# Bivariate Analysis

This is a bivariate analysis where we perform the analysis on a real data set. All the data analysis procedures are applied in this article. In addition, we will fit a bivariate and a multiple linear regression to understand the baseline characteristics of the variables.

## Methods

A subset of records from the CHS changed into applied that allows you to discover the institutions among baseline measurements and the improvement of coronary heart disease (CHD) in adults ≥ 65years. Frequency and probabilities had been stated for express variables. The suggest and widespread deviations had been stated for quantitative variables with ordinary distributions while the median and interquartile stages had been stated for quantitative variables with skewed distributions. BMI, alcohol consumption, and %-of years of smoking had been converted into express variables to increase interpretability due to the fact measures of primary tendency had been now no longer appropriate.We also used the square root for physical activity and log-transformed serum insulin because they were not normally distributed continuous variables. BMI was divided into three categories: underweight/normal, overweight, and obese. Alcohol use was categorized in drinks per week: 0, >0 to 7, and >7. Finally, smoking status was transformed into pack-years of smoking: 0, >0 to 25, >25 to 50, and >50.Bivariate analyses had been used to discover the affiliation among CHD and every variable on the 6-yr follow-up (Table 1). Pearson chi-squared exams had been used to inspect the institutions of CHD and express variables, along with sex, race, ADA diabetes status,BMI, hypertension, antihypertensive medicine use, own circle of relatives' records of MI,alcohol consumption, smoking status, and percent years of smoking. A two-samplet-take a look at became used to evaluate the affiliation among CHD and general cholesterol,the simplest quantitative variable that became typically distributed. Mann-Whitney Uexams had been used to evaluate the institutions among CHD and quantitativevariables with skewed distributions, along with age, HDL cholesterol, serum insulin level, Factor VII, and bodily hobby in step with week.

Bivariate and multivariate linear Regressionhas been then used to discover baseline demographic characteristics, fitness habits,and mental measurements related to HDL LDL cholesterol on the six-yrfollow- up (Table 2). In order to decide whether or not baseline HDL LDL cholesterolranges have been predictive of incident CHD, common sense bivariate regression became appliedto evaluate the affiliation regarding HDL and coronary coronary heart ailment followedwith the aid of using multivariate logistic regression fashions to manipulate for different variables. Forthe bivariate Logistic Regression, institutions for each the HDL LDL cholesteroland apercent of standard serum LDL cholesterol variables (HDL/Total LDL cholesterol * 100)have been assessed. Pack yearssmoking and serum insulin have been eliminated from the fashions because of their correlationwith modern smoking fame and diabetes, respectively (Table 3). With theexception of the aforementioned variables, all different predictor variables have beenprotected withinside the first multivariate fashions. Variables that have been significantlyrelated to HDL LDL cholesterol in Table 2 have been excluded from the secondmultivariate logistic regression version. Finally, we carried out a multivariatelogistic regression version to decide whether or not the affiliation among baselineHDL ranges and prevalence of CHD differed with the aid of using intercourse on the 6-yr follow-up (Table four). Continuous variables – age, BMI, aspect VII, the herbal log of insulin level, the rectangular root of bodily sports consistent with week, HDL LDL cholesterol, and HDL/Total cholesterol*100 – have been mean-targeted for the linear and logistic regressions toresource the interpretations of the intercept estimates and regression results. We testedfor an interplay among intercourse and HDL for growing CHD with the aid of using developing a productof the two variables with male and girl as reference groups (Table four and 5).

A both sided significant level of 0.05 was used for the analyses, which were performed using Version 1.2.1335 of statistical software package R (R Core Team, 2017).

**Results**

Table 1

Preliminary analyses of thisbased, longitudinal study of the adult population aged 65 years old compared demographic variables (age, sex, and race) with the main variables of interest, development of CHD. A significant difference was found between the median participant's age who developed CHD and those who did not develop CHD, p = 0.034. Participants who developed CHD were slightly older than those who did not develop CHD. Also, a significant relationship was found between sex and development of CHD, p <0.001. There were no significant associations found between CHD and race, p = 0.410. Other than the demographic variables, some other factors were also tested, of which a significant association was discovered between the development of CHD and Serum insulin level, HDL cholesterol, Diabetes Status, Smoking status, and Pack-years of smoking.

Table 2

Results of the bivariate regression analysis used to assess factors associated with HDL cholesterol in females and males after 6 years of follow up indicated the following variables as significant predictors of HDL cholesterol: Age, BMI, Factor VII, Serum insulin level, Family History, Sex, Antihypertensive medication, Race and Diabetes Status. Physical activity per week was the only non-significant predictor of cholesterol in females and males after 6 years of follow up. When each of these variables was tested while accounting for the others, in a multivariate regression analysis, the number of significant predictors reduced to BMI, Factor VII, Family History, Sex, Race, and Diabetes Status.

Table 3

Table 3 summarizes the results of the logistic Regression used to compare factors associated with CHD in females and males after 6 years of follow up. The significant factors that can be used to determine whether one develops CHD. Among the significant factors are HDL, the ratio of HDL to Total Cholesterol, Age, Serum insulin level, Sex, Diabetes Status, Smoking Status (Former), Pack year smoking(>25 to 50).

Table 4

The results of the Logistic Regression for testing for interaction between sex and HDL for developing CHD after 6 years of follow up shows an insignificant association between the HDL by Sex interaction and CHD, p=0.489.

**Discussion**

This population-based, longitudinal study of adults≥65 years old was set to determine the risk factors associated with the onset and progression of coronary heart disease (CHD) and stroke. Bivariate and multivariate analyses were used to identify factors associated with CHD, factors associated with HDL cholesterol,and to determine whether HDL cholesterol level is a significant predictor of CHD development.

The resultsshow a strong association between baseline demographic characteristics and HDL cholesterol at the six-year follow- up. This is in accordance with our hypothesis that HDL cholesterol is significantly associated with CHD development.Baseline HDL cholesterol levels are predictive of incident CHD.Cardiovascular disease is the leading cause of death and disability in older adults.

Results from this population-based longitudinal study of adults≥65 years old can, therefore, be used to control cardiovascular disease, which is the leading cause of death and disability in older adults.

**Tables & Figures**

Table 1. Study Participants Characteristics and bivariate associations with the incidence of CHD after 6 years of follow up

All

N=1,000 No CHD

N=857 Developed CHD

N=143

Median (IQR) Median (IQR) Median (IQR) p-valuea

Age (years) 71.0 (68.0,76.0) 71.0 (68.0,76.0) 72.0 (69.0,79.0) 0.034*

Factor VII (%) 121.0 (105.0,139.0) 121.0 (105.0,140.0) 121.0 (103.0,139.0) 0.842

Serum insulin level (IU/ml) 13.0 (10.0,17.0) 13.0 (10.0,17.0) 14.0 (10.0,20.0) 0.010*

Total cholesterol (mg/dl) 208.8 (138.8,232.8) 209.8 (183.3,233.3) 203.8 (183.8,226.8) 0.324

Physical activity per week (kcal) 1262.5 (534.1,2760.5) 1282.5 (540.0,2771.2) 1117.5 (450.0,2765.0) 0.456

Mean (SD) Mean (SD) Mean (SD) p-valueb

HDL cholesterol (mg/dl) 26.1 (7.9) 26.4 (7.9) 24.2 (7.5) <0.001*

1 N (%) N (%) N (%) p-valuec

Sex <0.001*

Female 500 (50.0) 457 (91.4) 43 (8.6)

Male 500 (50.0) 400 (80) 100 (20)

Race 0.410

Non-black 957 (95.7) 822 (85.9) 135 (14.1)

Black 43 (4.3) 35 (81.4) 8 (18.6)

Diabetes Status <0.001*

Normal 718 (71.8) 636 (88.6)82 (11.4)

Impaired 152 (15.2) 124 (81.6) 28 (18.4)

Diabetic 130 (13) 97 (74.6) 33 (25.4)

BMI 0.419

Underweight/Normal 388 (38.8) 339 (87.4) 49 (12.6)

Overweight 442 (44.2) 372 (84.2) 70 (15.8)

Obese 170 (17) 146 (85.9) 24 (14.1)

MI family history 0.084

No 711 (71.1) 618 (86.9) 93 (13.1)

Yes 289 (28.9) 239 (82.7) 50 (17.3)

Antihypertensive medications 0.060

No623 (62.3) 544 (87.3) 79 (12.7)

Yes 377 (37.7) 313 (83.0) 64 (17.0)

Smoking status 0.038*

Never 483 (48.3) 427 (88.4) 56 (11.6)

Former 409 (40.9) 337 (82.4) 72 (17.6)

Current 108 (10.8) 93 (86.1) 15 (13.9)

Alcohol consumptions (drinks/week) 0.625

0 479 (47.9) 406 (84.8) 73 (15.2)

>0 to 7 396 (39.6) 341 (86.1) 55 (13.9)

>7 125 (12.5) 110 (88.0) 15 (12.0)

Pack year smoking 0.037*

0 483 (48.3) 427 (88.4) 56 (11.6)

>0 to 25 229 (22.9) 197 (86.0) 32 (14.0)

>25 to 50 167 (16.7) 134 (80.2) 33 (19.8)

>50 121 (12.1) 99 (81.8) 22 (18.2)

aMann Whitney test bTwo sample t-test cChi-square test *.05 Significance level

Column percentages are reported for the total sample column (All), and row percentages are reported for the No CHD and Developed CHD group columns.

Table 2. Linear Regression Analysis

Factors associated with HDL cholesterol in females and males after 6 years of follow up

Bivariate Analysis Multivariate Analysis

Coefficient Estimate (SE) 95% CI p-value Coefficient Estimate (SE) 95% CI p-value

Age (years) 0.2110 (0.084) 0.047, 0.375 0.012* 0.140 (0.900) -0.006, 0.285 0.060

BMI (kg/m2) -0.912 (0.100) -1.108, -0.717 <0.001* -0.753 (0.095) -0.938, -0.567 <0.001*

Factor VII (%) 0.0617 (0.016) 0.029, 0.094 <0.001* 0.031 (0.015) 0.001, 0.061 0.043*

Serum insulin level (IU/ml) natural log of -10.750 (0.861) -12.438, -9.061 <0.001* ------------------------------------------------------------

Physical activity per week (sqrtkcal) square root of 0.012 (0.021) -0.028, 0.053 0.555 0.006 (0.018) -0.029, 0.042 0.717

Family History MI

(yes vs no) -3.231 (1.015) -5.223, -1.238 0.002* -2.808 (0.862) -4.499, -1.117 0.001*

Sex (male vs female) -10.560 (0.863) -12.253, -8.867<0.001 -10.522 (0.865) -12.219, -8.825 <0.001*

Anti-hypertensive medication (yes vs no) -2.175 (0.952) -4.044, -0.307 0.023* -0.660 (0.825) -2.280, 0.960 0.424

Race (black vs non-black) 4.673 (2.276) 0.208, 9.138 0.040* 5.968 (1.931) 2.178, 9.758 0.002*

Diabetes Status <0.001* <0.001*

Normal (reference)

Impaired -8.016 (1.251) -10.471, -5.561 <0.001* -5.346 (1.120) -7.545, -3.147 <0.001*

Diabetic -10.688 (1.336) -13.309, -8.068 <0.001* -6.536 (1.212) -8.915, -4.158 <0.001*

Smoking Status 0.005* 0.032*

Never (reference)

Former -3.113 (0.978) -5.033, -1.193 0.002* -1.048 (0.858) -2.732, 0.636 0.222

Current -2.413 (1.550) -5.454, 0.628 0.120 -3.435 (1.332) -6.048, -0.822 0.010*

Alcohol Consumption (drinks/wk) <0.001* <0.001*

0 (reference)

>0 to 7 2.493 (0.980) 0.571, 4.416 0.011* 2.201 (0.851) 0.530, 3.872 0.010*

>7 7.714 (1.450) 4.871, 10.557 <0.001* 9.145 (1.275) 6.644, 11.647 <0.001*

Pack year smoking 0.010* ----------

0 (reference)

>0 to 25 -2.247 (1.168) -4.539, 0.045 0.055 ------------------------------------------------------------

>25 to 50 -3.277 (1.307) -5.842, -0.712 0.012*

>50 -3.901 (1.480) -6.805, -0.996 0.009*

*.05 Significance level ------------Factors not included in the multivariate model due to duplication with other factors

Table 3. Logistic Regression Analysis

Comparing factors associated with CHD in females and males after 6 years of follow up

Multivariate Model 1 Multivariate Model 2

Crude OR (95% CI) p-value Adjusted OR (95% CI) p-value Adjusted OR (95% CI) p-value

HDL (mg/dl) 0.972 (0.958, 0.985) <0.001* 0.990 (0.973, 1.006) 0.219 0.970 (0.956, 0.984) <0.001*

HDL/Total Cholesterol x 100 0.960 (0.936, 0.984) 0.001* ~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~

Age (years) 1.044 (1.012, 1.076) 0.006* 1.049 (1.015, 1.085) 0.005* 1.050 (1.018, 1.083) 0.002*

BMI (kg/m2) 1.026 (0.987, 1.066) 0.181 1.016 (0.968, 1.065) 0.504 -----------------------------------------

Factor VII (%) 0.999 (0.992, 1.005) 0.701 1.005 (0.997, 1.012) 0.205 -----------------------------------------

Serum insulin level (IU/ml) natural log of 1.756 (1.264, 2.433) 0.001* ~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~

Physical activity per week (sqrtkcal) square root of 0.998 (0.990, 1.006) 0.683 1.001 (0.993, 1.010) 0.790 1.001 (0.992, 1.009) 0.862

Family History MI

(yes vs no) 1.390 (0.951, 2.014) 0.085 1.377 (0.923, 2.037) 0.113 -----------------------------------------

Sex (male vs female) 2.657 (1.826, 3.925) <0.001* 2.445 (1.546, 3.928) <0.001* -----------------------------------------

Anti-hypertensive medication (yes vs no) 1.408 (0.982, 2.012) 0.061 1.251 (0.850, 1.833) 0.253 1.316 (0.911, 1.896) 0.141

Race (black vs non-black) 1.392 (0.589, 2.919) 0.412 1.499 (0.608, 3.324) 0.345 -----------------------------------------

Diabetes Status <0.001* 0.014* ---------

Normal (reference)

Impaired 1.751 (1.080, 2.774) 0.020* 1.506 (0.902, 2.461) 0.109 ------------------------------------------

Diabetic 2.639 (1.655, 4.140) <0.001* 2.069 (1.246, 3.393) 0.004*

Smoking Status 0.039* 0.201 ----------

Never (reference)

Former 1.629 (1.119, 2.383) 0.011* 1.411 (0.944, 2.119) 0.094 ------------------------------------------

Current 1.230 (0.647, 2.218) 0.508 1.455 (0.742, 2.723) 0.255

Alcohol Consumption (drinks/wk) 0.619 0.700 ----------

0 (reference)

>0 to 7 0.897 (0.612, 1.307) 0.574 1.017 (0.678, 1.523) 0.933 ------------------------------------------

>7 0.758 (0.405, 1.339) 0.362 0.780 (0.398, 1.453) 0.449

Pack year smoking 0.043* ~~~~~ ~~~~~~

0 (reference)

>0 to 25 1.239 (0.770, 1.962) 0.368 ~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~

>25 to 50 1.878 (1.163, 2.996) 0.010*

>50 1.694 (0.972, 2.872) 0.055

OR= Odds Ratio *.05 Significance level

~~~~~~~Factors not included in multivariate model 1 due to duplication with other factors

---------- Factors not included in multivariate model 2 due to statistically significant association with HDL (see Table 2)

Table 4. Logistic Regression for testing for interaction between sex and HDL for developing CHD after 6 years of follow up

Multivariate Model 1 Multivariate Model 2

Adjusted OR (95% CI) p-value Adjusted OR (95% CI) p-value

HDL 0.980 (0.965, 0.995) 0.010* 0.986 (0.963, 1.009) 0.245

Age 1.043 (1.011, 1.076) 0.008* 1.044 (1.011, 1.077) 0.008*

Sex (male vs female)^ 2.178 (1.451, 3.311) <0.001* 2.145 (1.413, 3.284) <0.001*

Physical activity 1.000 (0.991, 1.008) 0.911 1.000 (0.991, 1.008) 0.910

Anti-hypertensive medication 1.397 (0.963, 2.021) 0.077 1.400 (0.965, 2.026) 0.075

HDL by Sex 0.989 (0.960, 1.020) 0.489

*.05 Significance level ^reference for sex is female

Table 5. Logistic Regression for testing for interaction between sex and HDL for developing CHD after 6 years of follow up

Multivariate Model 1 Multivariate Model 2

Adjusted OR (95% CI) p-value Adjusted OR (95% CI) p-value

HDL 0.980 (0.965, 0.995) 0.010* 0.976 (0.956, 0.995) 0.016*

Age 1.043 (1.011, 1.076) 0.008* 1.044 (1.011, 1.077) 0.008*

Sex (female vs male)^ 0.459 (1.301, 2.331) <0.001* 0.466 (0.305, 0.708) <0.001*

Physical activity 1.000 (0.991, 1.008) 0.911 1.000 (0.991, 1.008) 0.910

Anti-hypertensive medication 1.397 (0.963, 2.021) 0.077 1.400 (0.965, 2.026) 0.075

HDL by Sex 1.011 (0.980, 1.041) 0.489

*.05 Significance level ^reference for sex is male