Integration of data from probability surveys and big found data for finite population inference using mass imputation
Section 7. Real-data application

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7.1   Data description

To demonstrate the practical use, we apply the proposed method to the survey data from the Korea National Health and Nutrition Examination Survey (KNHANES) and the big data from National Health Insurance Sharing Service (NHISS). The KNHANES is an annual national survey that studies the health and nutritional status of Koreans since 1998. The surveys have been conducted by the Korea Centers for Disease Control and Prevention. This nationally representative cross-sectional survey includes approximately 10,000 individuals each year as a survey sample and collects information on socioeconomic status, health-related behaviours, quality of life, healthcare utilization, anthropometric measures, biochemical and clinical profiles for non-communicable diseases and dietary intakes with three component surveys: health interview, health examination, and nutrition survey. More details of the KNHANES can be found in Kweon, Kim, jin Jang, Kim, Kim, Choi, Chun, Khang and Oh (2014). The data set used in this study has 4,929 samples.

On the other hand, the big data from NHISS provides health-related information collected from National Health Screening Program (NHSP) in South Korea. The NHSP was launched with the goal of improving the overall health of the South Korean citizens and preventing the costly chronic diseases. All beneficiaries are eligible for screening once every year or two depending on their demographic or occupational status. The specific screening items are stipulated by the implementation standards, which include, but not limited to, various blood tests and cancer screening. The total number of eligible beneficiaries is about 16 million, where approximately 75% of them participated the screening. The data that we have used in this study is the subset corresponding to the blood test results that are associated with metabolic syndrome from the 2014 program. The variables in this data set are demographics as sex and age, and clinical measurements such as total glycerides (mg/dL), total cholesterol (mg/dL), high-density lipoprotein cholesterol (HDL, mg/dL), and medical diagnosis on whether having anemia. The data set is made publicly available after anonymization and randomly selecting 1 million observations (National Health Insurance Data Sharing Service, 2014). Note that more thorough data can be purchased with a paid subscription and expert panel review.

7.2   Analysis and results

To apply the proposed method of mass imputation, we assume that total cholesterol is not available in KNHANES data, and use the big data from NHSP to perform mass imputation for total cholesterol variable. The actual survey values from KNHANES are used to compute a benchmark so that we can validate the efficacy of our proposed method. We consider the six different estimators: 

• HT: the Horvitz-Thompson estimator based on the Sample A data. This is used for a benchmark comparison;
• NN: the nearest neighbor imputation estimator;
• kNN: the $k$ nearest neighbor imputation estimator with $k\mathrm{<mo>=</mo>}5;$
• GAM: the generalized additive model imputation estimator;
• LM: the linear regression model imputation estimator using sex, age group, HDL cholesterol and total glycerides as the covariates;
• IPW: the inverse propensity score weighting estimator;
• NAIVE: the naive estimator using the Sample B without any treatment.

Total cholesterol is affected by the amount of HDL, because HDL is one of the components that constitute the total cholesterol, and is known to be also affected by sex and age. Unless Sample B is from a particular sub-population such as cardiovascular stenosis patients group, we may assume that the relationship between the total cholesterol and other variables remain the same. Hence ignorability holds. Also the covariates are all medical/biological measurements, meaning they should stay within the similar range both for Samples A and B. The variance estimator for each estimator is calculated, and 95% Wald confidence interval for ${\mu }_g$ is obtained using asymptotic normality. Figure 7.1 depicts the intervals, where the population mean estimate from each method is presented as a vertical bar. The interval obtained from HT can be viewed as a reference. It can be seen that all estimators produce intervals that are slightly overestimated compared to the one from HT. It is because of the inherent bias in total cholesterol level in NHSP data; the sample mean values of the total cholesterol from NHSP data is 7 point or 3.7 per cent higher than HT estimator calculated with KNHANES data, as seen from the naive result. One can see that all the proposed methods substantially reduce such bias to make the estimator close to the HT estimator, which shows the benefit of the proposed methods. IPW estimator produced a relatively poor estimate compared to other methods, which is probably because of either misspecification in logistic regression model, or considerable discrepancy in sample sizes between KNHANES (4,929) and NHSP data (1 million). We also tried the DR estimator but not included here, because the effect from the IPW is very marginal due to the limited auxiliary variables available.

To better understand the prediction performance of the mass imputation methods, we calculated RMSE, mean bias, and correlation of imputed values by comparing the imputed values and actual survey values. Because we can observe the actual survey values from KNHANES, we can compute the prediction quality measures. Table 7.1 presents the summarized table, where we compared the results at individual levels and subgroup mean levels divided by age group and sex. For subgroup levels, we first obtain the subgroup mean estimates and then calculate the statistics aggregated over different groups. It can be seen that GAM performs better than the other methods in terms of RMSE and correlation. Overall, mass imputation method provides reasonable results for subgroup level as can be seen in Figure 7.2.

These quality measures need a predicted value for Sample A, hence IPW estimators are excluded in the comparison. Estimating the population and subgroup means using Sample B can give a very biased result $–$ in the case of NHSP data, the difference between the mean of NHSP data and the HT estimator from KNHANES is about 7.09, or 3.7 per cent.

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