Assignment 1
Sajjad
10/3/2017
Introduction
We are given a data set that contains the systolic vs. diastolic blood pressure of 32 participants in two different positions; their arms at their sides while lying down and standing with their arms supported at hear level. We are interested in observing the differences between these conditions and see how blood pressure might differ depending on the position of the patient.
Statistical raw data
The code chunk below reads the data set and save it as a data frame in a variable called HyperData.
HyperData <- read.delim("HyperDataAR.txt", sep = "\t")
HyperData <- as.data.frame(HyperData)Two new columns were added to the original data set containing the differences of systolic and diastolic BP between each position for each subject. The new data set was saved as BPData.
BPData <- HyperData
BPData$SystolicDifference <- HyperData$recumbent.sbp - HyperData$standing.sbp
BPData$DiastolicDifference <- HyperData$recumbent.dbp - HyperData$standing.dbp
Table 1
| SubjectID | recumbent.sbp | recumbent.dbp | standing.sbp | standing.dbp | SystolicDifference | DiastolicDifference |
|---|---|---|---|---|---|---|
| 101 | 99 | 71 | 105 | 79 | -6 | -8 |
| 102 | 126 | 74 | 124 | 76 | 2 | -2 |
| 103 | 108 | 72 | 102 | 68 | 6 | 4 |
| 104 | 122 | 68 | 114 | 72 | 8 | -4 |
| 105 | 104 | 64 | 96 | 62 | 8 | 2 |
| 106 | 108 | 60 | 96 | 56 | 12 | 4 |
The code chunk below computes arithmetic mean and median for systolic and diastolic blood pressure in different positions. Mean and median of the differences in systolic and diastolic blood pressure was calculated as well. We’ll also compute standard deviation (sd), variance, and coefficient of variation to aid us in further interpretation of the data set.
#RSA is the abbriviation for Recumbent Systolic Average
#SDA is the abbriviation for Standing Distolic Average
RSA <- mean(BPData$recumbent.sbp)
RDA <- mean(BPData$recumbent.dbp)
SSA <- mean(BPData$standing.sbp)
SDA <- mean(BPData$standing.dbp)
#RSM is the abbriviation for Recumbent Systolic Median
#SDM is the abbriviation for Standing Distolic Median
RSM <- median(BPData$recumbent.sbp)
RDM <- median(BPData$recumbent.dbp)
SSM <- median(BPData$standing.sbp)
SDM <- median(BPData$standing.dbp)
#DA stands for Difference Average, and DM stands for Difference Median
SystolicDA <- mean(BPData$SystolicDifference)
SystolicDM <- median(BPData$SystolicDifference)
DiastolicDA <- mean(BPData$DiastolicDifference)
DiastolicDM <- median(BPData$DiastolicDifference)
#Standard deviation
SDRS <- sd(BPData$recumbent.sbp)
SDRD <- sd(BPData$recumbent.dbp)
SDSS <- sd(BPData$standing.sbp)
SDSD <- sd(BPData$standing.dbp)
SDDS <- sd(BPData$SystolicDifference)
SDDD <- sd(BPData$DiastolicDifference)
#Coefficient of Variation (CV)
CVRS <- (SDRS / RSA) * 100
CVRD <- (SDRD / RDA) * 100
CVSS <- (SDSS / SSA) * 100
CVSD <- (SDRS / SDA) * 100
CVDS <- (SDDS / SystolicDA) * 100
CVDD <- (SDDD / DiastolicDA) * 100The results are presented in a new table containing all the mean and median values.
MeanMedian <- matrix(c(RSA, RSM, SDRS, CVRS, RDA, RDM, SDRD, CVRD, SSA, SSM, SDSS, CVSS, SDA, SDM, SDSD, CVSD, SystolicDA, SystolicDM, SDDS, CVDS, DiastolicDA, DiastolicDM, SDDD, CVDD), ncol = 4, byrow = TRUE)
MeanMedian <- as.data.frame(MeanMedian)
colnames(MeanMedian) <- c("Mean", "Median", "Standard Deviation", "Coefficient of Variation (%)")
rownames(MeanMedian) <- c("Recumbent Systolic BP", "Recumbent Diastolic BP", "Standing Systolic BP", "Standing Diastolic BP", "Systolic Difference", "Diastolic Difference")
Table 2
| Mean | Median | Standard Deviation | Coefficient of Variation (%) | |
|---|---|---|---|---|
| Recumbent Systolic BP | 117.40625 | 118.0 | 12.788249 | 10.89231 |
| Recumbent Diastolic BP | 73.96875 | 74.0 | 8.464287 | 11.44306 |
| Standing Systolic BP | 108.59375 | 105.5 | 15.131380 | 13.93393 |
| Standing Diastolic BP | 73.03125 | 71.0 | 10.501872 | 17.51065 |
| Systolic Difference | 8.81250 | 8.0 | 7.735288 | 87.77632 |
| Diastolic Difference | 0.93750 | 1.0 | 6.116807 | 652.45937 |
To gain better understanding of the data some of the computed values are visualized.
boxplot(BPData$recumbent.sbp, BPData$standing.sbp, BPData$recumbent.dbp, BPData$standing.dbp, names = c("Recumbent Systolic", "Standing Systolic", "Recumbent Diastolic", "Standing Diastolic"), boxwex = 0.3, col = c("grey"), xlab = "Type", ylab = "Blood pressure (mmHg)", main = "Different Types of Blood Pressure (fig. 1)", cex.axis = 0.8)
boxplot(BPData$SystolicDifference, BPData$DiastolicDifference, names = c("Systolic Difference", "Diastolic Difference"), boxwex = 0.3, col = c("grey"), xlab = "Type", ylab = "Blood pressure (mmHg)", main = "Blood Pressure Differences in Systolic and Diastolic (fig. 2)", cex.axis = 0.8)
plot(BPData$SystolicDifference, BPData$DiastolicDifference, xlab = "Differences in Systolic BP (mmHg)", ylab = "Differences in Diastolic BP (mmHg)", main = "BP Differences in Systolic and Diastolic (fig. 3)")
The code chunk below computes the 10% and 90% quantile for the different types of blood pressure and calculate the percentage of the subjects who fall within this range
QRS <- quantile(BPData$recumbent.sbp, probs = c(0.1,0.9))
NQRS <- (nrow(subset(BPData, recumbent.sbp > QRS[1] & recumbent.sbp < QRS[2]))/nrow(BPData))*100
QRD <- quantile(BPData$recumbent.dbp, probs = c(0.1,0.9))
NQRD <- (nrow(subset(BPData, recumbent.dbp > QRD[1] & recumbent.dbp < QRD[2]))/nrow(BPData))*100
QSS <- quantile(BPData$standing.sbp, probs = c(0.1,0.9))
NQSS <- (nrow(subset(BPData, standing.sbp > QSS[1] & standing.sbp < QSS[2]))/nrow(BPData))*100
QSD <- quantile(BPData$standing.dbp, probs = c(0.1,0.9))
NQSD <- (nrow(subset(BPData, standing.dbp > QSD[1] & standing.dbp < QSD[2]))/nrow(BPData))*100
QDS <- quantile(BPData$SystolicDifference, probs = c(0.1, 0.9))
NQDS <- (nrow(subset(BPData, SystolicDifference > QDS[1] & SystolicDifference < QDS[2]))/nrow(BPData))*100
QDD <- quantile(BPData$DiastolicDifference, probs = c(0.1, 0.9))
NQDD <- (nrow(subset(BPData, DiastolicDifference > QDD[1] & DiastolicDifference < QDD[2]))/nrow(BPData))*100
Table 3
| 10% Quantile | 90% Quantile | Percentage of subjects within the range (%) | |
|---|---|---|---|
| Systolic BP of recumbent subjects | 104.2 | 135.8 | 75.00 |
| Systolic BP of standing subjects | 94.0 | 127.8 | 68.75 |
| Diastolic BP of recumbent subjects | 62.2 | 85.6 | 75.00 |
| Diastolic BP of standing subjects | 60.0 | 88.0 | 68.75 |
| Differences in Systolic BP | 0.2 | 15.8 | 75.00 |
| Differences in Diastolic BP | -5.8 | 7.8 | 75.00 |
Analysis
- Glancing over figure 1, it is obvious that both of the systolic BP (recumbent and standing) are higher than the diastolic BP. The figure 2 also confirms this finding by comparing the differences between the systolic BP in different positions with the differences diastolic BP in different positions. However, the most important findings from the figure 2 is that it shows body position affects the systolic BP more than diastolic pressure. The boxplot (fig. 2) and table 2 both confirm that the mean of systolic difference is more than diastolic. Another way of confirming this finding is by interpreting the figure 3. Most of the clutter is in the middle of graph in which differences in systolic BP is 5 to 15 mmHg whereas the differences in diastolic BP is between 0 to 5 mmHg.
- Variation in systolic BP due to body position can also be confirmed by table 3, where the normal range is 0.2 to 15.8. Although the normal range for diastolic differences is -5,8 to 7.8, but the negative values indicate the inconsistency of which body position increases the diastolic BP.
- Another valuable piece of information that can be inferred from the data is the effect of standing or lying down on systolic and diastolic BP separately. Table 2 indicates that the mean of BP (both systolic and diastolic) is higher when the patient is recumbent compared to standing.
- Another noteworthy comment is the coefficient of variation (CV) for each of categories in our data set. The lower the CV, the more precise the estimation. CV of recumbent and standing systolic BP are both lower than standing counterparts which indicates more precise numbers in our data set.
- There could possibly be more statistical measures to improve our interpretation. One useful statistical measure is calculating the 95% confidence interval. Also, computing the normal distribution in the population based on our sample data set is another useful way to get a sense of the measurements in the whole population.