Diabetes Relation Analysis
Aashay Sharma
24/07/2020
In this Particular analysis we will try to find out relations between different variables given in the data set and we will try to fit a model to predict the diabetes outcome.
Reading the Data and Performing some Exploratory Analysis
Data is already clean and does not recquire some specific cleaning but we will just convert the Outcome Variable to a factor variable to perform some plots.
data <- "/Users/aashaysharma/Desktop/RStudio/diabetes/diabetes.csv"
diabetes <- read.csv(data)
head(diabetes)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 0Now we have many variables but our outcome is discrete that is it is binary data 1 or 0.
Now I will perform aov analysis to get the variance distribution of the data so we can see that what variables account for what amount of variance.
variance_analysis <- aov(Outcome ~ . , data = diabetes)
summary(variance_analysis)## Df Sum Sq Mean Sq F value Pr(>F)
## Pregnancies 1 8.59 8.59 53.638 6.16e-13 ***
## Glucose 1 34.02 34.02 212.406 < 2e-16 ***
## BloodPressure 1 0.12 0.12 0.771 0.380213
## SkinThickness 1 0.86 0.86 5.393 0.020481 *
## Insulin 1 0.26 0.26 1.594 0.207108
## BMI 1 6.78 6.78 42.331 1.40e-10 ***
## DiabetesPedigreeFunction 1 1.82 1.82 11.349 0.000793 ***
## Age 1 0.46 0.46 2.865 0.090922 .
## Residuals 759 121.57 0.16
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Now we can see that the variables which account for high variance and lowest p-Values are : - Pregnancies - Glucose - BMI - DiabetesPedigreeFunction - and SkinThickness but it accounts for a bit higher p-Value compared to others in this list.
Converting the outcome to factor variable :
diabetes$Outcome2 <- as.factor(diabetes$Outcome)Some Exploratory analysis :
a <-ggplot(data = diabetes, aes(x = Outcome2, y = Pregnancies)) + geom_boxplot()
b <-ggplot(data = diabetes, aes(x = Outcome2, y = Glucose)) + geom_boxplot()
c <-ggplot(data = diabetes, aes(x = Outcome2, y = BMI)) + geom_boxplot()
d <-ggplot(data = diabetes, aes(x = Outcome2, y = DiabetesPedigreeFunction)) + geom_boxplot()
e <-ggplot(data = diabetes, aes(x = Outcome2, y = SkinThickness)) + geom_boxplot()grid.arrange(a, b, c, d, e, nrow = 3, ncol = 2)
Inference from the GRAPHS
Okay so after looking at the graphs we can infer that Pregnancies and Glucose have a significant mean difference with least outliers, BMI and PedigreeFunction have a lesser mean difference but have many outliers which can account for lesser accurate fit and the last graph SkinThickness has a lesser mean difference but one outlier.
So we can fit 3 Different models :
- Pregnancies and Glucose as features
- BMI and PedigreeFunction as feature along with the first 2
- and all the feautres including SkinThickness.
We will use caret package for fitting and plotting.
Models :
First we will separate the data into a training and testing set.
set.seed(1234)
inTrain <- createDataPartition(y = diabetes$Outcome2, list = FALSE, p = 0.65)
train <- diabetes[inTrain,]
test <- diabetes[-inTrain,]Model 1 ( Features : Pregnancies + Glucose)
Random Forest :
RF_model <- train(Outcome2 ~ Pregnancies + Glucose, method = "rf", data = train, ntree = 100)## note: only 1 unique complexity parameters in default grid. Truncating the grid to 1 .RF_predict <- predict(RF_model, test)
confusionMatrix(test$Outcome2, RF_predict)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 139 36
## 1 36 57
##
## Accuracy : 0.7313
## 95% CI : (0.674, 0.7835)
## No Information Rate : 0.653
## P-Value [Acc > NIR] : 0.003716
##
## Kappa : 0.4072
##
## Mcnemar's Test P-Value : 1.000000
##
## Sensitivity : 0.7943
## Specificity : 0.6129
## Pos Pred Value : 0.7943
## Neg Pred Value : 0.6129
## Prevalence : 0.6530
## Detection Rate : 0.5187
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7036
##
## 'Positive' Class : 0
## Logistic Regression:
LR_model <- train(Outcome2 ~ Pregnancies + Glucose, method = "glm", family = "binomial", data = train)
LR_predict <- predict(LR_model, test)
confusionMatrix(test$Outcome2, LR_predict)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 155 20
## 1 40 53
##
## Accuracy : 0.7761
## 95% CI : (0.7214, 0.8246)
## No Information Rate : 0.7276
## P-Value [Acc > NIR] : 0.04112
##
## Kappa : 0.4798
##
## Mcnemar's Test P-Value : 0.01417
##
## Sensitivity : 0.7949
## Specificity : 0.7260
## Pos Pred Value : 0.8857
## Neg Pred Value : 0.5699
## Prevalence : 0.7276
## Detection Rate : 0.5784
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7604
##
## 'Positive' Class : 0
## Model 2 ( Features : Pregnancies + Glucose + BMI + DiabetesPedigreeFunction)
Random Forest :
RF_model2 <- train(Outcome2 ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction, method = "rf", data = train, ntree = 100)
RF_predict2 <- predict(RF_model2, test)
confusionMatrix(test$Outcome2, RF_predict2)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 150 25
## 1 32 61
##
## Accuracy : 0.7873
## 95% CI : (0.7334, 0.8347)
## No Information Rate : 0.6791
## P-Value [Acc > NIR] : 5.73e-05
##
## Kappa : 0.5223
##
## Mcnemar's Test P-Value : 0.4268
##
## Sensitivity : 0.8242
## Specificity : 0.7093
## Pos Pred Value : 0.8571
## Neg Pred Value : 0.6559
## Prevalence : 0.6791
## Detection Rate : 0.5597
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7667
##
## 'Positive' Class : 0
## Logistic Regression:
LR_model2 <- train(Outcome2 ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction, method = "glm", family = "binomial", data = train)
LR_predict2 <- predict(LR_model2, test)
confusionMatrix(test$Outcome2, LR_predict2)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 154 21
## 1 37 56
##
## Accuracy : 0.7836
## 95% CI : (0.7294, 0.8314)
## No Information Rate : 0.7127
## P-Value [Acc > NIR] : 0.005295
##
## Kappa : 0.5024
##
## Mcnemar's Test P-Value : 0.048885
##
## Sensitivity : 0.8063
## Specificity : 0.7273
## Pos Pred Value : 0.8800
## Neg Pred Value : 0.6022
## Prevalence : 0.7127
## Detection Rate : 0.5746
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7668
##
## 'Positive' Class : 0
## Model 3 ( Features : Pregnancies + Glucose + BMI + DiabetesPedigreeFunction + SkinThickness)
Random Forest :
RF_model3 <- train(Outcome2 ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction + SkinThickness, method = "rf", data = train, ntree = 100)
RF_predict3 <- predict(RF_model3, test)
confusionMatrix(test$Outcome2, RF_predict3)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 149 26
## 1 36 57
##
## Accuracy : 0.7687
## 95% CI : (0.7135, 0.8178)
## No Information Rate : 0.6903
## P-Value [Acc > NIR] : 0.002792
##
## Kappa : 0.4763
##
## Mcnemar's Test P-Value : 0.253038
##
## Sensitivity : 0.8054
## Specificity : 0.6867
## Pos Pred Value : 0.8514
## Neg Pred Value : 0.6129
## Prevalence : 0.6903
## Detection Rate : 0.5560
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7461
##
## 'Positive' Class : 0
## Logistic Regression:
LR_model3 <- train(Outcome2 ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction + SkinThickness, method = "glm", family = "binomial", data = train)
LR_predict3 <- predict(LR_model3, test)
confusionMatrix(test$Outcome2, LR_predict3)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 155 20
## 1 37 56
##
## Accuracy : 0.7873
## 95% CI : (0.7334, 0.8347)
## No Information Rate : 0.7164
## P-Value [Acc > NIR] : 0.00512
##
## Kappa : 0.5097
##
## Mcnemar's Test P-Value : 0.03407
##
## Sensitivity : 0.8073
## Specificity : 0.7368
## Pos Pred Value : 0.8857
## Neg Pred Value : 0.6022
## Prevalence : 0.7164
## Detection Rate : 0.5784
## Detection Prevalence : 0.6530
## Balanced Accuracy : 0.7721
##
## 'Positive' Class : 0
## Printing the model Accuracies :
1 -> Pregnancies 2 -> Glucose 3 -> BMI 4 -> DiabetesPedigreeFunction 5 -> SkinThickness
Random Forest
print("RF Model 1 + 2")## [1] "RF Model 1 + 2"confusionMatrix(test$Outcome2, RF_predict)$overall[1]## Accuracy
## 0.7313433print("RF Model 1 + 2 + 3 + 4")## [1] "RF Model 1 + 2 + 3 + 4"confusionMatrix(test$Outcome2, RF_predict2)$overall[1]## Accuracy
## 0.7873134print("RF Model 1 + 2 + 3 + 4 + 5")## [1] "RF Model 1 + 2 + 3 + 4 + 5"confusionMatrix(test$Outcome2, RF_predict3)$overall[1]## Accuracy
## 0.7686567Logistic Regression
print("LR Model 1 + 2")## [1] "LR Model 1 + 2"confusionMatrix(test$Outcome2, LR_predict)$overall[1]## Accuracy
## 0.7761194print("LR Model 1 + 2 + 3 + 4")## [1] "LR Model 1 + 2 + 3 + 4"confusionMatrix(test$Outcome2, LR_predict2)$overall[1]## Accuracy
## 0.7835821print("LR Model 1 + 2 + 3 + 4 + 5")## [1] "LR Model 1 + 2 + 3 + 4 + 5"confusionMatrix(test$Outcome2, LR_predict3)$overall[1]## Accuracy
## 0.7873134Final Conclusion
We can see the accuracies and they are a bit close, but there are some outliers in BMI and PedigreeFunction Variables thus the fit can be faulty in some manner but over all we can see all this 5 variables have some significant effect over diabetes outcome.
Further we can try more combinations and other models to see what fits the best, we cannot just rely on accuracies