1 Load library

library(table1)
## 
## Attaching package: 'table1'
## The following objects are masked from 'package:base':
## 
##     units, units<-
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.1.2
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(reshape2)
## Warning: package 'reshape2' was built under R version 4.1.3
library(psych)
## Warning: package 'psych' was built under R version 4.1.2
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(readr)
library(explore)
## Warning: package 'explore' was built under R version 4.1.2
## 
## Attaching package: 'explore'
## The following object is masked from 'package:psych':
## 
##     describe
library(car)
## Warning: package 'car' was built under R version 4.1.2
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
## The following object is masked from 'package:dplyr':
## 
##     recode

2 Load data

This dataset includes the following variables: l.dia: left IMA diameter l.tamax: left tamax l.bf: left IMA flow r.dia: right IMA diameter r.tamax: right tamax r.bf: right IMA flow rx: the radiated group (1), the non-radiated group: (0) m.side: mastectomy side (0: left, 1: right) x.dia: the radiated IMA diameter cx.dia: the contralateral IMA diameter x.tamax: the radiated IMA tamax cx.tamax: the contralateral IMA tamax x.bf: the radiated IMA flow cx.bf: the contralateral IMA flow lx.dia: diameter of the left radiated IMA rx.dia: diameter of the right radiated IMA lx.tamax: tamax of the left radiated IMA rx.tamax: tamax of the right radiated IMA lx.bf: blood flow of the left radiated IMA rx.bf: blood flow of the right radiated IMA

t= "C:/Users/Macbook pro 2015/OneDrive/Documents/Thesis/IMA.csv "
dat= read.csv(t, header = T)
dat$rx=factor(dat$rx)
datx=subset(dat, rx==1)
datc= subset(dat, rx==0)
datx$m.side=factor(datx$m.side)
datxl= subset(datx, m.side==0)
datxr= subset(datx, m.side==1)
datx$x.dia= ifelse(datx$m.side==0,datx$l.dia, datx$r.dia)
datx$cx.dia= ifelse(datx$m.side==0, datx$r.dia, datx$l.dia)
datx$x.tamax= ifelse(datx$m.side==0, datx$l.tamax, datx$r.tamax)
datx$cx.tamax= ifelse(datx$m.side==0, datx$r.tamax, datx$l.tamax)
datx$x.bf= ifelse(datx$m.side==0,datx$l.bf,datx$r.bf)
datx$cx.bf= ifelse(datx$m.side==0,datx$r.bf,datx$l.bf)
datc.all.dia=melt(datc,id=c("age"), measure.vars = c("l.dia","r.dia"))
datc.all.tamax=melt(datc,id=c("age"), measure.vars = c("l.tamax","r.tamax"))
datc.all.bf=melt(datc,id=c("age"), measure.vars = c("l.bf","r.bf"))
datx.all.dia=melt(datx,id=c("age"), measure.vars = c("x.dia","cx.dia"))
datx.all.tamax=melt(datx,id=c("age"), measure.vars = c("x.tamax","cx.tamax"))
datx.all.bf= melt(datx, id=c("age"), measure.vars = c("x.bf","cx.bf"))
head(datx)
##   No  bmi hbp cad smoking diabetes      datex      datep days age m.side l.dia
## 1  1 31.0   0   0       0        0   8/8/2019 11/12/2021  827  45      0  0.17
## 2  2 21.2   0   0       0        0  12/9/2016 11/15/2021 1802  60      1  0.17
## 3  3 19.0   0   0       0        0 12/23/2017 11/12/2021 1420  55      1  0.18
## 4  4 24.0   0   0       0        0  8/21/2016 11/18/2021 1915  52      1  0.18
## 5  5 22.0   0   0       0        0   1/1/2017 11/19/2021 1783  49      1  0.19
## 6  6 23.0   0   0       0        0   1/1/2018 11/19/2021 1418  44      1  0.19
##   l.tamax   l.bf rx  r.bf r.tamax r.dia x.dia cx.dia x.tamax cx.tamax  x.bf
## 1   34.14  40.42  1 45.23   36.23  0.16  0.17   0.16   34.14    36.23 40.42
## 2   31.43  42.38  1 43.68   30.93  0.17  0.17   0.17   30.93    31.43 43.68
## 3   29.63  46.43  1 36.09   31.11  0.16  0.16   0.18   31.11    29.63 36.09
## 4   43.60  63.16  1 97.73   79.47  0.16  0.16   0.18   79.47    43.60 97.73
## 5   33.79  56.94  1 38.96   25.40  0.18  0.18   0.19   25.40    33.79 38.96
## 6   72.57 124.75  1 50.21   42.33  0.16  0.16   0.19   42.33    72.57 50.21
##    cx.bf
## 1  45.23
## 2  42.38
## 3  46.43
## 4  63.16
## 5  56.94
## 6 124.75

3 Descriptive analysis with table1

dat$hbp <- as.factor(dat$hbp)
dat$cad <- as.factor(dat$cad)
dat$diabetes <- as.factor(dat$diabetes)
dat$smoking <- as.factor(dat$smoking)
table1(~ age + bmi + hbp + cad + diabetes + smoking | rx, dat)
0
(N=108)		 1
(N=122)		 Overall
(N=230)
age
Mean (SD) 40.8 (12.2) 53.6 (8.45) 47.6 (12.2)
Median [Min, Max] 40.0 [18.0, 75.0] 53.0 [31.0, 76.0] 49.0 [18.0, 76.0]
bmi
Mean (SD) 21.8 (1.80) 21.6 (1.93) 21.7 (1.87)
Median [Min, Max] 22.0 [18.0, 26.0] 22.0 [18.0, 31.0] 22.0 [18.0, 31.0]
hbp
0 89 (82.4%) 97 (79.5%) 186 (80.9%)
1 19 (17.6%) 25 (20.5%) 44 (19.1%)
cad
0 107 (99.1%) 119 (97.5%) 226 (98.3%)
1 1 (0.9%) 3 (2.5%) 4 (1.7%)
diabetes
0 104 (96.3%) 118 (96.7%) 222 (96.5%)
1 4 (3.7%) 4 (3.3%) 8 (3.5%)
smoking
0 108 (100%) 121 (99.2%) 229 (99.6%)
1 0 (0%) 1 (0.8%) 1 (0.4%) 
datx$m.side= factor(datx$m.side)
dat$rx=factor(dat$rx)
table1(~ age+ l.dia +l.tamax + l.bf + r.dia+r.tamax+ r.bf,datc)
Overall
(N=108)
age
Mean (SD) 40.8 (12.2)
Median [Min, Max] 40.0 [18.0, 75.0]
l.dia
Mean (SD) 0.181 (0.0159)
Median [Min, Max] 0.180 [0.140, 0.220]
l.tamax
Mean (SD) 38.4 (10.2)
Median [Min, Max] 37.4 [18.2, 77.2]
l.bf
Mean (SD) 60.1 (20.3)
Median [Min, Max] 56.7 [21.8, 144]
r.dia
Mean (SD) 0.182 (0.0154)
Median [Min, Max] 0.180 [0.140, 0.220]
r.tamax
Mean (SD) 39.9 (10.8)
Median [Min, Max] 37.7 [3.41, 64.2]
r.bf
Mean (SD) 62.4 (19.0)
Median [Min, Max] 61.0 [23.2, 122] 
table1(~ age+ x.dia + x.tamax + x.bf + cx.dia + cx.tamax + cx.bf, datx)
Overall
(N=122)
age
Mean (SD) 53.6 (8.45)
Median [Min, Max] 53.0 [31.0, 76.0]
x.dia
Mean (SD) 0.172 (0.0186)
Median [Min, Max] 0.170 [0.120, 0.220]
x.tamax
Mean (SD) 38.5 (12.1)
Median [Min, Max] 36.2 [15.6, 79.5]
x.bf
Mean (SD) 55.2 (24.6)
Median [Min, Max] 52.4 [13.8, 155]
cx.dia
Mean (SD) 0.185 (0.0196)
Median [Min, Max] 0.180 [0.120, 0.270]
cx.tamax
Mean (SD) 40.7 (13.2)
Median [Min, Max] 38.4 [16.6, 86.7]
cx.bf
Mean (SD) 68.6 (32.9)
Median [Min, Max] 62.7 [10.6, 258] 
table1(~ age +x.dia + x.tamax + x.bf + cx.dia + cx.tamax +cx.bf| m.side,datx)
0
(N=63)		 1
(N=59)		 Overall
(N=122)
age
Mean (SD) 54.5 (8.74) 52.7 (8.10) 53.6 (8.45)
Median [Min, Max] 53.0 [31.0, 76.0] 52.0 [41.0, 74.0] 53.0 [31.0, 76.0]
x.dia
Mean (SD) 0.173 (0.0203) 0.171 (0.0168) 0.172 (0.0186)
Median [Min, Max] 0.180 [0.120, 0.220] 0.170 [0.130, 0.210] 0.170 [0.120, 0.220]
x.tamax
Mean (SD) 36.3 (11.9) 40.9 (12.0) 38.5 (12.1)
Median [Min, Max] 34.1 [15.6, 70.7] 37.4 [21.0, 79.5] 36.2 [15.6, 79.5]
x.bf
Mean (SD) 53.1 (26.2) 57.5 (22.7) 55.2 (24.6)
Median [Min, Max] 47.9 [13.8, 144] 55.6 [22.0, 155] 52.4 [13.8, 155]
cx.dia
Mean (SD) 0.186 (0.0235) 0.184 (0.0144) 0.185 (0.0196)
Median [Min, Max] 0.180 [0.120, 0.270] 0.180 [0.150, 0.220] 0.180 [0.120, 0.270]
cx.tamax
Mean (SD) 42.3 (12.6) 38.9 (13.7) 40.7 (13.2)
Median [Min, Max] 40.5 [16.6, 74.9] 36.4 [18.4, 86.7] 38.4 [16.6, 86.7]
cx.bf
Mean (SD) 72.9 (36.1) 64.0 (28.6) 68.6 (32.9)
Median [Min, Max] 69.1 [10.6, 258] 57.5 [27.4, 180] 62.7 [10.6, 258]

3.0.1 Age, hypertension between the groups

shapiro.test(datx$age)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$age
## W = 0.97679, p-value = 0.03337
shapiro.test(datc$age)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$age
## W = 0.98499, p-value = 0.2672
wilcox.test(datx$age, datc$age)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$age and datc$age
## W = 10614, p-value = 1.273e-15
## alternative hypothesis: true location shift is not equal to 0
cor.test(datc$age, datc$l.dia, method = "spearman")
## Warning in cor.test.default(datc$age, datc$l.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datc$age and datc$l.dia
## S = 185118, p-value = 0.2231
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.1182081
cor.test(datc$age, datc$r.dia, method="spearman")
## Warning in cor.test.default(datc$age, datc$r.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datc$age and datc$r.dia
## S = 194349, p-value = 0.4451
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## 0.07423567
cor.test(datx$age, datx$cx.dia, method = "spearman")
## Warning in cor.test.default(datx$age, datx$cx.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datx$age and datx$cx.dia
## S = 290572, p-value = 0.6632
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## 0.03981668

4 Exploratory analysis with explore

explore_all(datx)
## Warning in explore_bar(data_tmp, !!sym(var_name)): number of bars limited to 30
## by parameter max_cat

## Warning in explore_bar(data_tmp, !!sym(var_name)): number of bars limited to 30
## by parameter max_cat

explore_all(datc)

explore_all(dat)
## Warning in explore_bar(data_tmp, !!sym(var_name)): number of bars limited to 30
## by parameter max_cat

## Warning in explore_bar(data_tmp, !!sym(var_name)): number of bars limited to 30
## by parameter max_cat

5 Comparative analysis with nonparameter (Wilcoxon) test and graphical analysis

5.1 Differences between the left and right IMA in the control group

5.1.1 IMA diameter

5.1.1.1 Test of hypothesis

shapiro.test(datc$l.dia)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$l.dia
## W = 0.95547, p-value = 0.001168
qqnorm(datc$l.dia)
qqline(datc$l.dia)

shapiro.test(datc$r.dia)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$r.dia
## W = 0.94041, p-value = 0.0001109
qqnorm(datc$r.dia)
qqline(datc$r.dia)

wilcox.test(datc$l.dia, datc$r.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datc$l.dia and datc$r.dia
## W = 5669.5, p-value = 0.717
## alternative hypothesis: true location shift is not equal to 0

5.1.1.2 Histogram

p= ggplot(data=datc.all.dia, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("Distribution of IMA diameter in the control group")+ ylab("Probability")

5.1.1.3 Boxplot

p= ggplot(data=datc.all.dia, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" Boxplot of IMA diameter in control group ", y="IMA diameter (cm)")+ theme(legend.position = "none")

5.1.2 IMA tamax

5.1.2.1 Test of hypothesis

shapiro.test(datc$l.tamax)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$l.tamax
## W = 0.96997, p-value = 0.01515
qqnorm(datc$l.tamax)
qqline(datc$l.tamax)

shapiro.test(datc$r.tamax)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$r.tamax
## W = 0.95957, p-value = 0.002339
qqnorm(datc$r.tamax)
qqline(datc$r.tamax)

wilcox.test(datc$l.tamax, datc$r.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datc$l.tamax and datc$r.tamax
## W = 5361, p-value = 0.3056
## alternative hypothesis: true location shift is not equal to 0

5.1.2.2 Histogram

p= ggplot(data=datc.all.tamax, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("IMA tamax in the control group")+ ylab("Probability")

5.1.2.3 Boxplot

p= ggplot(data=datc.all.tamax, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" IMA ", y="IMA tamax")+ theme(legend.position = "none")

5.1.3 IMA blood flow

5.1.3.1 Test of hypthesis

shapiro.test(datc$l.bf)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$l.bf
## W = 0.95941, p-value = 0.002274
qqnorm(datc$l.bf)
qqline(datc$l.bf)

shapiro.test(datc$r.bf)
## 
##  Shapiro-Wilk normality test
## 
## data:  datc$r.bf
## W = 0.97807, p-value = 0.07136
qqnorm(datc$r.bf)
qqline(datc$r.bf)

wilcox.test(datc$l.bf, datc$r.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datc$l.bf and datc$r.bf
## W = 5396.5, p-value = 0.3436
## alternative hypothesis: true location shift is not equal to 0

5.1.3.2 Histogram of the left IMA blood flow

hist(datc$l.bf, prob=T, breaks=20, col="blue", border = "white", xlab = "Left IMA flow", ylab = "Number of people", xlim = c(5,150), main = "Distribution of the left IMA blood flow")
lines(density(na.omit(datc$l.bf)), col="red", lwd=3)

5.1.3.3 Histogram of the right IMA blood flow

hist(datc$r.bf, prob=T, breaks=20, col="blue", border = "white", xlab = "Right IMA flow", ylab = "Number of people", xlim = c(5,150), main = "Distribution of the right IMA blood flow")
lines(density(na.omit(datc$r.bf)), col="red", lwd=3)

5.1.3.4 Histogram in the same window

p= ggplot(data=datc.all.bf, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("IMA blood flow in the control group")+ ylab("Probability")

5.1.3.5 Boxplot

p= ggplot(data=datc.all.bf, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" IMA ", y="IMA blood flow")+ theme(legend.position = "none")

5.1.4 Conclusion

There were no statistically significant differences between the left and right IMA in the control group with regard to diameter, time-averaged maximum velocity and blood flow.

5.1.5 Calculation some other values in the control group

datc16l= subset(datc, datc$l.dia < 0.16)
count(datc16l)
##   n
## 1 6
datc20l= subset(datc, datc$l.dia >0.20)
count(datc20l)
##   n
## 1 8
datc16r = subset(datc, datc$r.dia < 0.16)
count(datc16r)
##   n
## 1 6
datc20r= subset(datc, datc$r.dia > 0.2)
count(datc20r)
##   n
## 1 5

5.2 Differences between the irradiated vs controlateral non-irradiated IMA in the Rx group

5.2.1 IMA diameter

5.2.1.1 Test of hypothesis

shapiro.test(datx$x.dia)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$x.dia
## W = 0.96582, p-value = 0.003454
qqnorm(datx$x.dia)
qqline(datx$x.dia)

shapiro.test(datx$cx.dia)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$cx.dia
## W = 0.92728, p-value = 5.564e-06
qqnorm(datx$cx.dia)
qqline(datx$cx.dia)

wilcox.test(datx$x.dia, datx$cx.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.dia and datx$cx.dia
## W = 4754.5, p-value = 7.383e-07
## alternative hypothesis: true location shift is not equal to 0

5.2.1.2 Histogram

p= ggplot(data=datx.all.dia, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("Distribution of IMA diameter in the irradiated group")+ ylab("Probability")

5.2.1.3 Boxplot

p= ggplot(data=datx.all.dia, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" Rx vs Non-Rx ", y="Boxplot of IMA diameter in the irradiated group (cm)")+ theme(legend.position = "none")

5.2.2 IMA tamax

5.2.2.1 Test of hypothesis

shapiro.test(datx$x.tamax)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$x.tamax
## W = 0.94282, p-value = 5.783e-05
qqnorm(datx$x.tamax)
qqline(datx$x.tamax)

shapiro.test(datx$cx.tamax)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$cx.tamax
## W = 0.96749, p-value = 0.004817
qqnorm(datx$cx.tamax)
qqline(datx$cx.tamax)

wilcox.test(datx$x.tamax, datx$cx.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.tamax and datx$cx.tamax
## W = 6693, p-value = 0.1745
## alternative hypothesis: true location shift is not equal to 0

5.2.2.2 Histogram

p= ggplot(data=datx.all.tamax, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("Distribution of IMA tamax in the irradiated group")+ ylab("Probability")

5.2.2.3 Boxplot

p= ggplot(data=datx.all.tamax, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" Irradiated vs Non-irradiated IMA ", y="IMA tamax in the irradiated group (cm)")+ theme(legend.position = "none")

5.2.3 IMA blood flow

5.2.3.1 Test of hypothesis

shapiro.test(datx$x.bf)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$x.bf
## W = 0.91502, p-value = 1.05e-06
qqnorm(datx$x.bf)
qqline(datx$x.bf)

shapiro.test(datx$cx.bf)
## 
##  Shapiro-Wilk normality test
## 
## data:  datx$cx.bf
## W = 0.84754, p-value = 7.063e-10
qqnorm(datx$cx.bf)
qqline(datx$cx.bf)

wilcox.test(datx$x.bf, datx$cx.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.bf and datx$cx.bf
## W = 5388.5, p-value = 0.0001959
## alternative hypothesis: true location shift is not equal to 0

5.2.3.2 Histogram of IMA blood flow in the radiated patients

p= ggplot(data=datx.all.bf, aes(x=value, fill=variable))+geom_density(alpha=0.5)
p+ xlab("Distribution of IMA blood flow in the irradiated group")+ ylab("Probability")

5.2.3.3 Boxplot

p= ggplot(data=datx.all.bf, aes(x=variable, y= value,
fill=variable, col=variable))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x="Irradiated vs Non-irradiated IMA", y="IMA blood flow")+ theme(legend.position = "none")

5.2.4 Conclusion

In the patients who received postoperative radiotherapy,there were statistically significant differences between the irradiated IMAs and the controlateral non-irradiated IMAs with regard to diameter and blood flow, however, there was no significant difference between two groups in term of time-averaged maximum velocity

5.2.5 Calculation of some other values in the irradiated group

datx.x13 = subset(datx, datx$x.dia < 0.13)
count(datx.x13)
##   n
## 1 2
datx.x16 = subset(datx, datx$x.dia < 0.16)
count(datx.x16)
##    n
## 1 22
datx.x20 = subset(datx, datx$x.dia > 0.20)
count(datx.x20)
##   n
## 1 4
datx.cx16 = subset(datx, datx$cx.dia < 0.16)
count(datx.cx16)
##   n
## 1 3
datx.cx20 = subset(datx, datx$cx.dia > 0.20)
count(datx.cx20)
##    n
## 1 15

5.2.6 When the high outliers of diameters were excluded from analysis

datx.ex = subset(datx, datx$r.dia < 0.25)
count(datx.ex)
##     n
## 1 120
wilcox.test(datx.ex$x.dia, datx.ex$cx.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx.ex$x.dia and datx.ex$cx.dia
## W = 4667.5, p-value = 1.709e-06
## alternative hypothesis: true location shift is not equal to 0
wilcox.test(datx.ex$x.bf, datx.ex$cx.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx.ex$x.bf and datx.ex$cx.bf
## W = 5337.5, p-value = 0.0005353
## alternative hypothesis: true location shift is not equal to 0

5.3 Differences between the left and right radiated IMA

5.3.1 IMA Diameter

5.3.1.1 Test of the hypothesis

wilcox.test(datxl$l.dia, datxr$r.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.dia and datxr$r.dia
## W = 1994.5, p-value = 0.4808
## alternative hypothesis: true location shift is not equal to 0

5.3.1.2 Histogram

p= ggplot(data=datx, aes(x=x.dia, fill=m.side))+geom_density(alpha=0.5)
p+ xlab("IMA diameter in the irradiated group")+ ylab("Probability")

5.3.1.3 Boxplot

p= ggplot(data=datx, aes(x=m.side, y= x.dia,
fill=m.side, col=m.side))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" left and right IMA ", y="IMA diameter in the irradiated group (cm)")+ theme(legend.position = "none")

5.3.2 Tamax

5.3.2.1 Test of the hypothesis

wilcox.test(datxl$l.tamax, datxr$r.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.tamax and datxr$r.tamax
## W = 1405, p-value = 0.0203
## alternative hypothesis: true location shift is not equal to 0

5.3.2.2 Histogram

p= ggplot(data=datx, aes(x=x.tamax, fill=m.side))+geom_density(alpha=0.5)
p+ xlab("IMA tamax in the irradiated group")+ ylab("Probability")

5.3.2.3 Boxplot

p= ggplot(data=datx, aes(x=m.side, y= x.tamax,
fill=m.side, col=m.side))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" left and right IMA ", y="IMA tamax in the irradiated group (cm)")+ theme(legend.position = "none")

5.3.3 Blood flow

5.3.3.1 Test of the hypothesis

wilcox.test(datxl$l.bf, datxr$r.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.bf and datxr$r.bf
## W = 1589.5, p-value = 0.169
## alternative hypothesis: true location shift is not equal to 0

5.3.3.2 Histogram

p= ggplot(data=datx, aes(x=x.bf, fill=m.side))+geom_density(alpha=0.5)
p+ xlab("IMA flow in the irradiated group")+ ylab("Probability")

5.3.3.3 Boxplot

p= ggplot(data=datx, aes(x=m.side, y= x.bf,
fill=m.side, col=m.side))
p + geom_boxplot(alpha=0.5)+ geom_jitter(alpha=0.3)+ labs (x=" left vs right irradiated IMA ", y=" IMA blood flow in the irradiated group (cm)")+ theme(legend.position = "none")

5.4 Differences between the radiated IMA vs the left IMA in the control group

5.4.1 Diameter

wilcox.test(datx$x.dia, datc$l.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.dia and datc$l.dia
## W = 4723.5, p-value = 0.000162
## alternative hypothesis: true location shift is not equal to 0

5.4.2 Tamax

wilcox.test(datx$x.tamax, datc$l.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.tamax and datc$l.tamax
## W = 6341, p-value = 0.6245
## alternative hypothesis: true location shift is not equal to 0

5.4.3 Blood flow

wilcox.test(datx$x.bf, datc$l.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.bf and datc$l.bf
## W = 5381, p-value = 0.01659
## alternative hypothesis: true location shift is not equal to 0

5.4.4 Conclusion

There were statistically significant differences between the radiated IMA and the left IMA in the control group with regard to diameter and blood flow, however, tamax was not significantly different between two groups

5.5 Differences between the radiated IMA and the right IMA in the control group

5.5.1 Diameter

wilcox.test(datx$x.dia, datc$r.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.dia and datc$r.dia
## W = 4540, p-value = 3.421e-05
## alternative hypothesis: true location shift is not equal to 0

5.5.2 Tamax

wilcox.test(datx$x.tamax, datc$r.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.tamax and datc$r.tamax
## W = 5884.5, p-value = 0.1628
## alternative hypothesis: true location shift is not equal to 0

5.5.3 Blood flow

wilcox.test(datx$x.bf, datc$r.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.bf and datc$r.bf
## W = 4921.5, p-value = 0.0009396
## alternative hypothesis: true location shift is not equal to 0

5.5.4 Conclusion

There were statistically significant differences between the irradiated IMA and the right IMA in the control group with regard to diameter and blood flow, however, tamax was not significantly different between two groups

5.6 Differences between the irradiated IMA and all IMA in the control group

5.6.1 Diameter

wilcox.test(datx$x.dia, datc.all.dia$value)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.dia and datc.all.dia$value
## W = 9263.5, p-value = 3.649e-06
## alternative hypothesis: true location shift is not equal to 0

5.6.2 Tamax

wilcox.test(datx$x.tamax, datc.all.tamax$value)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.tamax and datc.all.tamax$value
## W = 12226, p-value = 0.2709
## alternative hypothesis: true location shift is not equal to 0

5.6.3 Blood flow

wilcox.test(datx$x.bf, datc.all.bf$value)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx$x.bf and datc.all.bf$value
## W = 10302, p-value = 0.000869
## alternative hypothesis: true location shift is not equal to 0

5.6.4 Conclusion

There were statistically significant differences between the irradiated IMA and both IMA in the control group with regard to diameter and blood flow, however, tamax was not significantly different between two groups

5.7 Differences between the left irradiated IMA and the left IMA in the control group

5.7.1 Diameter

wilcox.test(datxl$l.dia, datc$l.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.dia and datc$l.dia
## W = 2612.5, p-value = 0.009821
## alternative hypothesis: true location shift is not equal to 0

5.7.2 Tamax

wilcox.test(datxl$l.tamax, datc$l.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.tamax and datc$l.tamax
## W = 2857, p-value = 0.08123
## alternative hypothesis: true location shift is not equal to 0

5.7.3 Blood flow

wilcox.test(datxl$l.bf, datc$l.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.bf and datc$l.bf
## W = 2559, p-value = 0.006979
## alternative hypothesis: true location shift is not equal to 0

5.7.4 Conclusion

There were statistically significant differences between the left irradiated IMA and the left IMA in the control group with regard to diameter and blood flow, however, tamax was not significantly different between two groups

5.8 Differences between the right irradiated IMA vs the right IMA in the control group

5.8.1 Diameter

wilcox.test(datxr$r.dia, datc$r.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.dia and datc$r.dia
## W = 2014.5, p-value = 6.249e-05
## alternative hypothesis: true location shift is not equal to 0

5.8.2 Tamax

wilcox.test(datxr$r.tamax, datc$r.tamax)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.tamax and datc$r.tamax
## W = 3239, p-value = 0.8605
## alternative hypothesis: true location shift is not equal to 0

5.8.3 Blood flow

wilcox.test(datxr$r.bf, datc$r.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.bf and datc$r.bf
## W = 2590, p-value = 0.04617
## alternative hypothesis: true location shift is not equal to 0

5.8.4 Conclusion

There was significant difference between the left irradiated IMA and the left IMA in the control group with regard to diameter, however, the blood flow was not significantly different between two groups.

5.9 Differences between the left irradiated IMA and the contralateral non-irradiated IMA in the Rx group

5.9.1 IMA diameter

wilcox.test(datxl$l.dia,datxl$r.dia )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.dia and datxl$r.dia
## W = 1366, p-value = 0.002266
## alternative hypothesis: true location shift is not equal to 0

5.9.2 IMA tamax

wilcox.test(datxl$l.tamax,datxl$r.tamax )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.tamax and datxl$r.tamax
## W = 1384, p-value = 0.003417
## alternative hypothesis: true location shift is not equal to 0

5.9.3 IMA blood flow

wilcox.test(datxl$l.bf,datxl$r.bf )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxl$l.bf and datxl$r.bf
## W = 1186, p-value = 9.877e-05
## alternative hypothesis: true location shift is not equal to 0

5.9.4 Conclusion:

Subgroup analysis showed that there were significant differences between the left irradiated and the controlateral non-irradiated IMA in term of the diameter, time-averaged peak systolic velocity and blood flow.

5.10 Differences between the right irradiated IMA and the left non-irradiated IMA in the Rx group

5.10.1 IMA diameter

wilcox.test(datxr$r.dia,datxr$l.dia )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.dia and datxr$l.dia
## W = 993.5, p-value = 4.075e-05
## alternative hypothesis: true location shift is not equal to 0

5.10.2 IMA tamax

wilcox.test(datxr$r.tamax,datxr$l.tamax )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.tamax and datxr$l.tamax
## W = 1950.5, p-value = 0.2595
## alternative hypothesis: true location shift is not equal to 0

5.10.3 IMA blood flow

wilcox.test(datxr$r.bf,datxr$l.bf )
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datxr$r.bf and datxr$l.bf
## W = 1529, p-value = 0.2561
## alternative hypothesis: true location shift is not equal to 0

5.10.4 Conclusion

Subgroup analysis showed that there was a significant difference between the right irradiated and the left non-irradiated IMA in term of the diameter (P < 0.0001); however, there were not significant differences in term of time-averaged peak velocity and bood flow (P= 0.19, P=0.3, respectively)

6 Correlation analysis

datx$d1 <- as.Date(datx$datex, format = "%m/%d/%y")
datx$d2 <- as.Date(datx$datep, format = "%m/%d/%y")   
datx$rx.days= datx$d2-datx$d1
datx$rx.months = datx$days/30
datx$rx.months <- as.numeric(datx$rx.months)
cor.test(datx$rx.months,datx$x.dia, method = "spearman")
## Warning in cor.test.default(datx$rx.months, datx$x.dia, method = "spearman"):
## Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datx$rx.months and datx$x.dia
## S = 357247, p-value = 0.04663
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.1805083
cor.test(datx$rx.months, datx$x.bf, method = "spearman")
## Warning in cor.test.default(datx$rx.months, datx$x.bf, method = "spearman"):
## Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datx$rx.months and datx$x.bf
## S = 353746, p-value = 0.06286
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.1689399
scatterplot(datx$days ~ datx$x.dia, pch=16, smooth=F, col="blue", lwd=2, xlab="Diameter of the radiated IMA", ylab="Time from radiation completion")

scatterplot(datx$days ~ datx$x.bf, pch=16, smooth=F, col="blue", lwd=2, xlab="Blood flow of the radiated IMA", ylab="Time from radiation completion")

scatterplot(datx$rx.months ~ datx$x.dia, pch=16, smooth=F, col="blue", lwd=2, xlab="Diameter of the radiated IMA", ylab="Time from radiation completion")

scatterplot(datx$rx.months ~ datx$x.bf, pch=16, smooth=F, col="blue", lwd=2, xlab="Blood flow of the radiated IMA", ylab="Time from radiation completion")

6.0.1 Correlation between age and diameter and BF

cor.test(datc$age, datc$l.dia, method = "spearman")
## Warning in cor.test.default(datc$age, datc$l.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datc$age and datc$l.dia
## S = 185118, p-value = 0.2231
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.1182081
cor.test(datc$age, datc$r.dia, method="spearman")
## Warning in cor.test.default(datc$age, datc$r.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datc$age and datc$r.dia
## S = 194349, p-value = 0.4451
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## 0.07423567
cor.test(datx$age, datx$cx.dia, method = "spearman")
## Warning in cor.test.default(datx$age, datx$cx.dia, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datx$age and datx$cx.dia
## S = 290572, p-value = 0.6632
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## 0.03981668
cor.test(datx$age, datx$cx.bf, method = "spearman")
## Warning in cor.test.default(datx$age, datx$cx.bf, method = "spearman"): Cannot
## compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  datx$age and datx$cx.bf
## S = 292028, p-value = 0.7019
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## 0.03500423

6.0.2 Cut-off value = 50

datx49= subset(datx,age<50)
datx50= subset(datx, age>=50)
wilcox.test(datx49$cx.dia, datx50$cx.dia)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx49$cx.dia and datx50$cx.dia
## W = 1654, p-value = 0.9736
## alternative hypothesis: true location shift is not equal to 0
wilcox.test(datx49$cx.bf, datx50$cx.bf)
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  datx49$cx.bf and datx50$cx.bf
## W = 1663, p-value = 0.9914
## alternative hypothesis: true location shift is not equal to 0

6.0.3 Time from radiotherapy completion

summary(datx$rx.months)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.367  21.017  33.650  37.933  53.983 230.567