For this population-based panel data analysis, data were derived from four waves of the CHARLS 2011, 2013, 2015 and 2018. All information included in our study was self-report via face-to-face interviews with a structured questionnaire, from a nationally representative sample of Chinese residents aged 45 years and older, using multistage stratified probability-proportionate-to-size sampling. The overall response rate for the first wave of CHARLS was 80.5%. The CHARLS data included overlapping individuals across the waves. The total sample size for the 2011 CHARLS baseline survey was 17,708 individuals, who were followed up every 2–3 years to repeat the survey. New respondents were also added to each follow-up survey. A detailed description of the objectives and methods of CHARLS has been reported elsewhere [20]. For this study, 16,931 participants aged 45 years and older at 2011 baseline were included, of which 2,647, 3,029, and 4,587 participants were lost to follow-up at each wave, respectively.

In this study, multimorbidity was defined as the presence of two or more chronic non-communicable diseases [7]. 13 self-reported non-communicable diseases were used to measure multimorbidity, including diabetes, hypertension, dyslipidemia, heart disease, stroke, cancer, chronic lung disease, digestive disease, liver disease, kidney disease, arthritis, asthma, and psychological problems. The number of non-communicable diseases for each participant was added up to determine who had multimorbidity in each wave [21]. It is a categorical variable with the options “yes” (having two or more diseases) or “no” (having no or only one disease).

It is worth noting that, psychological problems originally refer to a broader range of psychological issues beyond depression, including emotional, nervous, and psychiatric problems. However, depression has been astonishingly ignored by Chinese older people and they seldom regard depression as a kind of disease [22], so psychological problems mainly denote to other psychiatric issues except depression. Furthermore, it is important to recognize that depression can be encompassed within psychotropic problems, and that stroke may induce vascular depression. In our study, the prevalence of psychotropic problems is relatively low (As shown in Supplementary Table 1), which supports our claim that depression is underestimated in China.

In each wave of CHARLS, participants were asked, “Do you often suffer from body pain?” Those who answered “yes” were then asked, “On what part of your body do you feel pain? Please list all parts of the body where you are currently experiencing pain.” Participants were given several options for body parts (head, shoulders, arms, wrists, fingers, chest, stomach, back, waist, buttocks, legs, knees, ankles, toes, and neck). The number of pain sites greater than 1 was defined as multiple pain points.

Self-reported sleep duration was obtained via a structured questionnaire that asked, “In the past month, how many hours have you actually slept at night (average hours for one night)?” and “In the past month, how long have you taken a nap after lunch?”. Hours of sleep at night and after lunch were added to derive sleep duration in each wave.

The dependent variable was depression. The 10-item Center for Epidemiological Studies Depression Scale (CESD-10) in CHARLS is a simplified version of the depression scale. Each participant’s depression scores in each wave were evaluated using CESD-10. Depression was treated as a dichotomous variable, in that a score greater than or equal to 10 was considered to indicate depression, and a score below 10 was considered normal [23].

Educational attainment and annual per-capita household consumption expenditure were used as proxies for socioeconomic status. Different socioeconomic groups were defined based on educational attainment (time-invariant, including illiterate; primary school; secondary school and above) and quartiles of per-capita household consumption expenditure (quartile 1 for the most deprived and quartile 4 for the most affluent).

The following variables were included as covariates: age, sex, marital status (married/partnered, and single/others), educational attainment (illiterate, primary school, secondary school and above), residence (rural, and urban), annual per-capita household consumption expenditure (quartiles 1–4), health insurance (public insurance, and others), geographic locations (east, middle, and west), activities of daily living (ADLs, impaired, and unimpaired), instrumental activities of daily living (IADLs, impaired, and unimpaired). Sex and geographic locations were time-invariant variables.

First, we conducted a descriptive statistical analysis of study participants from 2011 to 2018. Continuous variables were represented by means and standard deviation (SD), and classified variables were measured by frequencies and percentages. Prevalence was used to measure the trends of diseases. The prevalence of the exact 13 self-reported non-communicable diseases was shown in Supplementary Table 1.

Next, a panel data approach of random-effects linear regression was used to examine the associations between socioeconomic status and the number of non-communicable diseases. Random-effects negative binomial regression models were employed to investigate the association between the number of non-communicable diseases and body pain. For the negative binomial regression analysis, incidence rate ratios (IRRs) and 95% confidence intervals (CIs) were reported. Random-effects linear regression models were used to estimate the association between the number of non-communicable diseases and sleep duration.

Random-effects logistic regression models were used to estimate the association between the number of non-communicable diseases and the likelihood of developing depression. Specifically, the mediating effects of the number of body pain and sleep duration on the correlations between the number of non-communicable diseases and depression were examined by a stepwise regression method [24]. Odds ratios (ORs) and 95% CIs were reported. To explore the differential associations between the number of non-communicable diseases and depression in population groups, subgroup analyses stratified by socioeconomic status were performed, using the same regression analyses but removing stratified variables. A p values less than 0.05 was considered as significant.

To address the potential biases introduced by the overlapping individuals, we employed random-effects models, which accounted for the longitudinal nature of the data and the repeated observations of the same individuals across different waves. To consider the differences in follow-up time and loss to follow-up, we used multiple imputation techniques to estimate the missing values and create a more complete dataset for analysis. By estimating the missing values based on other observed variables, we can ensure that the results are comparable across different waves of the study. In addition, to account for the survey design, stratification, and clustering, we incorporated sampling weights in the analysis methods to ensure accurate representation of the population prevalence and unbiased estimation of parameters. All statistical analyses were performed using Stata (version 16.0).