Study population and data collection
According to the statistics of Anhui Statistics Bureau in 2016 , the gross domestic product (GDP) per capita was CNY (Chinese yuan, 1 US $ equals about CNY 7.10) 80,138 for Hefei, CNY 40,740 for Xuancheng, and CNY 17,642 for Fuyang. In addition, among sixteen cities of Anhui Province, Hefei, Xuancheng, and Fuyang ranked first, eighth, and last, respectively, in GDP per capita. These three cities were selected in this study. Based on the geographic location and economic levels , a multi-stage stratiﬁed cluster random sampling method was employed to recruit participants in order to have a representative sample. At the first stage, we selected three prefecture-level cities from the sixteen prefecture-level cities in Anhui province, China: Fuyang (north, lower economic level); Xuancheng (south, middle economic level); Hefei (central, higher economic level, the capital city of Anhui). Then, in each prefecture-level city, one county and one district were selected randomly. A total of six counties and districts were selected in this study. Next, in each selected county and district, one street community and one township were randomly selected and a total of 12 street communities and townships were used as sample sites for this study. Lastly, in each selected street community and township, two communities and two villages were selected randomly and 24 sampling areas were ascertained (Fig. 1). More information about our sampling process can also be founded elsewhere .
Between July and September 2017, we conducted cross-sectional surveys in these 24 sampling areas. Based on the local household registry, individuals aged ≥ 60 years were determined. Aided by local community workers, skilled and trained graduate students from Anhui Medical University visited each participant and conducted face to face interviews using a structured questionnaire. The participants received a verbal description of the purposes and procedures of the study and informed consent is needed before the interview. The process of data collection took about 40 minutes. Each respondent was compensated with a gift of about 2 US dollars (CNY 15) for the time and cooperation after the interview. Individuals who were not able to carry out proper verbal communication, due to being deaf or mute and dementia or cognitive impairments, were excluded. In the present study, 1,935 older adults were interviewed, of which 1,810 (93.54%) were eligible for analysis, with 567 in Fuyang, 603 in Xuancheng, and 640 in Hefei, respectively.
Measurement of social capital
Based on the framework of the World Bank’s Social Capital Assessment Tool and previous works of our research group [9, 16-18], six dimensions of social capital were included in the present study: social participation, social support, social connection, trust, cohesion, and reciprocity. We selected 22 commonly used and easily understandable items to measure social capital and adapted them to the Chinese context. In the present study, the five-point Likert scale was adopted in the social capital questionnaire, and respondents were asked to rate their agreement (1“never”, 2 “seldom”, 3 “usually”, 4 “often”, and 5 “more often”). The measurement of social capital has also been described elsewhere  and more detailed information about the questionnaire can be found in Additional file 1.
For each domain of social capital, answers to the items were summated to obtain an overall score with higher scores indicating better social capital status. Construct validity was tested to estimate the validity of our instrument by exploring the correlations of each item of social capital dimension and the scores of social capital dimensions, respectively, where large effect size (correlation coefficient ≥ 0.50) was observed in all magnitude , indicating construct validity of our instrument. Internal consistency was calculated to prove the reliability of the measurement tool. Cronbach’s α of the questionnaire was 0.919, showing an excellent internal consistency for our scale with this specific sample. For each dimension, Cronbach’s α for social participation, social support, social connection, trust, cohesion, and reciprocity was 0.752, 0.921, 0.767, 0.883, 0.940, and 0.869, respectively.
Measurement of depressive symptoms
The Zung Self-Rating Depression Scale (SDS), a widely used screening tool for depressive feelings [20, 21], was adopted to assess the depression status of the participants. Construct validity was tested to estimate the validity of our instrument by exploring the correlations of each item of the scale and the scores of depression. The correlation coefficient ranges from 0.682 to 0.888, which shows a large effect size (correlation coefficient ≥ 0.50) , indicating a good validity of our instrument. Cronbach’s α of the scale was 0.965, indicating excellent internal consistency in this sample.
In this study, we selected 16 items to measure depression of older adults, which were more understandable and acceptable for the Chinese community older dwellers. We summated the items to calculate the total depression score, ranging from 16 to 64, with higher scores indicating a lower likelihood of depression.
Assessment of demographic variables
Information on the demographic and health-related variables was collected. These variables included age (60 - 64, 65 - 69, 70 - 74, ≥ 75, years), gender (male, female), body mass index (BMI, kg/m2), residence (urban, rural), living status (living alone, living with spouse/children/grandchildren and else), marital status (married/cohabited, never married/divorced, widowed), and education (primary school and below, junior high school, high school, college and above). Information on smoking and drinking status was also collected.
Continuous variables were presented as mean ± standard deviation and range, categorical variables were presented as number (%). A general linear model (GLM) was used to initially investigate the relationship between different social capital dimensions and depression scores. The GLM model can be specified as follows:
Other confounders such as shorter sleeping time and physical disability  were not included as no data was available for this study. Collinearity between all independent variables was not existing according to the variance inflation factor (VIF) results (Additional file 2). At last, to explore the combinative relationship between social capital and depression, a classification and regression tree (CART) model was developed by dividing all social capital dimensions (social participation, social support, social connection, trust, cohesion, and reciprocity) and demographic variables into subsets. The classification and regression tree (CART) model is a flexible, robust, and non-parametric model that was previously used in depression disease study [24, 25]. The best model is defined as having the smallest tree size and an estimated error rate within one standard error of the minimum . The GLM model and CART model were stratified according to the economic levels separately. All statistical analyses were performed with SPSS statistics software, version 23 (SPSS Inc.; Chicago, IL, USA) and R version 3.4.0. P < 0.05 was considered statistically significant.