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Relationship between mortality and BMI

Discuss about the Formulation and Evaluation of Research Objectives.

The study sample labelled CVD-Data holds information regarding the followed up mortality labelled as “DEATH” and body mass index of the corresponding individual labelled as BMI which has 4 ordinal categories of body mass index. The following figure explains the relationship between mortality and BMI.

It is to be investigated whether patients who have a history of undergoing treatment with Drug - X on a regular basis have systolic blood pressure (SBP), diastolic blood pressure (DBP) and cholesterol level (CHL) which are significantly different as compared to that of patients who did not have a history of being treated with Drug - X.

The data collected which speaks for the information on the systolic blood pressure, diastolic blood pressure and cholesterol level are of interval scale. The information regarding whether a patient has been treated with Drug - X is represented by a categorical variable with binary levels where 0 stands for “No” and 1 stands for “Yes”.

It is therefore useful to compare the mean value of systolic blood pressure between two groups of individuals divided on the basis of the categorical variable indicating whether they were treated with Drug – X or not in order to check whether there is significant difference being effected by the Drug – X on systolic blood pressure (SBP). The difference in expected levels for diastolic blood pressure (DBP) and cholesterol level or CHL were also compared the same way to check if the application of the treatment Drug – X proved to have any significant positive effect in lowering them respectively.

One way ANOVA was done to check for the difference in levels of SBP, CHL and DBP with factor levels being taken as application of treatment Drug X. Thus there were two levels, namely, the expected or mean systolic blood pressure when drug X was used and when it was not used. If the means were found to be equal then it is said that there was no real effect of the treatment otherwise it was assumed that there is significant difference. If the SBP is found to be lower for group with history of being treated with Drug X is, it is concluded that the treatment was beneficial. The same was done for measures on Diastolic blood pressure or DBP and cholesterol level or CHL. The significance level for the tests were taken to be 5% level of significance or 0.05. ANOVA or analysis of variance tests are used to compare means of different groups. Groups or levels refer to groups in the same independent variable. ANOVA analyses the variances to test for the difference between the means of two or more groups. It tests for general differences rather than specific differences and therefore it ought to be followed up by post hoc tests such as Tukey’s HSD. The test makes use of the F-statistic which computes the ratio between the between group variance and within group variance. If the F-statistic is found to be greater than the critical value the null hypothesis which represents the no difference case is rejected.

Investigation of the effect of Drug-X on SBP, DBP, and CHL

To test whether there exists an impact on systolic blood pressure owing to the treatment of Drug X, the null hypothesis was defined as “There exists no difference between average systolic blood pressure of the group having had history of treatment with Drug X and group with no history of treatment with drug X”. Systolic blood pressure was found to be 141.03 for the group with no history of being treated by Drug X and 140.05 for groups with history of being treated by the drug X.  447 of the participants reported to have no history of being treated by the drug X whereas 950 people reported to have a history of a drug X. The grand mean of the systolic blood pressure of all the 1427 on whom data was available in the study was found to be 140.98 and the confidence interval was found to be (139.37,141.39). The between group mean squared error variation was found to be 303.593, the within group mean squared error variation was found to be 375.928 and the F-statistic was therefore found to be 0.808. The significance level which is the cut-off point for statistical significance at 0.05 or 5% level of significance was found to be 0.369. Therefore the null was failed to be rejected in favour of the alternative and it was concluded that use of treatment Drug X has no positive impact on systolic blood pressure.

To test whether there exists an impact on diastolic blood pressure owing to the treatment of Drug X, the null hypothesis was defined as “There exists no difference between average diastolic blood pressure of the group having had history of treatment with Drug X and group with no history of treatment with drug X”. Diastolic blood pressure was found to be 77.57 for the group with no history of being treated by Drug X and 77.42 for groups with history of being treated by the drug X.  447 of the participants reported to have no history of being treated by the drug X whereas 950 people reported to have a history of a drug X. The grand mean of the diastolic blood pressure of all the 1427 on whom data was available in the study was found to be 77.47 and the confidence interval was found to be (76.89, 78.06).The between group mean squared error variation was found to be 6.771, the within group mean squared error variation was found to be 126.534 and the F-statistic was therefore found to be 0.054. The significance level which is the cut-off point for statistical significance at 0.05 or 5% level of significance was found to be 0.817. Therefore the null was failed to be rejected in favour of the alternative and it was concluded that use of treatment Drug X has no positive impact on diastolic blood pressure. 

Use of ANOVA to compare means of different groups

To test whether there exists an impact on cholesterol level owing to the treatment of Drug X, the null hypothesis was defined as “There exists no difference between average cholesterol level of the group having had history of treatment with Drug X and group with no history of treatment with drug X”. Cholesterol level was found to be 181.5961 for the group with no history of being treated by Drug X and 176.6093 for groups with history of being treated by the drug X.  447 of the participants reported to have no history of being treated by the drug X whereas 952 people reported to have a history of a drug X. The grand mean of the diastolic blood pressure of all the 1429 people on whom data was available in the study was found to be 178.2739 and the confidence interval was found to be (176.3313, 180.2165). The between group mean squared error variation was found to be 7902.460, the within group mean squared error variation was found to be 1396.877 and the F-statistic was therefore found to be 5.657. The significance level which is the cut-off point for statistical significance at 0.05 or 5% level of significance was found to be 0.18. Therefore the null was rejected in favour of the alternative and it was concluded that use of treatment Drug X does have a positive impact on cholesterol level since the mean is lower for group with history of treatment with Drug X.

The following table shows the summary of the tests for SBP, DBP and CH. 

Variable

Summary Statistics

p-value

95% CI (where appropriate)

Yes Drug X

No Drug X

Systolic blood pressure

140.05

141.03

0.369

(139.37,141.39)

Diastolic blood pressure

77.42

77.57

0.817

(76.89,78.06)

Cholesterol Level

176.6093

181.5691

0.18

(176.3313,180.2165)

Therefore it is concluded that Drug X is useful for treatment for lowering cholesterol level but not enough evidence was found to suggest that it is effective for lowering diastolic blood pressure and systolic blood pressure.

It is to be tested whether there exists significant difference in SBP levels between individuals with BMI less than 25, BMI between 25 and 30 and BMI greater than 30kg/m2. The ANOVA method is used to test for the difference in mean BMI levels of the BMI groups. The mean systolic blood pressure for individuals with less than 25 BMI was found to be 138.99, the mean BMI was found to be 140.17 for the group 25 to 30, it was found to be 142.37 for the group with BMI 30 to 35 and it was found to be 141.05 for the group with BMI greater than 35. 

Descriptives

Systolic Blood Pressure

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

<25

408

138.99

18.530

.917

137.19

140.80

84

200

25 to <30

585

140.17

18.942

.783

138.63

141.71

80

200

30 to <35

298

142.37

21.300

1.234

139.94

144.80

90

204

>=35

136

141.05

19.229

1.649

137.79

144.31

80

199

Total

1427

140.38

19.388

.513

139.37

141.39

80

204

Test for impact of Drug-X on SBP, DBP, and CHL

The results of the ANOVA test show that the significance level is 0.141 which is greater than 0.05 which is the 5% level of significance and hence there is not enough evidence to say there is difference in SBP for the various BMI levels. The following table shows the summary of the ANOVA. 

ANOVA

Systolic Blood Pressure

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

2054.821

3

684.940

1.825

.141

Within Groups

533946.834

1423

375.226

Total

536001.655

1426

The relationship between age and stroke status was gauged using the independent sample t-test, whereby the mean age of the individuals who have had experience a stroke and those who have not were compare to see whether individuals of older age have a stroke or is it more prone for those who are of younger age or if it is more or less same, making the average ages at which one experiences stroke not being statistically much different. The null hypothesis was then taken to be “Age of individuals who have had strokes is same as that of those who have not had strokes”. This was tested against an alternative testing that there is a general significant difference. The mean age of those who have had stroke was observed to be equal to 71.1082 and those who have not had stroke was observed to be 71.9504. 

Group Statistics

Previous stroke

N

Mean

Std. Deviation

Std. Error Mean

Age

No

1406

71.9504

8.53021

.22749

Yes

23

71.1082

9.99297

2.08368

The difference in the means of the two groups was found to be equal to 0.84227.The p-value of the test was observed to be 0.199 which is greater than 0.05, which is the assumed level of significance of the test. Hence the null hypothesis was rejected in favor of the alternate hypothesis. 

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Age

Equal variances assumed

1.649

.199

.468

1427

.640

.84227

1.79830

-2.68533

4.36986

Equal variances not assumed

.402

22.528

.692

.84227

2.09606

-3.49880

5.18334

Considering the DBP dataset, data on the blood pressure of the 35 subjects in a clinical trial on whom the dataset is based was compared for before and after 10 days of a particular treatment. It is to be determined whether the treatment had a positive impact in lowering their blood pressure levels. Since the data is available on the before and after status of the individuals, a pairwise t-test could be employed to test whether significant change has occurred for the same individual. This the difference in blood pressure levels could be considered and it could be tested whether there is zero difference in the before and after levels on blood pressure or not. The null hypothesis assumed thus can be stated to be “There is no difference in blood pressure level for before and after the treatment” against the alternative that there is some positive difference. The mean of the baseline blood pressure or DBP was found to be 105.9714 and that of the end of study DBP was found to be 81.0857. 

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Baseline DBP

105.9714

35

13.86380

2.34341

End of Study DBP

81.0857

35

12.84150

2.17061

The mean difference in the baseline and end of study DBP was found to be 24.8857 with a confidence interval estimate of 19.138 lower bound and 30.633 upper bound. The p-value was found to be less than 0.05 and hence it was found to be significant at 0.05 level of significance. Therefore the null was rejected at 5% level of significance implying that the treatment was indeed effective in lowering blood pressure. The following table gives the summary results of the paired sample t test. 

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Baseline DBP - End of Study DBP

24.88571

16.73104

2.82806

19.13840

30.63303

8.800

34

.000

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