were assigned 0 points.

Psychological: Psychological was measured using the Epidemiologic Studies Depression Scale [27]. A score of < 12 was considered intact and assigned 1 point, whereas a score of ≥ 12 was regarded as impaired and assigned 0 points.

Information on leisure activities in the past month were assessed using the “health status and function” module of CHARLS. According to previous research, leisure activities were divided into two categories, the social activities and intellectual activities. Social activities include four types of activities: (1) interacting with friends; (2) going dancing, exercising, or practicing Qigong; (3) participating in community-related organizations; and (4) doing voluntary charity work or assisting others. Intellectual activities include four types of activities: (1) playing Mahjong, cards, or chess; (2) attending an educational or training course; (3) investing in stock; and (4) surfing the internet [28, 29]. The frequency of each activity was rated as almost daily (score = 3), almost every week (score = 2), not regularly (score = 1), or never (score = 0). The total score for each respondent was calculated by summing the individual activity scores. This resulted in a score ranging from 0 to 12 points. To categorize the level of engagement, these total scores were then divided into three groups: 0 points, 1–2 points, and ≥ 3 points.

In the current analyses, baseline demographic variables were included as covariates, including age, sex, marital status, and residence location. Age was categorized as continuous variable. Marital status was categorized as either “married” or “others”, and residence location was grouped into “rural” and “urban”.

Group-based trajectory modeling (GBTM) was employed to identify the trajectories of IC. This method is notably advantageous as it focuses on identifying trajectories, which could otherwise conceal distinctions between different groups of people [30]. By applying this method, we hope to uncover important differences in the trajectories of IC that may be linked to specific types of leisure activities. A maximum of six trajectory groups was predetermined. Models were fitted ranging from a single group trajectory to six group trajectories, the survey year serving as the timescale.

The optimal number of classes for IC score trajectories was determined using six factors: model entropy, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), trajectory shape fitting between predicted and observed data, the average posterior probability of class membership, and the proportion of individuals in each class [31]. While no gold standard exists for model selection, the best-fit model was evaluated based on criteria outlined by Nagin, the creator of group-based trajectory modeling, and other influential studies. These criteria included: (1) improvements in BIC, (2) at least 5% of respondents in each trajectory class, (3) mean posterior class membership probabilities above 70%, (4) odds of correct classification greater than 5, and (5) visually distinct trajectories. Trajectory labels were assigned based on their modeled patterns. To identify the model with the optimal number of distinct IC trajectories, longitudinal trajectories of IC scores were modeled using a polynomial model (up to cubic models) with survey year as the independent predictor. The BIC and AIC values were then compared across models with different group numbers to select the best-fit model. The specific fit statistics and selection rationale are presented in the Results section. A good fit was indicated by an average posterior probability of group assignment greater than 70%, and models with more than 5% membership in each trajectory group were chosen. GBTM accounted for all available IC scores under the assumption that missing data were missing at random.

A multinomial logistic regression model was then employed to assess the relationship between social and intellectual activities and the trajectories of IC measures. The results were expressed as odds ratios (OR) along with their 95% confidence intervals (CI). The multivariable-adjusted model included the following covariates: social and intellectual activity scores (0, 1–2, ≥ 3), baseline age (continuous), sex (male, female), marital status (married, others), and residence (urban, rural).

Separate models were used to conduct association analyses by age group (< 70 years and ≥ 70 years) and sex (male and female). To test for effect modification, multiplicative interaction terms (i.e., social activity scores × sex) were added to the fully adjusted model. All analyses were conducted using R version 4.0.3 (R Foundation for Statistical Computing). Statistical significance was based on a two-tailed p value < 0.05.