Study design and data
The data used in this study was derived from the 2014 National Internal Migrant Population Dynamic Monitoring Survey , which covered 348 cities in 32 provincial units and collected by the National Health Commission of China. The purpose of the survey was to investigate the utilization of health services among internal migrants. The sampling frame for this study was taken using the stratified multistage random sampling method by probability proportional to size (PPS) approach. All respondents in this study were aged 15-59 years who had been living in local residence without the ‘Hukou’ for more than one month, including migrants from both rural and urban areas. For more details on sampling, design and approvals of the survey, please refer to an earlier study.  The detailed sampling process was shown in Fig. 1. Finally, a total of 7592 migrants with inpatient service need were included in this nationally representative analysis.
In this study, migrants’ inpatient service need was measured by questions about whether they were asked to be hospitalized by a doctor during the last 12 month (inpatient need). Based on the inpatient service need, the outcome was categorized into unmet inpatient services need and receiving inpatient services. The unmet need for inpatient service referred to the proportion migrants who were asked to be hospitalized but did not utilize it. The key independent variable was socioeconomic status (SES). SES was an economic and sociological combined total measure of a person's work experience and an individual's or family's economic and social position in relation to others, based on household income, individual education, and employment status . In this study, we assessed the SES in two ways. First, in order to compare the inequity of the high-low SES in inpatient service utilization from a macro perspective, we integrated the educational level, economic status (household income per month) and employment status into a single SES index using principal component analysis (PCA)  method (details see in Appendix Table A1). Then, we used three specific indicators (economic status, employment status and educational attainment) to show the associations between SES and inpatient service utilization. All three socioeconomic status types were measured in two categories: low SES and high SES. Low and high SES was defined in the following ways: 1) educational attainment, as middle school or below vs. high school or above; 2) economic status was created using a median split based on household income per month; 3) employment status which means whether the respondent had a job, as employed vs. unemployed.
Referring to previous studies [26-28] on the confounding factors of health service utilization, controlled variables included gender, age, marital status (married or single), number of children and ethnic group (Han or ethnic minority), whether had a health record, Hukou types (urban or rural), health insurance, movement area (across province, city or county), duration of migration, region, and willingness for long-term residence of more than 5 years (yes, no, and not decided yet). Types of health insurance were divided into five subgroups: no health insurance, having New Rural Cooperative Medical Scheme (NCMS), having Urban Employee Basic Medical Insurance (UEBMI) and having Urban Resident Basic Medical Insurance (URBMI). Movement area was categorized into three types: migration across provinces; migration across prefectural cities but within a province and migration across counties but within a prefectural city. All the controlled variables were available through the 2014 National Internal Migrant Population Dynamic Monitoring Survey and were included in multivariate logistic regression model 2.
Data analyses were conducted by using the STATA 14.2. Descriptive analyses were performed to compare the inpatient service utilization across different subgroups of the participants using t-test or chi-square test as appropriate and reported their p-values. Sample weights were applied in all the analysis to represent the China population.
First, we estimated the concentration index (CI) and constructed a concentration curve (CC) to illustrate inequity in unmet inpatient service need among migrants. The CC graphs the cumulative percentage of the sample on the x-axis, ranked by SES index, beginning with the lowest. CI was used to quantify the magnitude of inequity in unmet need and corresponds to twice the area between the CC and the 45° line . CC runs from -1 (over-diagonal) to +1 (under-diagonal), indicating whether the unmet inpatient service need is concentrated among the low-SES (CI < 0), the high-SES (CI >0), or equally distributed (CI = 0) .
The concentration index was calculated by the following formula:
[Please see the supplementary files section to view the equation] (1)
[Please see the supplementary files section to view the equation] (2)
Where stands for the mean of y, is the measure of unmet inpatient service need of ith individual, denotes the fractional rank of the ith individual in the SES index, and is the covariance with sampling probability weights. The concentration index and the associated p-values were obtained by the delta method . If the is significantly smaller than 0, low SES individuals are more likely to have unmet inpatient service need, and vice versa .
Then, we adopted logistic regression method to investigate the SES disparities in multivariate analyses adjusted for confounding variables. Those who received inpatient services were defined as the reference group. Binary logistic regression (model 1) to examine the association between SES and inpatient service utilization without controlled variables. In order to control for potential confounding factors, multiple logistic regression (model 2) were used to estimate the adjusted odds ratio and the 95% confidence intervals. The model was specified as:
[Please see the supplementary files section to view the equation] (3)
[Please see the supplementary files section to view the equation] (4)
Where represented the probability of inpatient service utilization; represented the socioeconomic status of ith individual; indicated the confounding variables; Coefficients and represented intercept and SES inequalities, respectively; indicated error terms; OR indicated Odds Ratio.
Finally, the decomposition of the gap in inpatient service use between the high and low SES migrants was assessed using the Blinder-Oaxaca (BO) decomposition method. The BO decomposition method was originally developed to explain wage gaps between whites and blacks and between men and women since the seminal work of Oaxaca and Blinder in the early 1970s [33, 34]. The BO decomposition was a counterfactual method with an assumption that “what the probability of unmet inpatient service need would be if low SES migrants had the same characteristics as their high SES counterparts”. In this part, SES was created using a median split with low SES categorized as below the median of SES index total score and high SES categorized as above the median. Based on it, the SES inequity was divided into two parts by using BO decomposition as followed:
[Please see the supplementary files section to view the equation] (5)
Where l represented low SES migrants and h represented high SES migrants; Z represented all the independent variables in our study; represented the estimated coefficients. The first term in Equation (1) corresponded to the proportion of the gap in outcomes between two groups that were accounted for by group differences in the distribution of observable characteristics, it indicated “endowments effect”; while the second term was “gradient effect” traces the differences that are attributable to the effect of the variables. Decomposing SES differences in inpatient service utilization into endowments and gradient effects has strong policy implications since the evidence of gradient effect would reflect that high-low SES migrants endowed with the same characteristics do not enjoy the same level of inpatient service.