Using Tobit Model for Studying Factors Affecting Blood Pressure in Patients with Renal Failure

  • Raz Muhammad H. Karim Department of Statistics and Informatics, College of administration and Economic, University of Sulaimani, Sulaymaniyah, Iraq
  • Samira Muhamad Salh Department of Statistics and Informatics, College of administration and Economic, University of Sulaimani, Sulaymaniyah, Iraq

Abstract

In this study, the Tobit Model as a statistical regression model was used to study factors affecting blood pressure (BP) in patients with renal failure. The data have been collected from (300) patients in Shar Hospital in Sulaimani city. Those records contain BP rates per person in patients with renal failure as a response variable (Y) which is measured in units of millimeters of mercury (mmHg), and explanatory variables (Age [year], blood urea measured in milligram per deciliter [mg/dl], body mass index [BMI] expressed in units of kg/m2 [kilogram meter square], and Waist circumference measured by the Centimeter [cm]). The two levels of BP; high and low were taken from the patients. The mean arterial pressure (MAP) was used to find the average of both levels (high and low BP). The average BP rate of those patients equal to or >93.33 mmHg only remained in the dataset. The 93.33 mmHg is a normal range of MAP equal to 12/8 mmHg normal range of BP. The others have been censored as zero value, i.e., left censored. Furthermore, the same data were truncated from below. Then, in the truncated samples, only those cases under risk of BP (greater than or equal to BP 93.33mmHg) are recorded. The others were omitted from the dataset. Then, the Tobit Model applied on censored and truncated data using a statistical program (R program) version 3.6.1. The data censored and truncated from the left side at a point equal to zero. The result shows that factors age and blood urea have significant effects on BP, while BMI and Waist circumference factors have not to affect the dependent variable(y). Furthermore, a multiple regression model was found through ordinary least Square (OLS) analysis from the same data using the Stratigraphy program version 11. The result of (OLS) shows that multiple regression analysis is not a suitable model when we have censored and truncated data, whereas the Tobit model is a proficient technique to indicate the relationship between an explanatory variable, and truncated, or censored dependent variable.

References

[1] T. Amemiya. “Tobit models: A survey”. Search Results Journal of Economics, vol. 24, no. 1-2, pp. 3-61, 1984.
[2] W. Wang and M. E. Griswold. “Natural interpretations in Tobit regression models using marginal estimation methods”. Statistical Methods in Medical Research, vol. 26, no. 6, pp. 2622-2632, 2017.
[3] D. C. Crews, A. K. Bello and G. Saadi. “2019 World kidney day editorial-burden, access, and disparities in kidney disease”. Brazilian Journal of Nephrology, vol. 41, pp. 1-9, 2019.
[4] R. A. Preston, I. Singer, and M. Epstein. “Renal parenchymal hypertension: Current concepts of pathogenesis and management”. Archives of Internal Medicine, vol. 156, no. 6, pp. 602-611, 1996.
[5] J. A. Staessen, Y. Li, A. Hara, K. Asayama, E. Dolan and E. O’Brien. “Blood pressure measurement anno 2016”. American Journal of Hypertension, vol. 30, no. 5, pp. 453-463, 2017.
[6] R. N. Kundu, S. Biswas and M. Das. “Mean arterial pressure classification: A better tool for statistical interpretation of blood pressure related risk covariates”. Cardiology and Angiology: An International Journal, vol. 6, no. 1, pp. 1-7, 2017.
[7] D. Yu, Z. Zhao and D. Simmons. “Interaction between mean arterial pressure and HbA1c in prediction of cardiovascular disease hospitalisation: A population-based case-control study”. Journal of Diabetes Research, vol. 2016, p. 8714745, 2016.
[8] C. Wilson and C. A. Tisdell.“OLS and Tobit estimates: When is substitution defensible operationally?” In: Economic Theory, Applications and Issues Working Papers, University of Queensland, School of Economics, Queensland , 2002.
[9] M. H. Odah, A. S. M. Bager and B. K. Mohammed. “Tobit regression analysis applied on Iraqi bank loans”. American Journal of Applied Mathematics and Statistics, vol. 7, no. 4, p. 179, 2017.
[10] A. Prahutama, A. Rusgiyono, M. A. Mukid and T. Widiharih. “Analysis of Household Expenditures on Education in Semarang City, Indonesia Using Tobit Regression Model”. In: E3S Web of Conferences, vol. 125, p. 9016, 2019.
[11] N. M. Ahmed. “Limited Dependent Variable Modelling (Truncated and censored Regression models) with Application”. Vol. 7377. Cambridge University Press, New York, pp. 82-96, 2018.
[12] M. F. Ahmad, M. Ishtiaq, K. Hamid, M. U. Khurram and A. Nawaz. “Data envelopment analysis and Tobit analysis for firm efficiency in perspective of working capital management in manufacturing sector of Pakistan”. International Journal of Economics and Financial Issues, vol. 7, no. 2, pp. 706-713, 2017.
[13] S. Samsudin, A. S. Jaafar, S. D. Applanaidu, J. Ali and R. Majid. “Are public hospitals in Malaysia efficient? An application of DEA and Tobit analysis”. Southeast Asian Journal of Economics, vol. 4, no. 2, pp. 1-20, 2016.
[14] M. H. Odah, A. S. M. Bager and B. K. Mohammed. “Studying the determinants of divortiality in Iraq. A two-stage estimation model with tobit regression”. International Journal of Applied Mathematics and Statistics, vol. 7, no. 2, pp. 45-54, 2018.
[15] P. Zorlutuna, N. A. Erilli and B. Yücel. “Lung cancer study with tobit regression analysis: Sivas case”. Eurasian Eononometrics, Statistics and Emprical Economics Journal, vol. 3, no. 3, pp. 13-22, 2016.
[16] P. C. Anastasopoulos, A. P. Tarko and F. L. Mannering. “Tobit analysis of vehicle accident rates on interstate highways”. Accident Analysis and Prevention, vol. 40, no. 2, pp. 768-775, 2008.
[17] A. Henningsen. “Estimating censored regression models in R using the censReg Package”. R Packag Vignettes, Vol. 5. University of Copenhagen, Copenhagen, p. 12, 2010.
[18] A. C. Michalos. Encyclopedia of Quality of Life and Well-Being, Springer, Berlin, 2014.
[19] M. H. Odah. “Asymptotic least squares estimation of tobit regression model. An application in remittances of Iraqi immigrants in Romania”. International Journal of Applied Mathematics and Statistics, vol. 8, no. 2, pp. 65-71, 2018.
[20] C. Ekstrand and T. E. Carpenter. “Using a tobit regression model to analyse risk factors for foot-pad dermatitis in commercially grown broilers”. Preventive Veterinary Medicine, vol. 37, no. 1-4, pp. 219-228, 1998.
[21] J. S. Long. Regression Models for Categorical and Limited Dependent Variables. Vol. 7. Sage Publications, Thousand Oaks, 1997.
[22] A. Flaih, J. Guardiola, H. Elsalloukh and C. Akmyradov. “Statistical inference on the ESEP tobit regression model”. J. Stat. Appl. Probab. Lett., vol. 6, pp. 1-9, 2019.
[23] B. R. Humphreys. “Dealing with zeros in economic data”. University of Alberta, Department of Economics, vol. 1, pp. 1-27, 2013.
[24] K. A. M. Gajardo. “An Extension of the Normal Censored Regression”. Pontificia Universidad Catolica De Chile, Santiago, Chile, 2009.
[25] W. H. Greene. Limited Dependent Variables Truncation, Censoring and Sample Selection. Sage, Thousand Oaks, CA, 2003.
Published
2020-07-01
How to Cite
H. KARIM, Raz Muhammad; SALH, Samira Muhamad. Using Tobit Model for Studying Factors Affecting Blood Pressure in Patients with Renal Failure. UHD Journal of Science and Technology, [S.l.], v. 4, n. 2, p. 1-9, july 2020. ISSN 2521-4217. Available at: <http://journals.uhd.edu.iq/index.php/uhdjst/article/view/745>. Date accessed: 03 dec. 2020. doi: https://doi.org/10.21928/uhdjst.v4n2y2020.pp1-9.
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Articles