Statistical Methods And Their Application For Successive Survey With Sample Rotation In Complicated Sampling

Objective:In order to survey on the population’s value, variation, cumulative total and the average, the successive survey should be applied. Many medical reference ranges change over time. In epidemiology cohort study, the dropping out rate for the sample units is usually high due to long duration, so the appropriate sample rotation methods and statistical analysis formulae are needed. The frequently successive sampling is the main method used in sample survey system constructed in our country. From other perspective, surveying on fixed sample repeatedly would cause two serious issues, of which one is the reduction of sample representation, and the other one is sample fatigue. However, there are also problems about drawing the new samples in repeated surveys, such as that the samples can’t reflect the variation of population over time; the accurate combined regression estimation for the present population is hard to obtain without the prior information of fixed samples; and the problems of more cost, time and complexity also exist compared to fixed samples. To take both aspects into consideration, the statisticians have excogitated the good method of sample rotation (under the condition of same sample size, a part of the sample may be drawn afresh each time). Since the sample rotation retains some of original sample units and adds the new sample units, this method assembles the advantages of both the fixed sample and completely new sample, and keeps balance between sampling cost and sampling precision, which is the important way to reduce and control the non-sampling error.There have been a lot of sound statistical theories and methods for one-time sample survey (transect survey). However the research for successive sample survey is only limited in the sample rotation in simple random sampling, and there is few statistical research on sample rotation of successive sampling for all kinds of complicated sampling which needs to be applied in practice. On that account, in the first part of this paper, we deduced the statistical formulae for sample rotation of successive survey under stratified sampling, cluster sampling, stratified cluster sampling, two-stage sampling, stratified two-stage sampling and stratified two-stage cluster sampling, filling the corresponding gap in the researches. In the second part, the sample rotation of successive survey under two-stage sampling was conducted for the hematology parameters from one nuclear power station employees, to provide the solid data with high precision for evaluation of nuclear power station employees’health condition and the discussion of risk factors for the health; on the other hand, the sample rotation of successive survey under stratified cluster sampling was conducted for the physical parameters of middle and primary students from one city, to provide solid and precise data for the constitution assessment of middle and primary students; moreover, the practical application of successive survey methods and statistical formulae in this paper was demonstrated through the surveys in practice. In the third part, for the sample rotation of successive survey methods and formulae under six kinds of complicated sampling, we adopt the large sample computer simulation and statistical analysis, to evaluate the validity and reliability of these methods.Methods:For survey design and the deduction of formulae, theories and methods of sampling, regression estimation, ratio estimation, successive survey, sample rotation and probability statistics were applied. Six complicated sampling methods:stratified sampling, cluster sampling, stratified cluster sampling, two-stage sampling, stratified two-stage sampling and stratified two-stage cluster sampling were applied. In the real survey, the survey methods and statistical formulae derived in this paper were employed, together with the methods of interval estimation and Z test. The validity and reliability were evaluated based on the theories of validity and reliability, computational simulation, SAS programming and interval estimation.Results:1. For the successive survey with sample rotation in stratified sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae.2. For the successive survey with sample rotation in cluster sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae. 3. For the successive survey with sample rotation in stratified cluster sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae.4. For the successive survey with sample rotation in two-stage sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae.5. For the successive survey with sample rotation in stratified two-stage sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae.6. For the successive survey with sample rotation in stratified two-stage cluster sampling, survey method was designed and the formulae of the population mean estimate, its variance and estimated variance, the optimum ratio of sample rotation and the optimum combined estimated weight were deduced. SAS programs were compiled for all the statistical formulae.7. During2009-2011, the staff’s hematological parameters of one nuclear power station were surveyed for three times by two-stage sampling with sample rotation. Overall,619person-times were surveyed.9bureaus were surveyed each time. For each year, taking WBC for example, the sample mean and its estimated variance, the regression coefficient and correlation coefficient (2009vs.2010,2010vs.2011), the optimum ratio of sample rotation, the optimum combined estimated weight, the population mean estimate and its estimated variance were obtained. The95%confidence intervals of population mean were (5.40,6.36) and (5.34,6.34) for2010and2011respectively. Hypothesis tests were done between the estimated population mean and the general population mean (p<0.05), which indicated that staff’s WBC of this nuclear power station was lower than the average level of adults.8. The middle and primary students’physical parameters of one city were surveyed twice on Oct2010and Jun2011by stratified cluster sampling with sample rotation. Overall,1971person-times were surveyed. For each time, taking vital capacity for example, the sample mean and its estimated variance, the regression coefficient and correlation coefficient (2011vs.2010), the optimum ratio of sample rotation, the optimum combined estimated weight, the population mean estimate and its estimated variance were obtained. The95%confidence interval of population mean on2011was (2065,2374). Hypothesis tests were done between the estimated population mean and the general population mean (p>0.05), which indicated that middle and primary students’vital capacity of this city was identical with the average level of middle and primary students in China.9. For the successive survey with sample rotation in stratified sampling, at the sampling ratio of both10%and40%, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.10. For the successive survey with sample rotation in cluster sampling, at the sampling ratio of both10%and40%, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.11. For the successive survey with sample rotation in stratified cluster sampling, at the sampling ratio of both10%and40%, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.12. For the successive survey with sample rotation in two-stage sampling, at the sampling ratio of both10%and40%in the second stage for the situation that sample rotation is applied in the second stage and in both the two-stages, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.13. For the successive survey with sample rotation in stratified two-stage sampling, at the sampling ratio of both10%and40%in the second stage, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.14. For the successive survey with sample rotation in stratified two-stage cluster sampling, at the sampling ratio of both10%and40%in the second stage, almost all the confidence intervals of the100estimated population mean included the simulated population mean from results of100simulated samples.15. For the six complicated sampling methods in this paper, at the sampling ratio of10%, except for the two-stage sampling in which sample rotation is applied in both two-stages, the methods with sample rotation applied had the better sampling precision than the method without sample rotaion; At the sampling ratio of40%, except for the stratified two-stage sampling and two-stage sampling (the sampling precision was equal for two-stage sampling), the sampling precision is better for the method with sample rotation applied relative to the method without sample rotation.Conclusion:the survey methods and statistical formulae of the successive survey applied sample rotation in the six complicated sampling methods are scientific and feasible with high precision of parameter estimation, which is innovative with theoretical and practical significance. The staff’s hematological parameters (e.g. WBC) of the nuclear power station in this paper were lower than the general level, indicating that the environment of nuclear power station may affect staff’s health and the radiation protection should be strengthened. The physical parameters (e.g. vital capacity) of the middle and primary students in the city in this paper were the same as the general level. The validity and reliability is very good for the survey methods and statistical formulae of the successive survey with sample rotation in the six complicated sampling methods.