Case Study: Blood Pressure in a Clinical Trial
Background:
Suppose you are conducting a clinical trial to assess the effectiveness of a new medication in
managing blood pressure. You have collected pre-treatment and post-treatment blood pressure
measurements from a sample of 100 patients.
Data Set:
Here are the pre-treatment systolic blood pressure (SBP) measurements (in mmHg) for the 100
patients:
120,122,125,118,130,128,121,135,124,128,132,129,125,126,130,127,122,133,1
29,128,131,123,126,134,120,128,136,132,125,130,138,122,129,132,137,131,12
8,123,130,129,127,135,123,126,130,121,134,128,127,126,129,133,137,124,130,
126,122,129,130,134,128,125,133,131,128,126,130,123,128,131,129,137,122,1
25,130,134,128,126,123,135,121,127,132,128,130,129,126,124,123,120,135,13
2,127,129,123,130,136,131,125,127,124,128120,122,125,118,130,128,121,135,
124,128,132,129,125,126,130,127,122,133,129,128,131,123,126,134,120,128,1
36,132,125,130,138,122,129,132,137,131,128,123,130,129,127,135,123,126,13
0,121,134,128,127,126,129,133,137,124,130,126,122,129,130,134,128,125,133
,131,128,126,130,123,128,131,129,137,122,125,130,134,128,126,123,135,121,
127,132,128,130,129,126,124,123,120,135,132,127,129,123,130,136,131,125,1
27,124,128
Analysis:
Calculating Quartiles:
Q1 (First Quartile): Median of the first half of the data.
Q2 (Second Quartile/Median): Median of the entire dataset.
Q3 (Third Quartile): Median of the second half of the data.
Calculating Deviation:
Calculate the mean of the pre-treatment SBP data.
Determine the deviation of each pre-treatment SBP measurement from the mean.
Interpretation:
Explore how the quartiles provide insights into the distribution of pre-treatment blood pressure
in the patient population.
Analyze the deviation values to understand how much each patient's pre-treatment SBP varies
from the mean.
Post-Treatment Comparison:
Repeat the above steps for post-treatment SBP measurements.
Compare quartiles and deviations between pre-treatment and post-treatment to assess the
medication's impact.
Outcome:
Quartiles can help identify the central tendency of blood pressure in the patient population,
while deviation values indicate the variability of individual measurements.
Comparing pre-treatment and post-treatment quartiles and deviations can provide insights into
the medication's effectiveness in managing blood pressure.
This case study demonstrates how quartiles and deviation can be applied in the context of a
medical study to analyze and interpret blood pressure measurements before and after
treatment.
Case Study: Blood Pressure Measurements
Background:
Consider a study examining the blood pressure levels of a group of patients before and after a
new medication was introduced. The systolic blood pressure (SBP) readings were recorded for
each patient.
Data Set:
Let's assume we have SBP measurements (in mmHg) for a sample of 60 patients before and
after taking the medication:
Before Medication:
120,122,118,130,125,128,115,122,130,135,125,124,118,132,128,129,123,117,1
21,126,119,128,130,125,131,133,120,122,128,126,129,123,135,122,118,130,12
7,125,121,128,126,124,129,130,128,126,127,125,123,122,130,135,119,128,130,
121,123,127120,122,118,130,125,128,115,122,130,135,125,124,118,132,128,1
29,123,117,121,126,119,128,130,125,131,133,120,122,128,126,129,123,135,12
2,118,130,127,125,121,128,126,124,129,130,128,126,127,125,123,122,130,135
,119,128,130,121,123,127
After Medication:
116,118,112,125,120,123,110,118,125,130,122,121,114,128,122,124,120,112,1
16,120,115,123,128,120,129,132,118,120,124,122,125,118,130,118,116,124,12
1,118,115,122,120,121,125,128,121,120,121,118,116,119,125,130,115,124,126,
115,118,121116,118,112,125,120,123,110,118,125,130,122,121,114,128,122,1
24,120,112,116,120,115,123,128,120,129,132,118,120,124,122,125,118,130,11
8,116,124,121,118,115,122,120,121,125,128,121,120,121,118,116,119,125,130
,115,124,126,115,118,121
Step 1: Descriptive Statistics
Calculate Quartiles:
1BeforeQ1Before, 2BeforeQ2Before, 3BeforeQ3Before for before medication.
1AfterQ1After, 2AfterQ2After, 3AfterQ3After for after medication.
Calculate Mean and Deviation:
Calculate the mean SBP for both before and after medication.
Calculate the deviation of each SBP measurement from the respective mean.
Step 2: Interpretation
Identify changes in quartiles and means before and after medication.
Examine the deviation to understand the variation in blood pressure measurements for each
group.
Example Output:
Suppose you find that the mean SBP decreased after medication. The first quartile (Q1) and
third quartile (Q3) might also indicate a shift in the distribution. Additionally, analyzing
deviation could reveal how individual patients responded to the medication.
This case study can provide insights into the effectiveness of the medication in managing blood
pressure levels within the patient population. The quartiles and deviations help in
understanding the central tendency and variability in blood pressure measurements before and
after the introduction of the medication.
It seems that there might be a slight confusion or misspelling in your request. If you're referring to
quartiles and deviations in the context of a case study in medicine, I assume you're interested in
understanding how these statistical measures can be applied to medical data. However, "quartile
queviation" is not a standard term. It's possible that you meant "quartile deviation."
Let's create a hypothetical case study in medicine to illustrate the application of quartiles and deviations:
Case Study: Blood Pressure Measurements
Background:
Imagine a study conducted to assess the blood pressure levels of a group of patients in a medical clinic.
Blood pressure is a critical parameter in determining cardiovascular health.
Data Set:
The systolic blood pressure (in mmHg) of 50 patients in the study is as follows:
120,125,130,115,122,128,110,118,123,132,129,112,120,126,131,124,119,128,1
34,108,114,127,133,116,121,117,129,135,125,122,130,126,118,134,113,119,12
8,132,121,129,133,126,123,131,134,121,125,133,136120,125,130,115,122,128,
110,118,123,132,129,112,120,126,131,124,119,128,134,108,114,127,133,116,1
21,117,129,135,125,122,130,126,118,134,113,119,128,132,121,129,133,126,12
3,131,134,121,125,133,136
Step 1: Sorting the Data
Sort the data in ascending order:
108,110,112,113,114,115,116,117,118,118,119,119,120,120,121,121,121,122,1
22,123,123,124,125,125,125,126,126,126,127,128,128,128,129,129,129,130,13
0,131,131,132,132,133,133,133,134,134,134,135,136108,110,112,113,114,115,
116,117,118,118,119,119,120,120,121,121,121,122,122,123,123,124,125,125,1
25,126,126,126,127,128,128,128,129,129,129,130,130,131,131,132,132,133,13
3,133,134,134,134,135,136
Step 2: Finding Quartiles
Q1 (First Quartile): The median of the first half of the data.
In this case, (119+119)/2=119(119+119)/2=119 .
Q2 (Second Quartile/Median): The median of the entire dataset.
(125+125)/2=125(125+125)/2=125.
Q3 (Third Quartile): The median of the second half of the data.
(129+129)/2=129(129+129)/2=129.
Step 3: Calculating Deviation
Calculate the mean of the dataset: (approximately).
124.42 (approximately).
Deviation of each blood pressure measurement from the mean:
[−16.42,−14.42,−12.42,−11.42,−10.42,−9.42,−8.42,−7.42,−6.42,−6.42,−5.42,−5
.42,−4.42,−4.42,−3.42,−3.42,−3.42,−2.42,−2.42,−1.42,−1.42,0.58,0.58,0.58,0.5
8,1.58,1.58,1.58,2.58,3.58,3.58,3.58,4.58,4.58,4.58,5.58,5.58,6.58,6.58,7.58,7.5
8,8.58,8.58,8.58,9.58,9.58,9.58,10.58,11.58][−16.42,−14.42,−12.42,−11.42,−10.
42,−9.42,−8.42,−7.42,−6.42,−6.42,−5.42,−5.42,−4.42,−4.42,−3.42,−3.42,−3.42,
−2.42,−2.42,−1.42,−1.42,0.58,0.58,0.58,0.58,1.58,1.58,1.58,2.58,3.58,3.58,3.58
,4.58,4.58,4.58,5.58,5.58,6.58,6.58,7.58,7.58,8.58,8.58,8.58,9.58,9.58,9.58,10.5
8,11.58]
Step 4: Interpretation
Quartiles provide insights into the distribution of blood pressure levels in the patient group.
Deviation values show how much each blood pressure measurement varies from the mean. Negative
values indicate measurements below the mean, and positive values indicate measurements above the
mean.
This case study illustrates how quartiles and deviations can be used to analyze the distribution and
variability of blood pressure measurements in a medical context.
Case Study: Cholesterol Levels
Background:
Consider a study on cholesterol levels of patients in a clinical trial. Cholesterol levels are crucial
indicators of cardiovascular health.
Data Set:
The total cholesterol levels (in mg/dL) of 50 patients in the study are as follows:
200,210,190,180,220,215,205,195,200,225,230,185,198,212,220,207,190,215,2
30,175,185,218,235,192,210,188,220,240,210,205,225,212,195,230,182,198,21
5,228,205,222,235,200,212,225,240,198,205,235,245200,210,190,180,220,215,
205,195,200,225,230,185,198,212,220,207,190,215,230,175,185,218,235,192,2
10,188,220,240,210,205,225,212,195,230,182,198,215,228,205,222,235,200,21
2,225,240,198,205,235,245
Step 1: Calculate the Mean
Calculate the mean (average) of the cholesterol levels:
Mean=150∑�=150��Mean=501∑i=150xi
Mean=150(sum of all values)Mean=501(sum of all values)
Mean≈1090050Mean≈5010900
Mean≈218Mean≈218
Step 2: Calculate Mean Deviation
Calculate the mean deviation for each cholesterol level from the mean:
Mean Deviation=150∑�=150∣��−Mean∣Mean Deviation=501∑i=150∣xi−Mean∣
Mean Deviation=150∑�=150∣��−218∣Mean Deviation=501∑i=150∣xi−218∣
Step 3: Interpretation
Mean deviation provides a measure of the average absolute difference between each cholesterol
level and the mean cholesterol level in the patient group.
For each patient, calculate the absolute difference between their cholesterol level and the mean
(218 mg/dL).
Sum up all these absolute differences and divide by the total number of patients (50).
The mean deviation gives an indication of the average variability of cholesterol levels in the
patient group relative to the mean. A higher mean deviation suggests greater variability in
cholesterol levels.
In this case study, you would interpret the mean deviation in the context of the clinical trial to
understand how closely patients' cholesterol levels cluster around the mean value.