Comparison of three equations for estimating low‐density lipoprotein‐cholesterol in the rural northeastern region of Thailand

Abstract Background Cardiovascular disease is the most common cause of death worldwide, and the detection of LDL‐C contributes to reducing risks. However, the LDL‐C is rarely evaluated according to the gold standard method because it is costly and time‐consuming. This study aimed to determine the agreement of LDL‐C among three equations, namely Friedewald's equation, Puavilai's equation, and Dansethakul's equation. Methods A cross‐sectional descriptive study. Results Using the data of lipid measurement from a specific group of people in the remote rural area, we found that the Thai equations have more superior agreement with direct measurement than the Friedewald equation (ICC = 0.870, 95% CI = 0.857‐0.882) when the agreement of continuous data was used for total analysis. Although the categorical analysis that gave better agreement was from Friedewald equation (K index = 0.730, 95% CI = 0.720‐0.751), the findings from this study confirmed the population‐specific use of Pauvilai's equation and Dansethakul's equation for determining the LDL‐C. Conclusion Pauvilai's equation showed better agreement with direct measurement for LDL‐C. Thus, it could be considered as an alternative for the direct method, particularly in laboratories in rural areas in Thailand.

used in this method, and underestimation compared to direct measurements has been reported when the limitation was violated. [12][13][14] Recently, several equations based on various concepts and statistical methods have been reported. Some variables such as total cholesterol (TC), TG, and high-density lipoprotein-cholesterol (HDL-C) were included to develop appropriate formulas involving multiple linear regression, pace regression, and mathematical modeling. [15][16][17] Nevertheless, most equations were developed for a target population based on specific areas, such as those identified to have higher rates of disease. For instance, the incidence of atherogenic dyslipidemia (AD) has been reported to be higher in the urban population. Further, significant differences in lipid levels and the prevalence of dyslipidemia have been reported between urban and rural areas. 18,19 In Thailand, two equations have been proposed: One equation was developed by modifying the Friedewald method, and the other equation was developed by using pace regression. 17 In the modified Friedewald, the denominator is changed from five to six. 20 While both equations were validated in using similar data (ie lipid levels from Thai people), we noted that both equations were focused on hospital data of Thai people who were mostly living in the city or urban areas. The applicability of these methods was not validated in rural residents. Thus, this study aimed to evaluate the consistency and applicability of these methods for rural area residents, particularly those in the northeastern region in Thailand. Toward this goal, we determined the agreement of LDL-C among three equations, namely

| Study design
This was a descriptive cross-sectional study that evaluated the blood and lipid profile test results of residents of Nadun district who received medical care in Nadun Hospital, Maha Sarakham Province, Thailand, between 2011 and 2017. This study was approved by the ethical committee of Khon Kaen University under the category "expedited review" status (HE612229). The study involved analysis of existing data from the hospital information system, and all data were anonymized before analysis. Thus, the need for informed consent was waived.

| Study population
Patients who have undergone lipid profile tests and whose results were recorded in the hospital information system were evaluated.
The inclusion criterion was complete laboratory results for each of the four parameters needed for the direct measurement method: TC, TG, HDL-C, and LDL-C, irrespective of their sex and age. In total, data from 1503 patients were included in the analysis.

| Method
The direct detection of lipids and lipoprotein was performed using When we needed to convert lipid parameters into mmol/L, we divided cholesterol by 38.67 and triglycerides by 88.57 and converted it back to mg/dL using the opposite mathematical method ( Figure 1).

| Statistical analysis
The patients' general characteristics were presented as descriptive statistics, including frequency, percentages, range, mean or median, interquartile range (IQR), and standard deviation (SD), based on the types and distributions of data. According to the direct measurements of TC, TG, and HDL-C were used to estimate the LDL-C. Continuous LDL-C was compared using the Bland-Altman plot and intraclass correlation (ICC), while categorical LDL-C was classified into five groups, namely <2.59, 2.59-3.34, 3.35-4.11, 4.12-4.89, and ≥4.89 mmol/L based on the Thai guideline of internal medicine using only the weighted Kappa index (K index). Agreement according to the ICC was defined as good and moderate when the ICC was >0.75 and 0.5-0.75, respectively. 21 For agreement according to weighted Kappa index, substantial and moderate agreement were defined as a K index of 0.61-0.80 and 0.41-0.60, respectively. 22 All statistical analysis were performed using STATA 15.0 software (StataCorp LLC).

| D ISCUSS I ON
This study investigated the agreement in LDL-C between the direct method and three equations. We found that the Puavilai equation showed superior agreement over the other two equations, with a high ICC not only in the overall analysis, but also in the subgroup analysis of women, subjects with diabetes, and subjects with hypertension ( where most people have been reported to be at higher risk of higher levels of LDL-C and TG and lower level of HDL-C. 30 Further studies are needed to evaluate the reliability of various equations in specific disease groups in Thailand.
In conclusion, compared to Friedewald's and Dansethakul's equation, the Puavilai equation showed better agreement with direct measurement for LDL-C. Thus, it could be considered as an alternative method to the direct method for measuring LDL-C, particularly in laboratories in rural areas.

ACK N OWLED G M ENT
We thank the director of Nadun Hospital for granting permission to access the hospital information system. This study was supported by a research grant from the Khon Kaen University Graduate School.