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

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.