Two-phase Sampling And Its Application In Personal Health Expenditure Survey

Objectives The study includes the following purposes. The first is to identify the available auxiliary variable for the construction of two-phase sampling estimators with auxiliary variable to estimate personal health expenditure (PHE). The second is to analyze the effects of the sampling rate and the correlation coefficient on the sampling efficiency, and to choose the efficient and reliable estimators for the estimations of means of per PHE and per capital income in Shannxi province in 2007. The third is to prove the feasibility of the application of two-phase sampling in the National Health Service Survey (NHSS). The last one is to give some suggestions of combining two-phase sampling with the NHSS to obtain PHE information in the face of no established PHE surveys.Methods The data was from the fourth NHSS in Shaanxi province in 2008. In this study, the 4161 households of Shannxi'NHSS were selected as the first phase sample, from which the second phase sample was drew out by simple random sampling without replacement, and then we choose the easily obtained household expenditure as auxiliary variable to constructπestimator, ratio estimator and regression estimator to estimate the means of per capital income and the sub-items of household expenditure. To find an appropriate sampling rate for the estimation of PHE, the study repeatedly sampled the first phase sample with a series sampling rate to exam the efficiency of three estimators. We choose bias, relative bias, standard error and root of mean square error as efficiency indicators and choose coefficient of variation (CV) as reliability indicator in this study.A SAS two-phase sampling macro was designed to conduct the repeating sampling for 100 times. The results of all the replications were summarized.Results The non-response rate of household expenditure, which was 1%, was the lowest one among the study variables. The correlation coefficient of per personal household income and household expenditure was 0.78. The correlation coefficients of the other sub-items of per household expenditure and per household expenditure were respectively 0.76, 0.66, 0.58, 0.42, 0.41, 0.27, 0.16. Finally, per household expenditure was chosen as the auxiliary variable after considering both the non-response rate and correlation coefficients.Sampling once didn't show obvious trend in sampling rates, correlation coefficients and types of estimators. The results of the repeating sampling showed that the efficiency of the same type of estimator improved as the sampling rate increased and for the same sampling rate, the efficiency ofπestimator was poorer than that of ratio estimator and regression estimator, and this kind of disparity enlarged as the sampling rate increased, but the efficiency of the latter two types were always close.The results of example analysis showed that when the sampling rate was 0.4, the estimations of ratio estimator and regression estimator were both efficient. The ratio estimation of per personal health expenditure of Shaanxi province in 2007 was 540 yuan. The disparity between urban and rural citizens was approximate 300 yuan, which was a little large. The disparity between rural citizens who were covered and not covered in the New Rural Cooperative Medical Scheme (NRCMS) was much larger, and the Non-NRCMS group was 1097 yuan, which was almost three times of that of NRCMS group. The north was 676 yuan, which was higher than both of the southern and central areas. The overall per capital income and urban and rural per capital income were respectively 6043 yuan, 8676 yuan and 3325 yuan.Conclusions: In practice, the researchers should choose the best estimator and the sampling rate under the considerations of both correlation coefficient and the sampling efficiency.The feasibility of the application of two-phase sampling in the NHSS to estimate the PHE was proved. When the NHSS's questionnaire is designed, it is feasible to apply two-phase sampling to request all the households to answer the item of household expenditure while parts of them answer the item of household income and sub-items of household expenditure. As a result, just parts of the first phase respondents need to report parts of the items, and this would reduce the recalling burden of the respondents and also the survey time.Generally, there are two available approaches to obtain the detailed PHE information cost-efficiently. For the NHSS and its western expanded sample areas, they can select a sub-sample using the NHSS sample households as the sampling frame, and than conduct a detailed PHE survey. For the Non-NHSS sample areas, they should obtain the PHE estimation using available auxiliary information from other information systems or implement independent PHE surveys.