Question

Write a R code

HW09  The National Institute of Diabetes and Digestive and Kidney Diseases

conducted a study on 768 adult female Pima Indians living near Phoenix.

The pima dataset resulting from the study is available in R and contains the following variables:

test - results of a test to determine if the female patient shows signs of diabetes

         (coded 0 if negative, 1 if positive)

age - Age (years)

bmi - Body mass index (weight in kg/(height in metres squared))

diastolic - Diastolic blood pressure (mm Hg)

diabetes - Diabetes pedigree function

glucose - Plasma glucose concentration at 2 hours in an oral glucose tolerance test

insulin - 2-Hour serum insulin (mu U/ml)

pregnant - Number of times pregnant

triceps - Triceps skin fold thickness (mm)

The following logistic model with test as the response was fit with the following table results:

logistic <- glm(test ~ age + bmi + diastolic + diabetes + glucose + insulin + pregnant +

triceps,family=binomial(logit),data=pima)

		Reference
		0	1
Prediction	0	446	117
	1	54	151

A positive test result (test=1) was modeled as an event. Compute the following measures:

Accuracy

Sensitivity

Specificity

Positive Predictive Value

Negative Predictive Value

Answer 1

R-code

#Importing the dataset
library(readr)
d <- read_csv("C:/Users/admin/Downloads/diabetes.csv",
col_types = cols(Age = col_integer(),
BMI = col_number(), BloodPressure = col_integer(),
DiabetesPedigreeFunction = col_number(),
Glucose = col_integer(), Insulin = col_integer(),
Outcome = col_integer(), Pregnancies = col_integer(),
SkinThickness = col_integer()))

# Understand the dataset
View(db)
head(db)
str(db)

#Finding the summary statistic of the dataset
summary(db)

#splitting the dataset into test train data with ratio 0.7
set.seed(5)
dt = sort(sample(nrow(db), nrow(db)*.7))
train<-db[dt,]
test<-db[-dt,]

#checking the splittitted datsets
nrow(db)
nrow(train)
nrow(test)

#Fitting logistic regression model with dataset db
logistic <- glm(Outcome ~ Age + BMI + BloodPressure + DiabetesPedigreeFunction + Glucose + Insulin + Pregnancies +SkinThickness,family=binomial(logit),data=train)
summary(logistic)

#Confusion Matrix less than 0.5 not survival
prdVal <- predict(logistic, type='response')
summary(prdVal)
prdBln <- ifelse(prdVal > 0.5, 1, 0)
cnfmtrx <- table(prd=prdBln, act=train$Outcome)
confusionMatrix(cnfmtrx)

# Build confusion matrix with a threshold value of 0.5

threshold_0.5 <- table(train$Outcome, prdVal > 0.5)
threshold_0.5

# Accuracy
accuracy_0.5 <- round(sum(diag(threshold_0.5))/sum(threshold_0.5),2)
sprintf("Accuracy is %s",accuracy_0.5)

#sensitivity
sensitivity_0.5 <- round(117/(117+77),2)
sprintf("Sensitivity at 0.5 threshold: %s", sensitivity_0.5)

#specificity
specificity_0.5 <- round(304/(304+39),2)
sprintf("Specificity at 0.5 threshold: %s", specificity_0.5)

Formulae:

Confusion Matrix: Compares the actual outcomes with the predicted ones

	Predicted = 0	Predicted = 1
Actual = 0	True Negatives (TN)	False Positives (FP)
Actual = 1	False Negatives (FN)	True Positives (TP)

Sensitivity = (TP / TP + FN) (True Positive rate)
Specificity = (TN / TN + FP) (True Negative rate)

The model with a higher threshold has lower Sensitivity but higher Specificity.
The model with a lower threshold has higher Sensitivity but lower Specificity.

Thresholding:(here considered as 0.5)

The outcome of a logistic regression model is a probability.
We can do this using a threshold value t

• If P(y=1) >= t, predict 1
• If P(y=1) < t, predict 0