Part-2 The table below illustrates the result for full logistic regression model that includes all 5
independent variables used to predict survival status. Below we see that both CPR, AGE have
a positive relationship to STA, and are both highly significant (P-values 0.0178 and 0.00529).
Logistic Regression: STA versus AGE, SER, CPR,HRA, and SEX. Call:
glm(formula = STA ~ AGE + SER + CPR + HRA + SEX, family = binomial,
data = icu)
Deviance Residuals:
Min
1Q
Median
-1.3536 -0.6943 -0.5212 3Q
-0.2758 Max
2.5479 Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.403217
1.075593 -2.234 0.02546 *
AGE
0.032910
0.011802
2.789 0.00529 **
SER1
-0.951211
0.424247 -2.242 0.02495 *
CPRYes
1.516537
0.640327
2.368 0.01787 *
HRA
-0.006277
0.007601 -0.826 0.40893
SEXFemale
-0.159958
0.391439 -0.409 0.68280
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 200.16
Residual deviance: 178.57
AIC: 190.57 on 199
on 194 degrees of freedom
degrees of freedom Number of Fisher Scoring iterations: 5 The P-value for Sex and HRA are high which suggested that these factor can be dropped from
our model. By doing manual variable selection, many models of different combinations were
made and only AGE, CPR and SER variables were selected in our logistic regression model.
Logistic Regression Model: HAR variable was dropped from model because it has high P-value.
As a result, P-value for AGE, CPR, and SER decreased compared to the full model. However, pvalue for sex variable decreased but it remained significant.
Logistic Regression: STA versus AGE, CPR, SER, and SEX
Call:
lm(formula = STA ~ AGE + CPR + SER + SEX, data = icu)
Residuals:
Min
1Q
Median
-0.57013 -0.21988 -0.15768
Coefficients:
(Intercept) 3Q
0.01125 Max
1.01029 Estimate Std. Error t value Pr(>|t|)
0.749232
0.164846
4.545 9.62e-06 *** AGE
0.003822
CPR
0.309358
SER
-0.114365
SEX
-0.027128
--Signif. codes: 0 ‘***’ 0.001361
0.114060
0.056077
0.056629 2.807
2.712
-2.039
-0.479 0.00550 **
0.00728 **
0.04276 *
0.63244 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3833 on 195 degrees of freedom
Multiple R-squared: 0.1045, Adjusted R-squared: 0.08615
F-statistic: 5.69 on 4 and 195 DF, p-value: 0.0002368 Logistic Regression: STA versus AGE, CPR, SER, and HRA.
Note: The sex factor was dropped from our logistic regression model. The result below illustrates
that P-value for HRA was high.
Call:
lm(formula = STA ~ AGE + CPR + SER + HRA, data = icu)
Residuals:
Min
1Q
Median
-0.57430 -0.22436 -0.15305 3Q
0.01081 Max
1.00778 Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7954076 0.1878510
4.234 3.53e-05 ***
AGE
0.0037972 0.0013554
2.802 0.00560 **
CPR
0.3066712 0.1133748
2.705 0.00744 **
SER
-0.1257248 0.0588971 -2.135 0.03404 *
HRA
-0.0007405 0.0010735 -0.690 0.49112
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Logistic Regression: STA versus AGE, CPR, and SER
We decided to drop two factors Sex and HRA from model. The result indicates that dropping
both factors result in an increase in the Adjusted R-squared value from 0.0836 to 0.087. Also the
feature HRA is coming out to be insignificant and therefore should be removed.
Call:
lm(formula = STA ~ AGE + CPR + SER, data = icu)
Residuals:
Min
1Q
Median
-0.57955 -0.21705 -0.15777 3Q
0.01344 Max
1.01720 Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.721265
0.153859
4.688 5.16e-06 ***
AGE
0.003759
0.001352
2.780 0.00597 **
CPR
0.303207
0.113112
2.681 0.00798 **
SER
-0.113095
0.055904 -2.023 0.04443 *
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3826 on 196 degrees of freedom
Multiple R-squared: 0.1035, Adjusted R-squared: 0.08974
F-statistic: 7.54 on 3 and 196 DF, p-value: 8.447e-05 The interpretation of logistic regression coefficients for the three variables.
The positive coefficients for the AGE and CPR are associated with higher probabilities of death
to hospital discharge of these patients. In contrast, having negative coefficients are associated
with higher survival to hospital discharge of these patients.
Age: an increase in age multiplies the expected odds in favor of probability of patient not
surviving by e0.00375 = 1.003. Another way of interpreting result, an increase in age (one year)
leads to an increase of 1 in the odds of death.
CPR: An increase in CPR multiplies the expected odds in favor of probability of patient not
surviving by e0.3032 = 1.354. As a result, the model predicts an increase of 1.354 in the odds of
death.
SER: An in SER multiplies the expected odd in favor of probability of patient not surviving
by e-0.1130= 0.8923. Thus, the model predicts decrease of 0.8923 in the odds of death. Part-3
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1 ## ## predicted probabilities, logit and odds
#Creating a new datframe with the given values to predict STA
df <- data.frame(matrix(ncol = 5, nrow = 5))
n <- c("AGE","SER","CPR","HRA","SEX")
colnames(df) <- n
df$AGE <- c(91,91,51,96,89)
df$SER <- c(0,0,1,0,0)
df$CPR <- c(1,0,0,0,0)
df$HRA <- c(89,79,98,79,79)
df$SEX <- c(1,1,1,1,1)
predicteddata=predict(icu4.lm,newdata=df,type='response')
predicteddata <- round(predicteddata)
# Below variable contains the STA predictions for the 5 people data given
predicteddata
2 3 4 5
1 1 1 1

 

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