Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Analysis of health-related quality of life using Beta regression

베타회귀분석 방법을 이용한 건강 관련 삶의 질 자료 분석

  • Jang, Eun Jin (Department of Information Statistics, Andong National University)
  • 장은진 (안동대학교 정보통계학과)
  • Received : 2017.04.18
  • Accepted : 2017.05.17
  • Published : 2017.05.31
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Abstract

The health-related quality of life data are commonly skewed and bounded with spike at the perfect health status, and the variance tended to be heteroscedastic. In this study, we have developed a prediction model for EQ-5D using linear regression model, beta regression model, and extended beta regression model with mean and precision submodel, and also compared the predictive accuracy. The extended beta regression model allows to model skewness and differences in dispersion related to covariates. Although the extended beta regression model has higher prediction accuracy than the linear regression model, the overlapped confidence intervals suggested that the extended beta regression model was superior to the linear regression model. However, the expended beta regression model could explain the heteroscedasticity and predict within the bounded range. Therefore, the expended beta regression model are appropriate for fitting the health-related quality of life data such as EQ-5D.

건강 관련 삶의 질 자료는 정규분포를 따르지 않고 치우친 분포를 보이며, 등분산 가정을 만족하지 않는 경우가 대부분이다. 또한 건강 관련 삶의 질 자료는 범위가 정해져 있는 자료이며, 건강한 상태를 나타내는 경우 최대값을 가지는 천장효과가 있는 자료이다. 본 연구에서는 건강 관련 삶의 질 자료인 EQ-5D에 대해 선형회귀모형과 베타회귀모형, 그리고 평균과 정밀도에 대한 하위모형을 가지고 있는 확장된 베타회귀모형을 이용하여 예측모형을 개발하고 모형의 예측 정확도를 비교하였다. 선형회귀모형에 비해 확장된 베타회귀모형의 예측 정확도가 높기는 하지만 신뢰구간이 겹치고 있기 때문에 확장된 베타회귀모형의 정확도가 더 높다고 할 수는 없다. 하지만 확장된 베타회귀모형은 공변량에 따라 분산이 달라지는 부분을 설명할 수 있으며 선형회귀모형이 제한된 범위를 벗어난 값을 예측하는 부분을 개선할 수 있다. 따라서 범위가 제한되고 이분산이 있는 치우친 자료에 대해 공변량들이 평균 및 정밀도에 영향을 주는 정도를 동시에 고려하는 확장된 베타회귀모형은 건강 관련 삶의 질 자료인 EQ-5D를 분석하는 방법으로 적절하다고 할 수 있다.

Keywords

References

  1. Austin P. C. (2002). A comparison of methods for analyzing health-related quality-of-life measures. Value Health, 5, 329-337. https://doi.org/10.1046/j.1524-4733.2002.54128.x
  2. Bang, S. Y. (2016). Quality of life and its related factors in patients with Korean chronic obstructive pulmonary disease. Journal of the Korean Data & Information Science Society, 27, 1349-1360. https://doi.org/10.7465/jkdi.2016.27.5.1349
  3. Brazier, J. E., Roberts, J. and Deverill, M. (2002). The estimation of a preference-based measure of health from the SF-36. Journal of Health Economics, 21, 271-292. https://doi.org/10.1016/S0167-6296(01)00130-8
  4. Brazier, J. E. and Roberts, J. (2004). The estimation of a preference-based measure of health from the SF-12. Medical Care, 42, 851-859. https://doi.org/10.1097/01.mlr.0000135827.18610.0d
  5. Conover, W. J., Johnson, M. E. and Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23, 351-361. https://doi.org/10.1080/00401706.1981.10487680
  6. Conrado, D. J., Denney, W. S. and Chen, D. (2014). An updated Alzheimer's disease progression model: Incorporating non-linearity, beta regression, and a third-level random effect in NONMEM. Journal of Pharmacokinetics and Pharmacodynamics, 41, 581-598. https://doi.org/10.1007/s10928-014-9375-z
  7. Cribari-Neto, F. and Zeileis, A. (2010). Beta regression in R. Journal of Statistical Software, 34, 1-24.
  8. Dolan, P. (1997). Modeling valuations for EuroQol health states. Medical Care, 35, 1095-108. https://doi.org/10.1097/00005650-199711000-00002
  9. Drummond, M. F., Sculpher, M. J., Torrance, G. W., O'Brien, B. J. and Stoddart, G. L. (2005). Methods for the economic evaluation of health care programmes, 3d ed., Oxford University Press, New York.
  10. EuroQol Group (1990). EuroQol-a new facility for the measurement of health-related quality of life. Health Policy, 16, 199-208. https://doi.org/10.1016/0168-8510(90)90421-9
  11. Ferrari, S. L. P. and Cribari-Neto, F. (2004). Beta regression for modeling rates and proportions. Journal of Applied Statistics, 31, 799-815. https://doi.org/10.1080/0266476042000214501
  12. Gheorghe, M., Brouwer, W. and van Baal, P. (2015). Did the health of the Dutch population improve between 2001 and 2008? investigating age- and gender-specific trends in quality of life. The European Journal of Health Economics, 16, 801-811. https://doi.org/10.1007/s10198-014-0630-4
  13. Han J. Y. and Park H. S. (2017). Factors influencing quality of health care: Based on the Korea health panel data. Journal of the Korean Data & Information Science Society, 28, 195-206. https://doi.org/10.7465/jkdi.2017.28.1.195
  14. Huang, I. C., Frangakis, C., Atkinson, M. J., Willke, R. J., Leite, W. L., Vogel, W. B. and Wu, A. W. (2008). Addressing ceiling effects in health status measures: A comparison of techniques applied to measures for people with HIV disease. Health Services Research, 43, 327-339.
  15. Hunger, M., Baumert, J. and Holle, R. (2011). Analysis of SF-6D index data: Is beta regression appropriate? Value In Health, 4, 759-767.
  16. Jeong, S. R., Doo, Y. T., and Lee, W. K. (2016). Effect on ambulatory dental visitation frequency according to pack-years of smoking. Journal of the Korean Data & Information Science Society, 27, 419-427. https://doi.org/10.7465/jkdi.2016.27.2.419
  17. Jo, M. W., Yun, S. C. and Lee, S. I. (2008). Estimating quality weights for EQ-5D health states with the time trade-off method in South Korea. Value In Health, 11, 1186-1189. https://doi.org/10.1111/j.1524-4733.2008.00348.x
  18. Kent, S., Gray, A. and Schlackow, I. (2015). Mapping from the Parkinson's disease questionnaire PDQ-39 to the generic EuroQol EQ-5D-3L: The value of mixture models. Medical Decision Making, 35, 902-911. https://doi.org/10.1177/0272989X15584921
  19. Lee, K. E. and Han, S. H. (2015). Factors affecting the health-related quality of life among male elders. International Journal of Bio-Science and Bio-Technology, 7, 65-74.
  20. Lee, Y. K., Nam, H. S., Chuang, L. H., Kim, K. Y., Yang, H. K., Kwon, I. S., Kind, P., Kweon, S. S. and Kim, Y. T. (2009). South Korean time trade-off values for EQ-5D health states: Modeling with observed values for 101 health states. Value In Health, 12, 1187-1193. https://doi.org/10.1111/j.1524-4733.2009.00579.x
  21. Longworth, L. and Rowen D. (2013). Mapping to obtain EQ-5D utility-values for use in NICE health technology assessments. Value In Health, 16, 202-210. https://doi.org/10.1016/j.jval.2012.10.010
  22. Lui, F. and Eugenio, E. C. (2016). A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression. Statistical Methods in Medical Research, Epub ahead of print.
  23. Paolino, P. (2001). Maximum likelihood estimation of models with beta-distributed dependent variables. Political Analysis, 9, 325-346. https://doi.org/10.1093/oxfordjournals.pan.a004873
  24. Powell, J. L. (1984). Least absolute deviations estimation for the censored regression model. Journal of Econometrics, 25, 303-325. https://doi.org/10.1016/0304-4076(84)90004-6
  25. Smithson, M. and Verkuilen, J. (2006). Better lemon squeezer? Maximum-likelihood regression with betadistributed dependent variables. Psychological Methods, 11, 54-71. https://doi.org/10.1037/1082-989X.11.1.54
  26. Song, T., Ding, Y., Sun, Y., He, Y. N., Qi, D., Wu, Y., Wu, B., Lang, L., Yu, K., Zhao, X., Zhu, L., Wang, S. and Yu, X. S. (2015). A population-based study on health-related quality of life among urban community residents in Shenyang, Northeast of China. BMC Public Health, 15, 921-932. https://doi.org/10.1186/s12889-015-2238-8
  27. Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26, 24-36. https://doi.org/10.2307/1907382
  28. Tutoglu, A., Boyaci, A. and Koca, I. (2014). Quality of life, depression, and sexual dysfunction in spouses of female patients with fibromyalgia. Rheumatology International, 34, 1079-1084. https://doi.org/10.1007/s00296-014-2944-z