Confidence Interval Estimates

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%100Running header: MULTIVARIATE ANALYSIS 1 MULTIVARIATE ANALYSIS 7

Applied Biostatistics in Health

Multivariate Analysis of Body Mass Index HCM-506 Masaud Alyami S199632635 February, 2021

Introduction

Body Mass Index (BMI) is an attribute calculated through the aspects of mass and height of a person.

The body mass is usually divided by the body height square, and its unit is expressed in kg/m2. BMI values of below 20 and above 25 are attributed to high cases of mortality. Thereby, the optimal range of Body Mass Index ranges from 20-25. The tissue mass is a factor that is used to determine the overweight and un- derweight of a person. There are a variety of factors that are used to determine the bodyweight of individuals. These factors include age, diabetes, sex, and ethnicity (Emel Önal, 2019). However, in this paper, we are going to use the Framingham Heart Study dataset to perform an ANOVA multivariable regression analysis with the use of BMI as a continuous variable. The results that will be obtained will determine the factors that affect BMI in an individual. The null and alternate hypothesis of the study is described below. · H0 the BMI is not related to the patient characteristics in the Framingham Heart Study. (Null Hypothesis) · H1 the BMI is related to the patient characteristics in the Framingham Heart Study. (Alternative Hypothesis) Findings of the Study After analyzing how different concepts relate to Body Mass Index using multivariate regression, the following results were obtained: Regression Statistics

Multiple R 0.05810995

R Square 0.00337677

Adjusted R Square 0.00327301

Standard Error 4.0303178

Observations 9607

ANOVA

Df SS MS F Significance F

Regression 1 528.62284 528.62284 32.5437307 1.1999E-08

Residual 9605 156018.449 16.2434616

Total 9606 156547.071

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 24.490722 0.23904879 102.450726 0 24.022136 24.9593081 24.022136 24.9593081

AGE 0.02472912 0.00433486 5.70471128 1.1999E-08 0.01623188 0.03322636 0.01623188 0.03322636

The p-value of the analysis between Body Mass Index and age is 1.1999E-08. The p-value is less than 0.05, thereby the null hypothesis is rejected, and the alternate hypothesis is accepted. From this analysis, the BMI is related to the age of patients in the Framingham Heart Study dataset. Older people tend to have an in- creased BMI in comparison to younger individuals. At old age, people tend to be less active, making them increase their body muscles. Regression Statistics

Multiple R 0.26630323

R Square 0.07091741

Adjusted R Square 0.07082068

Standard Error 3.89135587

Observations 9607

ANOVA

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Df SS MS F Significance F

Regression 1 11101.9133 11101.9133 733.155219 1.163E-155

Residual 9605 145445.158 15.1426505

Total 9606 156547.071

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 19.3693733 0.24203325 80.0277387 0 18.8949371 19.8438095 18.8949371 19.8438095

SYSBP 0.04761088 0.00175836 27.0768392 1.163E-155 0.04416412 0.05105764 0.04416412 0.05105764

In the second regression analysis, BMI is compared to systolic blood pressure, and the p-value is ascer- tained to be 1.163E-155, which is below 0.05. Thus, the null hypothesis is rejected, and the alternate hypo- thesis is accepted. Systolic blood pressure is related to BMI according to the provided dataset. An increase in Body Mass Index also has a positive impact on the systolic blood pressure. SUMMARY OUTPUT

Regression Statistics

Multiple R 0.16159796

R Square 0.0261139

Adjusted R Square 0.02601251

Standard Error 3.98407837

Observations 9607

ANOVA

Df SS MS F Significance F

Regression 1 4088.0545 4088.0545 257.54963 3.2438E-57

Residual 9605 152459.017 15.8728805

Total 9606 156547.071

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 26.4067177 0.05408639 488.232228 0 26.3006969 26.5127384 26.3006969 26.5127384

CURSMOKE -1.3157466 0.08198639 -16.048353 3.2438E-57 -1.4764572 -1.155036 -1.4764572 -1.155036

In the third regression analysis, the Body Mass Index of patients is compared to the smoking patterns in the dataset's data. From the analysis, the p-value was determined to be 3.2438E-57, which is below 0.05; thereby, the null hypothesis is rejected. Therefore, the smoking rate of an individual can be related to their Body Mass Index. Smoking lowers the BMI of individuals by reducing their general body weight. Smokers have a decreased appetite making them not improve on their bodies. SUMMARY OUTPUT

Regression Statistics

Multiple R 0.08598698

R Square 0.00739376

Adjusted R Square 0.00729042

Standard Error 4.02218729

Observations 9607

ANOVA

Df SS MS F Significance F

Regression 1 1157.47172 1157.47172 71.5460746 3.104E-17

Residual 9605 155389.6 16.1779906

Total 9606 156547.071

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 25.7611868 0.04193192 614.357399 0 25.6789914 25.8433822 25.6789914 25.8433822

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DIABETES 1.72531564 0.20397439 8.45849127 3.104E-17 1.32548278 2.12514849 1.32548278 2.12514849

Lastly, diabetes is another aspect that is compared in the multivariate regression analysis. After analyzing the data, it was established that the p-value was 3.104E-17, which is below 0.05, and

hence the alternate hypothesis was accepted. Diabetes is a factor that relates to the Body Mass Index of pa- tients ("Incorrect body mass index range in: Does body mass index adequately convey a patient's mortality risk?" 2017). An increase in the body mass index tends to make individuals highly susceptible to

diabetes. It is attributed to the increasing levels of sugar in the blood attributed to increased body weight. Conclusion In conclusion, the Body Mass Index is an attribute related to the weight and height of an individual. BMI is a factor in human beings that is determined by a variety of factors that are prevalent in the human body. According to the multivariate analysis that was done on the Framingham Heart Study dataset, diabetes, systolic blood pressure, age, and smoking rate were determined to be the factors that are related to BMI. These factors had a p-value of less than 0.05 in the multivariate regression that was conducted. Thereby, the alternate hypothesis is accepted in this analysis, which states that BMI is related to the patient characteristics in the Framingham Heart Study.

References

Emel Önal, A. (2019). undefined. Body-mass Index and Health. DOI:10.5772/intechopen.82142

Incorrect body mass index range in: Does body mass index adequately convey a patient's mortality risk? (2017). JAMA, 309(5), 442. doi:10.1001/jama.2013.15

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