Modelling Hypertension and Risk Factors among Adults Using Ordinal Logistics Regression Model

There is high prevalence of hypertension and is rapidly increasing around the world, despite the intervention programme implemented, this study aimed at estimating the prevalence rate, test of association between hypertension and risk factors and model hypertension rate. Data used was obtained from the health record of Federal Medical Centre, Keffi from January 2016 – January 2019. Ordinal logistic regression model was used; Model Fitting Information, Goodness-of-Fit, Pseudo R-Square and Test of Parallel Lines are fitted to the data sets to test the accuracy and correctness of the model. The results indicated that the overall prevalence of hypertension rate is high at 36.4%, among the adult population, body mass index and gender are statistically significant, and Age is not significant in the study. Individuals that are overweight are more likely to be hypertensive compare to other weights. At age 40 – 49 years which have the highest rate of 26.5% and the odd ratio is 0.75 compared to others. One year increase in age 30 – 39, the cumulative odd of being hypertensive is 0.91 while other independent variables are held constant. The odd ratio of female being hypertensive is 0.85, therefore the females are more likely to be hypertensive with 54.4% compared to the males at 45.6% . There is no presence of multicolinearity among the variables and Logit models were formulated to calculate probabilities of the various possible outcomes. Key words; Hypertension, Risk, Factors, Ordinal Logistics Regression, Odd Ratio 1.0 Introduction According to records National Bureau of Statistics in 2019, Nigeria has a growing population of about 200 million people and this has placed it seventh, and it is considered as the most populous Black Country in the world. Nigeria is one of the many developing countries where the health services have focused on treating infectious diseases, such as malaria, typhoid and tuberculosis Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 January 2020 doi:10.20944/preprints202001.0291.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. 2 etc. but in recent years, non-communicable conditions have become an increasing problem which affect many (WHO 2013). Previous research findings revealed that hypertension is responsible for 45% of death due to heart disease and 51% of death due to stroke worldwide, and billions of people being affected globally (Addo, Smeeth & Leon, 2007; Kearney, Whelton, Reynolds, Muntner & Whelton, 2004; WHO, 2013). In the case of Nigeria, hypertension is the most common cardiovascular disease reported with the death rate of 13.62% per 100,000 population as at 2014 (Ogah, 2013; WHO 2014). This paper modelled hypertension relation to some selected risk factors among adults using ordinal logistic regression. The risk factors are Body Mass Index, Age and Gender. 2.0 Empirical Review of Previous Studies Empirical review of previous related studies was carried out in this section Okechukwu et al (2012) carried out a study on Blood pressure, prevalence of hypertension and hypertension related complications in Nigeria. The study revealed that the prevalence rate of hypertension ranges from 8% to 46.4%. The study concluded that hypertension is more common in the rural settings than the urban. In another study, Baeta (2015) conducted a multivariate time series analysis of hypertension and heart disease. The study employed the Vector Autoregressive (VAR) model and the forecast for year 2015 predicts a slight increase for heart disease cases while the monthly forecast of hypertension and disease is at the highest for September to December. Kirubel & Mojgan (2015) studied the Epidemiology of Hypertension Stages in Ghana and South Africa and some factors associated with Hypertension stages. The study revealed that the Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 January 2020 doi:10.20944/preprints202001.0291.v1

etc. but in recent years, non-communicable conditions have become an increasing problem which affect many (WHO 2013).
Previous research findings revealed that hypertension is responsible for 45% of death due to heart disease and 51% of death due to stroke worldwide, and billions of people being affected globally (Addo, Smeeth & Leon, 2007;Kearney, Whelton, Reynolds, Muntner & Whelton, 2004;WHO, 2013). In the case of Nigeria, hypertension is the most common cardiovascular disease reported with the death rate of 13.62% per 100,000 population as at 2014 (Ogah, 2013;WHO 2014).
This paper modelled hypertension relation to some selected risk factors among adults using ordinal logistic regression. The risk factors are Body Mass Index, Age and Gender.

Empirical Review of Previous Studies
Empirical review of previous related studies was carried out in this section Okechukwu et al (2012) carried out a study on Blood pressure, prevalence of hypertension and hypertension related complications in Nigeria. The study revealed that the prevalence rate of hypertension ranges from 8% to 46.4%. The study concluded that hypertension is more common in the rural settings than the urban.
In another study, Baeta (2015) conducted a multivariate time series analysis of hypertension and heart disease. The study employed the Vector Autoregressive (VAR) model and the forecast for year 2015 predicts a slight increase for heart disease cases while the monthly forecast of hypertension and disease is at the highest for September to December. Kirubel & Mojgan (2015) studied the Epidemiology of Hypertension Stages in Ghana and South Africa and some factors associated with Hypertension stages. The study revealed that the prevalence of prehypertension and hypertension in Ghana was 30.7% and 42.4%, and that of South Africa was 29.4% and 46% respectively. Ikeloluwapo et al. (2016) investigated the Prevalence of hypertension and associated Factors among Residents of Ibadan -North local Government Area of Nigeria. A descriptive crosssectional design was used involving 806 respondents. The study employed binary logistic regression model, descriptive statistics and chi-square test. The result of the binary logistic regression revealed that hypertension was associated significantly with age group 30 -49years and, 50 years and above and with overweight patients.

Method and Methodology
Secondary data is used; a total of 1304 sample size was obtained from the health record of Federal Medical Centre keffi, Nasarawa State from the period of January 2016 to January 2019.

Model Specification
Assumptions of Ordinal Logistics Regression Model are as follows: 1. Dependent variable should be measured at the ordinal level.
2. One or more independent variables are continuous, ordinal or categorical.
3. There should be no multicollinearity.
4. Presence proportional odds. Walker and Duncan (1967) was first to introduce the proportional odds model and later described in more details by McChullagh (1980). The Proportional Odds Model is used for modeling the response variable that has more than two levels with K set of explanatory variables by defining the cumulative probabilities, cumulative odds and cumulative logits.

Ordinal Logistic Regression (Proportional Odds) Model
− and the cumulative probability can be defined as 12 ( ) ( / ) ... , 1, 2,..., 1 jj x P Y j X P P P j j , is the probability of being at or below category j, given that of K set of predictors. The odds of the cumulative probability of the response variable for the 1 J − categories () ( ) , 1, 2..., 1 1 ( ) The logarithm of the odds first j -1 cumulative probability () ( represents the threshold value and which the values do not depend on the values of the independent variables, the k  's are the logistic regression coefficients.

Deviance and Likelihood Ratio Test
Given D = -2 (log likelihood of the fitted model) where D represent the deviance. On the other hand, the log of this likelihood ratio test will produce negative value. Hence, smaller values indicated a better fitted model as it deviate less from the saturated model.

3.5.2a Wald Test
The Wald test assess the significance of explanatory variables in the model and is given as:  (Agresti,1990).

3.5.2b Goodness of Fit
Goodness of fit in a statistical model described how well the model fits a set of data (Liu et al 2016). The Pearson statistics for testing goodness of fit is given as

3.5.2c Pseudo R-Square
The Pseudo R-Square summaries the proportion of variance in the outcome that can be accounted for by the explanatory variable. A Larger 2 R values indicate that more of the variation in the outcome can be explained up to a maximum of 1. There is presence of multicollinearity if the VIF value do not lie between 0 to 10. Based on the coefficients of the output, the collinearity statistics obtained VIF are 1.056, 1.056 and 1.002 therefore since the value obtained is between 1 to 10, it is concluded that there is no presence of multicollinearity. The null hypothesis is accepted the null hypothesis and conclude that there is no significant association between age and the hypertension status with value of p(0.602> 0.05).

Hypertension and Body mass index
Is there significant relationship between hypertension and body mass index (BMI)?
From the output of the cross tabulation between grouped body mass index and hypertension category revealed that 215 persons at 53.8% that are overweight are hypertensive at stage one, and 192 persons at 41.6% are pre-hypertensive, this follow by 188 persons at 55.8% are hypertensive at stage two. It shows that the tendency of overweighed patients is higher than obsessed patients at 44.3% and 36.1% respectively. It also revealed a grand total of 665 numbers of persons at 51.0% that are overweight are hypertensive which is higher than all other BMI's followed by patients of normal weight at 35.1%.
The chi square test from the test of association between body mass index and hypertension level, shows that the pvalue (0.000 < 0.05). This concludes that there is a strong significant relationship between BMI and hypertension. This shows that BMI lead to hypertension.

Hypertension and Gender
Is there significant relationship between hypertension and gender? The chi square test output has the significant level as 0.000, value p < 0.05. This indicates that there is a strong association between gender and hypertension. Therefore gender lead to hypertension in this study under reference.

Ordinal Logistic Regression Model
Ordinal logistics regression analysis a. This parameter is set to zero because it is redundant.

Interpretation of Proportional Odd model
The age group between 30 -39 and 60 -69 are statistically significant likewise normal BMI, Obese and overweight are found to be statistically associated with hypertension stages.
Only age 30 -39 is found to positively affect hypertension stages therefore it has higher contribution to hypertension while the other risk factors stages negatively affect hypertension stages have lower contribution to risk of developing hypertension. BMI has four category, The normal weight with BMI< 18.5 -24.5 has a log odd of-.678and the odd ratio is0.5076312 have more chance of being hypertensive compared to being underweight.
Obese with BMI ≥ 30 has a log odd of -1.112 being hypertensive would increase by and the odd ratio of (using R) exp(-1.112) = 0.3289005 which is significant than zero. Over weight with BMI 25.0 -29.9 has log odd of -.871 and the odd ratio is (using R) exp(-.871) = 0.4185328.
The intercepts is represented as the threshold coefficients (in terms of a logit) therefore the hypertension status is predicted into the four categories model equations From the four ordered dependent variable of hypertension level, all the 0's are the reference point since the first estimate is bigger than zero, a positive beta meaning a high rating.

Test of Model Adequacy
The test of parallel lines table shows the value of p < 0.05, therefore it is statistically significant.
This shows the independent variables and logit are the same for all logits. The null hypothesis therefore states that the slope coefficients are the same across the response categories in the model and the lines are parallel. It is concluded that the assumption holds.
The Pearson and deviance statistic is considered significant if the significant level is greater than (>) 0.05. The result from the data suggest that the model does not fit very well because the significant level is p (0.001< 0.05). it is considered that the chi-square is highly likely to be significant when your sample size is large. The null hypothesis states that the location parameters (slope coefficients) are the same across response categories.

Model
a. Link function: Logit.
b. The log-likelihood value cannot be further increased after maximum number of step-halving.
c. The Chi-Square statistic is computed based on the log-likelihood value of the last iteration of the general model. Validity of the test is uncertain.

Variables in the Equation
Step 1 The variables in the binary equation output is used to predict the probability of an event occurring based on one unit in the independent variable when all independent are kept constant. Gender is significant in the study because value of p > 0.05. From the study, it shows that the females are more hypertensive than the males with the total rates of 54.4 % and 45.6%

Discussion of Results
respectively, therefore it is confirmed that the female tends to be hypertensive than the male in the study.

Recommendations
Based on the results of this study, we recommend the following interventions be put in place in Nasarawa state to reduce the health burden of hypertension in the state.
The following recommendations are suggested; 1. Since hypertension is a modifiable risk factor associated with Age, BMI and Gender, it is important that sporting activities be introduced to manage BMI in the treatment of hypertensive patients and age range with higher risk.
2. The government should provide good and functioning healthcare centers were treatment of hypertension and other non-communicable diseases are taking seriously.
3. People should be encouraged to visit the hospital frequently for medical checkup, upon being hypertensive, must take their medication just as prescribed by a doctor and good follow-up should be done.
4. Proper sensitization of the public on hypertension should be carried out on the radio stations, sharing of flyers in motor parks and public announcement in town hall meetings on healthy living.