Summary of BMI
BMISummary<-favstats(ReviewComplete_New$BMIC)
kable(BMISummary) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
min
|
Q1
|
median
|
Q3
|
max
|
mean
|
sd
|
n
|
missing
|
|
|
16.31228
|
20.8445
|
22.03302
|
24.26559
|
30.17699
|
22.57504
|
2.891191
|
70
|
0
|
Visualising and tabulating Data
|
Concussions
|
Freq
|
|
0
|
39
|
|
1
|
15
|
|
2
|
16
|
Subject Distribution by Concussions and UE injuries categorized into 0, 1 and 2+
|
|
No Conc
|
1 Conc
|
2+Conc
|
|
0
|
25
|
8
|
6
|
|
1
|
8
|
1
|
1
|
|
2+
|
6
|
6
|
9
|
Subject Distribution by Concussions and LE injuries
##
## 0 1 2
## 0 11 6 2
## 1 4 0 0
## 2+ 24 9 14
|
|
No Conc
|
1 Conc
|
2+Conc
|
|
0
|
11
|
6
|
2
|
|
1
|
4
|
0
|
0
|
|
2+
|
24
|
9
|
14
|
Subject Distribution by Concussions and Spinal
|
|
No Conc
|
1 Conc
|
2+Conc
|
|
0
|
19
|
8
|
6
|
|
1
|
5
|
0
|
1
|
|
2+
|
15
|
7
|
9
|
Initial Exploratory Data Analysis Chisquare and Fisher’s Exact Tests
##
## Pearson's Chi-squared test
##
## data: counts
## X-squared = 10.804, df = 4, p-value = 0.02886
##
## Fisher's Exact Test for Count Data
##
## data: counts
## p-value = 0.02973
## alternative hypothesis: two.sided
##
## Pearson's Chi-squared test
##
## data: countsLE
## X-squared = 6.6571, df = 4, p-value = 0.1552
##
## Fisher's Exact Test for Count Data
##
## data: countsLE
## p-value = 0.2058
## alternative hypothesis: two.sided
##
## Pearson's Chi-squared test
##
## data: countsSpinal
## X-squared = 3.5009, df = 4, p-value = 0.4777
##
## Fisher's Exact Test for Count Data
##
## data: countsSpinal
## p-value = 0.5688
## alternative hypothesis: two.sided
Fit ordered logit model
Table of Parameter Estimates
kable(Estimates) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
Value
|
Std. Error
|
t value
|
p value
|
|
BMIC
|
0.132
|
0.091
|
1.455
|
0.146
|
|
Spinal
|
-0.019
|
0.079
|
-0.240
|
0.810
|
|
LE
|
0.017
|
0.029
|
0.571
|
0.568
|
|
UE
|
0.223
|
0.119
|
1.870
|
0.061
|
|
0|1
|
3.624
|
2.061
|
1.758
|
0.079
|
|
1|2
|
4.753
|
2.097
|
2.267
|
0.023
|
Odds Ratio for a unit change
kable(TB.Review) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
OR
|
2.5 %
|
97.5 %
|
|
BMIC
|
1.141
|
0.957
|
1.370
|
|
Spinal
|
0.981
|
0.838
|
1.156
|
|
LE
|
1.017
|
0.961
|
1.079
|
|
UE
|
1.250
|
0.996
|
1.601
|
Odds Ratio for five Unit change
kable(TB5.Review) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
|
2.5 %
|
97.5 %
|
|
BMIC
|
1.933
|
0.801
|
4.826
|
|
Spinal
|
0.910
|
0.414
|
2.067
|
|
LE
|
1.086
|
0.819
|
1.465
|
|
UE
|
3.051
|
0.982
|
10.509
|
Odds Ratio for 10 Unit change
Please note the CI is very large indicating its not at all reliable and has large SE
kable(TB10.Review) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
|
2.5 %
|
97.5 %
|
|
BMIC
|
3.735
|
0.642
|
23.290
|
|
Spinal
|
0.828
|
0.171
|
4.274
|
|
LE
|
1.180
|
0.671
|
2.145
|
|
UE
|
9.309
|
0.964
|
110.437
|
Looking at the distribution of Injuries etc., since the CI is very wide
|
Spinal
|
Freq
|
|
0
|
33
|
|
1
|
6
|
|
2+
|
31
|
Trying Logistic Regression
two-way contingency table of categorical outcome and predictors we want to make sure there are no 0 or small cells
|
|
0
|
1
|
2+
|
|
0
|
19
|
5
|
15
|
|
1+
|
14
|
1
|
16
|
|
|
0
|
1
|
2+
|
|
0
|
11
|
4
|
24
|
|
1+
|
8
|
0
|
23
|
|
|
0
|
1
|
2+
|
|
0
|
25
|
8
|
6
|
|
1+
|
14
|
2
|
15
|
Fitting Logistic Regression
Since having three categories for each of the independent variable ( LE, UE and Spinal Injury) stretches the data too far resulting in some extreme small cells with freq <= 0, we will stick with two categories of indep variables.
Make sure to convert categorical indep variables to a factor to indicate they are categorical variable.
##
## Call:
## glm(formula = ConcB_1 ~ BMIC + UE3 + LE3 + Spinal3, family = "binomial",
## data = ReviewComplete_New)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4407 -1.0201 -0.8266 1.1519 1.6296
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.90492 2.10103 -1.383 0.167
## BMIC 0.10186 0.09002 1.131 0.258
## UE31+ 0.71880 0.50968 1.410 0.158
## LE31+ 0.17498 0.63153 0.277 0.782
## Spinal31+ -0.15226 0.57194 -0.266 0.790
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 96.124 on 69 degrees of freedom
## Residual deviance: 92.274 on 65 degrees of freedom
## AIC: 102.27
##
## Number of Fisher Scoring iterations: 4
## 2.5 % 97.5 %
## (Intercept) -7.22044177 1.1213373
## BMIC -0.07133217 0.2864450
## UE31+ -0.27415774 1.7367069
## LE31+ -1.06540270 1.4399246
## Spinal31+ -1.29089156 0.9728046
|
|
OR
|
2.5 %
|
97.5 %
|
|
(Intercept)
|
0.05
|
0.00
|
3.07
|
|
BMIC
|
1.11
|
0.93
|
1.33
|
|
UE31+
|
2.05
|
0.76
|
5.68
|
|
LE31+
|
1.19
|
0.34
|
4.22
|
|
Spinal31+
|
0.86
|
0.28
|
2.65
|
Since there can be association between the UE, LE and Spinal Injuries we will look at UE and BMI only
|
|
OR
|
2.5 %
|
97.5 %
|
|
(Intercept)
|
0.07
|
0.00
|
3.02
|
|
BMIC
|
1.10
|
0.93
|
1.32
|
|
UE31+
|
2.02
|
0.76
|
5.46
|
Since there can be association between the UE, LE and Spinal Injuries we will look at LE and BMI only
|
|
OR
|
2.5 %
|
97.5 %
|
|
(Intercept)
|
0.05
|
0.00
|
2.69
|
|
BMIC
|
1.12
|
0.95
|
1.34
|
|
LE31+
|
1.19
|
0.41
|
3.61
|
Since there can be association between the UE, LE and Spinal Injuries we will look at Spinal and BMI only
|
|
OR
|
2.5 %
|
97.5 %
|
|
(Intercept)
|
0.06
|
0.00
|
2.76
|
|
BMIC
|
1.12
|
0.94
|
1.33
|
|
Spinal31+
|
1.07
|
0.40
|
2.81
|
Chisquared Test for binary outcome (Concussions) and binary predictor (UE)
## UE3
## ConcB_1 0 1+
## 0 25 14
## 1+ 14 17
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: UE.2cats.tab
## X-squared = 1.8024, df = 1, p-value = 0.1794
Chisquared Test for binary outcome (Concussions) and binary predictor (LE)
LE.2cat.Chi<-chisq.test(LE.2cats.tab)
LE.2cats.tab
## LE3
## ConcB_1 0 1+
## 0 11 28
## 1+ 8 23
LE.2cat.Chi
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: LE.2cats.tab
## X-squared = 0, df = 1, p-value = 1
Chisquared Test for binary outcome (Concussions) and binary predicto (Spinal)
Spinal.2cat.Chi<-chisq.test(Spinal.2cats.tab)
Spinal.2cats.tab
## Spinal3
## ConcB_1 0 1+
## 0 19 20
## 1+ 14 17
Spinal.2cat.Chi
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: Spinal.2cats.tab
## X-squared = 0.0030348, df = 1, p-value = 0.9561
Association between indepndent count variables UE and LE
## UE3
## LE3 0 1+
## 0 12 7
## 1+ 27 24
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: UE.LE.tab
## X-squared = 0.24474, df = 1, p-value = 0.6208
Association between indepnednet count variables UE and Spinal
## UE3
## Spinal3 0 1+
## 0 22 11
## 1+ 17 20
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: UE.Spinal.tab
## X-squared = 2.2536, df = 1, p-value = 0.1333
Association between indepnednet count variables LE and Spinal
## LE3
## Spinal3 0 1+
## 0 16 17
## 1+ 3 34
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: LE.Spinal.tab
## X-squared = 12.411, df = 1, p-value = 0.0004269
##
## Fisher's Exact Test for Count Data
##
## data: LE.Spinal.tab
## p-value = 0.0002974
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 2.472796 62.658361
## sample estimates:
## odds ratio
## 10.28369
Looking at association between outcome/Concussions (categorical) and BMI ( covariate being adjusted for)
BMI.Conc.tab<-xtabs(~ConcB_1 + BMIB, data = ReviewComplete_New)
BMI.Conc.tab
## BMIB
## ConcB_1 0 1
## 0 28 11
## 1+ 19 12
BMI.Conc.Chi<-chisq.test(BMI.Conc.tab)
BMI.Conc.Chi
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: BMI.Conc.tab
## X-squared = 0.45334, df = 1, p-value = 0.5008
Looking at association between predictor/UE (categorical) and BMI (covariate being adjusted for)
BMI.UE.tab<-xtabs(~UE3 + BMIB, data = ReviewComplete_New)
BMI.UE.tab
## BMIB
## UE3 0 1
## 0 29 10
## 1+ 18 13
BMI.UE.Chi<-chisq.test(BMI.UE.tab)
BMI.UE.Chi
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: BMI.UE.tab
## X-squared = 1.4056, df = 1, p-value = 0.2358
Looking at association between predictor/UE (3 categories) and BMI (covariate being adjusted for)
BMI.UEB.tab<-xtabs(~UE2 + BMIB, data = ReviewComplete_New)
BMI.UEB.tab
## BMIB
## UE2 0 1
## 0 29 10
## 1 5 5
## 2+ 13 8
BMI.UEB.Chi<-chisq.test(BMI.UEB.tab)
## Warning in chisq.test(BMI.UEB.tab): Chi-squared approximation may be
## incorrect
BMI.UEB.Chi
##
## Pearson's Chi-squared test
##
## data: BMI.UEB.tab
## X-squared = 2.5138, df = 2, p-value = 0.2845
looking at associations between independent variables with 3 categories for each
countsLEUE <- table(ReviewComplete_New$LE2, ReviewComplete_New$UE2)
#
countsLEUE
##
## 0 1 2+
## 0 12 3 4
## 1 2 1 1
## 2+ 25 6 16
kable(countsLEUE,col.names=c("No UE", "1 UE","2+UE")) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
No UE
|
1 UE
|
2+UE
|
|
0
|
12
|
3
|
4
|
|
1
|
2
|
1
|
1
|
|
2+
|
25
|
6
|
16
|
LE.UE.Chi<-chisq.test(countsLEUE)
## Warning in chisq.test(countsLEUE): Chi-squared approximation may be
## incorrect
LE.UE.Chi
##
## Pearson's Chi-squared test
##
## data: countsLEUE
## X-squared = 1.49, df = 4, p-value = 0.8284
countsLESpinal <- table(ReviewComplete_New$LE2, ReviewComplete_New$Spinal2)
#
countsLESpinal
##
## 0 1 2+
## 0 16 1 2
## 1 2 1 1
## 2+ 15 4 28
kable(countsLESpinal,col.names=c("No SE", "1 SE","2+SE")) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
No SE
|
1 SE
|
2+SE
|
|
0
|
16
|
1
|
2
|
|
1
|
2
|
1
|
1
|
|
2+
|
15
|
4
|
28
|
LE.SE.Chi<-chisq.test(countsLESpinal)
## Warning in chisq.test(countsLESpinal): Chi-squared approximation may be
## incorrect
LE.SE.Chi
##
## Pearson's Chi-squared test
##
## data: countsLESpinal
## X-squared = 17.065, df = 4, p-value = 0.001877
countsSEUE <- table(ReviewComplete_New$Spinal2, ReviewComplete_New$UE2)
#
countsSEUE
##
## 0 1 2+
## 0 22 3 8
## 1 3 2 1
## 2+ 14 5 12
kable(countsSEUE,col.names=c("No UE", "1 UE","2+UE")) %>%
kable_styling(bootstrap_options = "striped", full_width = F, position = "left",font_size = 14)
|
|
No UE
|
1 UE
|
2+UE
|
|
0
|
22
|
3
|
8
|
|
1
|
3
|
2
|
1
|
|
2+
|
14
|
5
|
12
|
SE.UE.Chi<-chisq.test(countsLEUE)
## Warning in chisq.test(countsLEUE): Chi-squared approximation may be
## incorrect
SE.UE.Chi
##
## Pearson's Chi-squared test
##
## data: countsLEUE
## X-squared = 1.49, df = 4, p-value = 0.8284