2019-06-20-DASH Score (HTNST=1,2 and 3)
Zhaohu(Jonathan) Fan and Yichen Qin
- 1 HTNST dataset
- 2 The SuperWin scoring system(HTNST=1)
- 3 The Gunther’s scoring system(HTNST=1)
- 4 Correlation between Gunther and SuperWIN (HTNST=1)
- 5 The SuperWIN scoring system (HTNST=2)
- 6 The Gunther’s scoring system(HTNST=2)
- 7 Correlation between Gunther and SuperWIN (HTNST=2)
- 8 The SuperWIN scoring system (HTNST=3)
- 9 The Gunther’s scoring system(HTNST=3)
- 10 Correlation between Gunther and SuperWIN (HTNST=3)
1 HTNST dataset
We separate all the patients into four different data sets by their HTNST (hypertension status=1, 2, 3, 4). The corresponding sample size are given as follows
DASH_Score_HTNST1=subset(DASH_Score, DASH_Score$HTNST==1)
n1=dim(DASH_Score_HTNST1)[1]
n1## [1] 101DASH_Score_HTNST2=subset(DASH_Score, DASH_Score$HTNST==2)
n2=dim(DASH_Score_HTNST2)[1]
n2## [1] 62DASH_Score_HTNST3=subset(DASH_Score, DASH_Score$HTNST==3)
n3=dim(DASH_Score_HTNST3)[1]
n3## [1] 8DASH_Score_HTNST4=subset(DASH_Score, DASH_Score$HTNST==4)
n4=dim(DASH_Score_HTNST4)[1]
n4## [1] 12 The SuperWin scoring system(HTNST=1)
2.1 Scatterplots of SuperWIN DASH Score vs SBP/DBP
Figures of SuperWIN DASH Scores vs SBP/DBP
par(mfrow=c(1,2))
plot(DASHSC_SuperWIN,SBP, pch = 20)
plot(DASHSC_SuperWIN,DBP, pch = 20)
2.2 Correlation between SuperWIN DASH Score and SBP/DBP
From Wiki
- In statistics, the Pearson correlation coefficient, also referred to as Pearson’s r, the Pearson product-moment correlation coefficient (PPMCC) or the bivariate correlation, is a measure of the linear correlation between two variables X and Y.
Given paired data \({\displaystyle \left\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\right\}}\) consisting of n pairs, \(r_{xy}\) is defined as:
\({\displaystyle r_{xy}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{{\sqrt {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i=1}^{n}(y_{i}-{\bar {y}})^{2}}}}}}\)
where n is sample size, \(x_{i},y_{i}\) are the individual sample points indexed with i, \(\bar {x}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}\) and analogously for \(\bar{y}\).
- In statistics, Spearman’s rank correlation coefficient or Spearman’s \(\rho\), is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function.
For a sample of size n, the n raw scores \(X_{i},Y_{i}\) are converted to ranks \(\operatorname {rg} X_{i}\), \(\operatorname {rg} Y_{i}\) and \(r_{s}\) is computed from:
\({\displaystyle r_{s}=\rho _{\operatorname {rg} _{X},\operatorname {rg} _{Y}}={\frac {\operatorname {cov} (\operatorname {rg} _{X},\operatorname {rg} _{Y})}{\sigma _{\operatorname {rg} _{X}}\sigma _{\operatorname {rg} _{Y}}}}}\)
where \(\rho\) denotes the usual Pearson correlation coefficient, but applied to the rank variables. \(\operatorname {cov} (\operatorname {rg}_{X},\operatorname {rg}_{Y})\) is the covariance of the rank variables. \(\sigma_{\operatorname {rg} _{X}}\) and \(\sigma_{\operatorname{rg}_{Y}}\) are the standard deviations of the rank variables.
- In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall’s \(\tau\) coefficient, is a statistic used to measure the ordinal association between two measured quantities. A tau test is a non-parametric hypothesis test for statistical dependence based on the tau coefficient.
Let (\(x_1\), \(y_1\)), (\(x_2\), \(y_2\)), …, (\(x_n\), \(y_n\)) be a set of observations of the joint random variables X and Y respectively, such that all the values of ( \({\displaystyle x_{i}}\) ) and ( \({\displaystyle y_{i}}\)) are unique. Any pair of observations \({\displaystyle (x_{i},y_{i})}\) and \({\displaystyle (x_{j},y_{j})}\), where \({\displaystyle i<j}\), are said to be concordant if the ranks for both elements (more precisely, the sort order by x and by y) agree: that is, if both \({\displaystyle x_{i}>x_{j}}\) and \({\displaystyle y_{i}>y_{j}}\); or if both \({\displaystyle x_{i}<x_{j}}\) and \({\displaystyle y_{i}<y_{j}}\) . They are said to be discordant, if \({\displaystyle x_{i}>x_{j}}\) and \({\displaystyle y_{i}<y_{j}}\); or if \({\displaystyle x_{i}<x_{j}}\) and \({\displaystyle y_{i}>y_{j}}\). If \({\displaystyle x_{i}=x_{j}}\) or \({\displaystyle y_{i}=y_{j}}\), the pair is neither concordant nor discordant.
The Kendall \(\tau\) coefficient is defined as:
\({\displaystyle \tau ={\frac {({\text{number of concordant pairs}})-({\text{number of discordant pairs}})}{n(n-1)/2}}.}\)
We have pearson correlation as follows:
data111=data.frame(DASHSC_SuperWIN,SBP,DBP)
cor(data111, use="complete.obs", method="pearson") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.0000000 -0.17693881 -0.23834799
## SBP -0.1769388 1.00000000 -0.03844316
## DBP -0.2383480 -0.03844316 1.00000000We have spearman correlation as follows:
cor(data111, use="complete.obs", method="spearman") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.0000000 -0.15666968 -0.28233730
## SBP -0.1566697 1.00000000 -0.01330125
## DBP -0.2823373 -0.01330125 1.00000000We have kendall correlation as follows:
cor(data111, use="complete.obs", method="kendall") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.0000000 -0.111159691 -0.183487264
## SBP -0.1111597 1.000000000 -0.007433014
## DBP -0.1834873 -0.007433014 1.0000000002.3 Linear Regression
We build a linear regression with SBP/DBP as response and dash score as regressor with other covariates including age, sex, HTNST,WTKG,HTM,HTPCT,BMIcal,BMIPCT, DMETS, sleep,lightmin, Modmin, hardmin, vhardmin and actweek.
2.3.1 SBP as response
As a rule of thumb, a VIF value that exceeds 10 indicates a problematic amount of collinearity (James et al. 2014). Hence, we calculate variance-inflation factor to chek the multicollinearity in the model. We then update our model by removing the the predictor variables (WTKG,HTM, BMIcal, Sleep,lightmin,modmin,hardmin, actweek) with high VIF value. In our final proposed model, we can see that dash score is not statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = SBP ~ DASHSC_SuperWIN + Age + as.factor(Sex) + HTM +
## HTPCT + BMIcal + BMIPCT + DMETS + hardmin + vhardmin, data = data21)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.4706 -2.4327 0.7348 2.2451 7.8765
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 79.269708 11.777844 6.730 1.53e-09 ***
## DASHSC_SuperWIN -0.038593 0.037875 -1.019 0.31096
## Age 0.509630 0.332188 1.534 0.12850
## as.factor(Sex)2 -2.232490 1.195335 -1.868 0.06506 .
## HTM 23.656104 7.942889 2.978 0.00372 **
## HTPCT 0.012547 0.025378 0.494 0.62221
## BMIcal -0.101670 0.056546 -1.798 0.07553 .
## BMIPCT -0.006880 0.033169 -0.207 0.83616
## DMETS 0.116584 0.141633 0.823 0.41261
## hardmin -0.001458 0.002863 -0.509 0.61186
## vhardmin -0.008446 0.005817 -1.452 0.15001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.807 on 90 degrees of freedom
## Multiple R-squared: 0.4785, Adjusted R-squared: 0.4205
## F-statistic: 8.257 on 10 and 90 DF, p-value: 2.32e-09`
2.3.2 DBP as response
Similarly, we calculate variance-inflation factor to chek the multicollinearity in the model. Then, we update our model by removing the the predictor variables(WTKG, Sleep,lightmin,modmin,actweek) with high VIF value. We can see that dash score is statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = DBP ~ DASHSC_SuperWIN + Age + as.factor(Sex) + HTM +
## HTPCT + BMIcal + BMIPCT + DMETS + hardmin + vhardmin, data = data22)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.895 -4.236 1.523 5.191 12.533
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.021e+02 2.334e+01 4.373 3.29e-05 ***
## DASHSC_SuperWIN -1.752e-01 7.507e-02 -2.334 0.0218 *
## Age 7.487e-01 6.584e-01 1.137 0.2585
## as.factor(Sex)2 4.674e-01 2.369e+00 0.197 0.8441
## HTM -1.158e+01 1.574e+01 -0.735 0.4640
## HTPCT 8.004e-04 5.030e-02 0.016 0.9873
## BMIcal 2.049e-01 1.121e-01 1.828 0.0708 .
## BMIPCT -8.936e-02 6.574e-02 -1.359 0.1775
## DMETS -3.557e-01 2.807e-01 -1.267 0.2084
## hardmin 5.458e-03 5.674e-03 0.962 0.3387
## vhardmin 1.577e-02 1.153e-02 1.368 0.1749
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.546 on 90 degrees of freedom
## Multiple R-squared: 0.1429, Adjusted R-squared: 0.04771
## F-statistic: 1.501 on 10 and 90 DF, p-value: 0.1523 The Gunther’s scoring system(HTNST=1)
3.1 Scatterplots of Gunther DASH Score vs SBP/DBP
Figures of Gunther Dash Scores vs SBP/DBP.
par(mfrow=c(1,2))
plot(DASHSC_Gunther,SBP,pch=20)
plot(DASHSC_Gunther,DBP,pch=20)
3.2 Correlation between Gunther DASH Score and SBP
We have pearson correlation as follows:
## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.0000000 -0.11678900 -0.22683921
## SBP -0.1167890 1.00000000 -0.03844316
## DBP -0.2268392 -0.03844316 1.00000000We have spearman correlation as follows:
cor(data222, use="complete.obs", method="spearman") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 -0.09292451 -0.24604678
## SBP -0.09292451 1.00000000 -0.01330125
## DBP -0.24604678 -0.01330125 1.00000000We have kendall correlation as follows:
cor(data222, use="complete.obs", method="kendall") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 -0.063200483 -0.161356125
## SBP -0.06320048 1.000000000 -0.007433014
## DBP -0.16135612 -0.007433014 1.0000000003.3 Linear Regression
We build a linear regression with SBP/DBP as response and dash score as regressor with other covariates including age, sex, HTNST,WTKG,HTM,HTPCT,BMIcal,BMIPCT, DMETS, sleep,lightmin, Modmin, hardmin, vhardmin and actweek.
3.3.1 SBP as response
Again, we calculate variance-inflation factor to chek the multicollinearity in the model. Then, We update our model by removing the the predictor variables(WTKG, Sleep,lightmin,modmin,actweek) with high VIF value. We can see that dash score is not statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = SBP ~ DASHSC_Gunther + Age + +as.factor(Sex) + HTM +
## HTPCT + BMIcal + BMIPCT + DMETS + hardmin + vhardmin, data = data11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.0804 -2.5092 0.6457 2.2979 7.9679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 80.292604 11.778530 6.817 1.03e-09 ***
## DASHSC_Gunther -0.066594 0.050950 -1.307 0.19453
## Age 0.496350 0.331371 1.498 0.13767
## as.factor(Sex)2 -2.404417 1.204911 -1.996 0.04901 *
## HTM 23.626086 7.906586 2.988 0.00362 **
## HTPCT 0.012185 0.025287 0.482 0.63106
## BMIcal -0.097479 0.056570 -1.723 0.08830 .
## BMIPCT -0.008877 0.033036 -0.269 0.78878
## DMETS 0.113209 0.141148 0.802 0.42463
## hardmin -0.001265 0.002861 -0.442 0.65933
## vhardmin -0.008146 0.005797 -1.405 0.16344
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.793 on 90 degrees of freedom
## Multiple R-squared: 0.4823, Adjusted R-squared: 0.4247
## F-statistic: 8.384 on 10 and 90 DF, p-value: 1.719e-093.3.2 DBP as response
Similarly, we calculate variance-inflation factor to chek the multicollinearity in the model. Then, We update our model by removing the the predictor variables(WTKG, Sleep,lightmin,modmin,actweek) with high VIF value. We can see that dash score is statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = DBP ~ DASHSC_Gunther + Age + as.factor(Sex) + HTM +
## HTPCT + BMIcal + BMIPCT + DMETS + hardmin + vhardmin, data = data12)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.501 -3.968 1.406 4.796 13.210
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.025e+02 2.347e+01 4.367 3.36e-05 ***
## DASHSC_Gunther -2.296e-01 1.015e-01 -2.262 0.0261 *
## Age 7.284e-01 6.603e-01 1.103 0.2729
## as.factor(Sex)2 -1.872e-02 2.401e+00 -0.008 0.9938
## HTM -1.102e+01 1.576e+01 -0.699 0.4861
## HTPCT 7.583e-04 5.039e-02 0.015 0.9880
## BMIcal 2.132e-01 1.127e-01 1.891 0.0618 .
## BMIPCT -9.747e-02 6.583e-02 -1.481 0.1422
## DMETS -3.665e-01 2.813e-01 -1.303 0.1958
## hardmin 5.948e-03 5.701e-03 1.043 0.2996
## vhardmin 1.691e-02 1.155e-02 1.464 0.1467
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.559 on 90 degrees of freedom
## Multiple R-squared: 0.1399, Adjusted R-squared: 0.04436
## F-statistic: 1.464 on 10 and 90 DF, p-value: 0.1664 Correlation between Gunther and SuperWIN (HTNST=1)
plot(DASHSC_Gunther,DASHSC_SuperWIN,pch=20)
5 The SuperWIN scoring system (HTNST=2)
5.1 Scatterplots of SuperWIN DASH Score vs SBP/DBP
Figures of SuperWIN Dash Scores vs SBP/DBP
par(mfrow=c(1,2))
plot(DASHSC_SuperWIN,SBP, pch = 20)
plot(DASHSC_SuperWIN,DBP, pch = 20)
5.2 correlation between SuperWIN DASH Score and SBP
We have pearson correlation as follows:
data111=data.frame(DASHSC_SuperWIN,SBP,DBP)
cor(data111, use="complete.obs", method="pearson") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.00000000 0.03171442 0.01993377
## SBP 0.03171442 1.00000000 -0.24138687
## DBP 0.01993377 -0.24138687 1.00000000We have spearman correlation as follows:
cor(data111, use="complete.obs", method="spearman") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.000000000 0.007144684 0.00370576
## SBP 0.007144684 1.000000000 -0.16733660
## DBP 0.003705760 -0.167336596 1.00000000We have kendall correlation as follows:
cor(data111, use="complete.obs", method="kendall") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.000000000 0.004884999 0.001609611
## SBP 0.004884999 1.000000000 -0.123906963
## DBP 0.001609611 -0.123906963 1.0000000005.3 Linear Regression
We build a linear regression with SBP/DBP as response and dash score as regressor with other covariates including age, sex, HTNST,WTKG,HTM,HTPCT,BMIcal,BMIPCT, DMETS, sleep,lightmin, Modmin, hardmin, vhardmin and actweek.
5.3.1 SBP as response
We first calculate variance-inflation factor to chek the multicollinearity in the model.Then, we update our model by removing the the predictor variables(WTKG,HTM, BMIcal, Sleep,lightmin,modmin,hardmin, actweek) with high VIF value. In our final proposed model, we can see that dash score is not statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = SBP ~ DASHSC_SuperWIN + Age + as.factor(Sex) + HTPCT +
## BMIPCT + DMETS + vhardmin, data = data21)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0682 -2.0953 -0.0935 1.8962 13.0253
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.026e+02 7.860e+00 13.054 < 2e-16 ***
## DASHSC_SuperWIN -5.390e-03 5.416e-02 -0.100 0.921
## Age 1.969e+00 2.904e-01 6.780 9.39e-09 ***
## as.factor(Sex)2 -5.052e+00 1.172e+00 -4.309 7.00e-05 ***
## HTPCT 9.515e-02 1.948e-02 4.885 9.63e-06 ***
## BMIPCT -2.339e-02 3.278e-02 -0.714 0.478
## DMETS 8.532e-04 1.633e-01 0.005 0.996
## vhardmin 4.646e-03 6.309e-03 0.736 0.465
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.068 on 54 degrees of freedom
## Multiple R-squared: 0.6385, Adjusted R-squared: 0.5917
## F-statistic: 13.63 on 7 and 54 DF, p-value: 5.343e-105.3.2 DBP as response
Similarly, we calculate variance-inflation factor to chek the multicollinearity in the model.Hence, We update our model by removing the the predictor variables(WTKG,HTM, BMIcal, Sleep,lightmin,modmin,hardmin, actweek) with high VIF value. We can see that dash score is not statistically significance under \(\alpha\)=0.1.
#car::vif(l22)##
## Call:
## lm(formula = DBP ~ DASHSC_SuperWIN + Age + as.factor(Sex) + HTPCT +
## BMIPCT + DMETS + vhardmin, data = data22)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.8580 -4.6835 0.4557 5.7941 15.0046
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.516626 17.547160 3.164 0.00256 **
## DASHSC_SuperWIN 0.112030 0.120904 0.927 0.35826
## Age 1.092385 0.648271 1.685 0.09775 .
## as.factor(Sex)2 4.544998 2.617447 1.736 0.08819 .
## HTPCT -0.091394 0.043488 -2.102 0.04027 *
## BMIPCT -0.002351 0.073171 -0.032 0.97448
## DMETS 0.137116 0.364573 0.376 0.70832
## vhardmin -0.011446 0.014085 -0.813 0.42001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.081 on 54 degrees of freedom
## Multiple R-squared: 0.1965, Adjusted R-squared: 0.09231
## F-statistic: 1.886 on 7 and 54 DF, p-value: 0.089876 The Gunther’s scoring system(HTNST=2)
6.1 Scatterplots of Gunther DASH Score vs SBP/DBP
Figures of Gunther Dash Scores vs SBP/DBP.
par(mfrow=c(1,2))
plot(DASHSC_Gunther,SBP, pch=20)
plot(DASHSC_Gunther,DBP, pch=20)
6.2 Correlation between Gunther DASH Score and SBP
We have pearson correlation as follows:
## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 0.1110893 -0.03736854
## SBP 0.11108934 1.0000000 -0.24138687
## DBP -0.03736854 -0.2413869 1.00000000We have spearman correlation as follows:
cor(data222, use="complete.obs", method="spearman") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.000000000 0.09219924 -0.005319152
## SBP 0.092199239 1.00000000 -0.167336596
## DBP -0.005319152 -0.16733660 1.000000000We have kendall correlation as follows:
cor(data222, use="complete.obs", method="kendall") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.000000000 0.06676166 -0.004828833
## SBP 0.066761659 1.00000000 -0.123906963
## DBP -0.004828833 -0.12390696 1.0000000006.3 Linear Regression
We build a linear regression with SBP/DBP as response and dash score as regressor with other covariates including age, sex, HTNST,WTKG,HTM,HTPCT,BMIcal,BMIPCT, DMETS, sleep,lightmin, Modmin, hardmin, vhardmin and actweek.
6.3.1 SBP as response
We first calculate variance-inflation factor to chek the multicollinearity in the model.Then, we update our model by removing the the predictor variables(WTKG,HTM, BMIcal, Sleep,lightmin,modmin,hardmin, actweek) with high VIF value. In our final proposed model, we can see that dash score is not statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = SBP ~ DASHSC_Gunther + Age + as.factor(Sex) + HTPCT +
## BMIPCT + DMETS + vhardmin, data = data11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.036 -2.175 -0.001 2.110 12.723
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 101.239214 8.074053 12.539 < 2e-16 ***
## DASHSC_Gunther 0.034399 0.080207 0.429 0.669718
## Age 1.980205 0.290095 6.826 7.89e-09 ***
## as.factor(Sex)2 -4.899582 1.192202 -4.110 0.000136 ***
## HTPCT 0.094557 0.019456 4.860 1.05e-05 ***
## BMIPCT -0.028574 0.032126 -0.889 0.377716
## DMETS 0.009699 0.163398 0.059 0.952885
## vhardmin 0.003775 0.006308 0.598 0.552034
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.061 on 54 degrees of freedom
## Multiple R-squared: 0.6397, Adjusted R-squared: 0.593
## F-statistic: 13.7 on 7 and 54 DF, p-value: 4.92e-106.3.2 DBP as response
Similarly, we calculate variance-inflation factor to chek the multicollinearity in the model.Hence, We update our model by removing the the predictor variables(WTKG,HTM, BMIcal, Sleep,lightmin,modmin,hardmin, actweek) with high VIF value. We can see that dash score is not statistically significance under \(\alpha\)=0.1.
##
## Call:
## lm(formula = DBP ~ DASHSC_Gunther + Age + as.factor(Sex) + HTPCT +
## BMIPCT + DMETS + vhardmin, data = data12)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.5433 -4.1471 0.5884 5.5230 15.1791
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.181300 18.144955 3.096 0.00311 **
## DASHSC_Gunther 0.100176 0.180250 0.556 0.58067
## Age 1.079164 0.651936 1.655 0.10366
## as.factor(Sex)2 4.499245 2.679255 1.679 0.09887 .
## HTPCT -0.090708 0.043723 -2.075 0.04280 *
## BMIPCT 0.009291 0.072198 0.129 0.89809
## DMETS 0.130439 0.367207 0.355 0.72381
## vhardmin -0.010153 0.014176 -0.716 0.47693
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.127 on 54 degrees of freedom
## Multiple R-squared: 0.1883, Adjusted R-squared: 0.08312
## F-statistic: 1.79 on 7 and 54 DF, p-value: 0.10837 Correlation between Gunther and SuperWIN (HTNST=2)
plot(DASHSC_Gunther,DASHSC_SuperWIN,pch=20)
8 The SuperWIN scoring system (HTNST=3)
#head(DASHSC_SuperWIN,10)8.1 Scatterplots of SuperWIN Dash Scores vs SBP/DBP
Figures of SuperWIN Dash Scores vs SBP/DBP
par(mfrow=c(1,2))
plot(DASHSC_SuperWIN,SBP,pch=20)
plot(DASHSC_SuperWIN,DBP,pch=20)
8.2 Correlation between SuperWIN DASH Score and SBP
We have pearson correlation as follows:
data111=data.frame(DASHSC_SuperWIN,SBP,DBP)
cor(data111, use="complete.obs", method="pearson") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.00000000 -0.13204066 0.07196395
## SBP -0.13204066 1.00000000 -0.07311197
## DBP 0.07196395 -0.07311197 1.00000000We have spearman correlation as follows:
cor(data111, use="complete.obs", method="spearman") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.00000000 -0.1091089 0.04761905
## SBP -0.10910895 1.0000000 -0.15760181
## DBP 0.04761905 -0.1576018 1.00000000We have kendall correlation as follows:
cor(data111, use="complete.obs", method="kendall") ## DASHSC_SuperWIN SBP DBP
## DASHSC_SuperWIN 1.00000000 -0.03779645 0.0000000
## SBP -0.03779645 1.00000000 -0.1133893
## DBP 0.00000000 -0.11338934 1.00000008.3 Linear Regression
Since we only have 8 subjects in this dataset, we can not perform regression analaysis.
9 The Gunther’s scoring system(HTNST=3)
9.1 Scatterplots of Gunther DASH Score vs SBP/DBP
Figures of Gunther Dash Scores vs SBP/DBP
par(mfrow=c(1,2))
plot(DASHSC_Gunther,SBP,pch=20)
plot(DASHSC_Gunther,DBP,pch=20)
9.2 Correlation between Gunther DASH Score and SBP
We have pearson correlation as follows:
## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 -0.12605314 0.07889886
## SBP -0.12605314 1.00000000 -0.07311197
## DBP 0.07889886 -0.07311197 1.00000000We have spearman correlation as follows:
cor(data222, use="complete.obs", method="spearman") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 0.01212322 0.1428571
## SBP 0.01212322 1.00000000 -0.1576018
## DBP 0.14285714 -0.15760181 1.0000000We have kendall correlation as follows:
cor(data222, use="complete.obs", method="kendall") ## DASHSC_Gunther SBP DBP
## DASHSC_Gunther 1.00000000 0.03779645 0.0000000
## SBP 0.03779645 1.00000000 -0.1133893
## DBP 0.00000000 -0.11338934 1.000000010 Correlation between Gunther and SuperWIN (HTNST=3)
plot(DASHSC_Gunther,DASHSC_SuperWIN,pch=20)