Predict-Diabetes.Rmd

---
title: "Data Mining with R: Predict Diabetes"
output: html_document
---

The dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. I downloaded from [UCI Machine Learning Repository](https://www.kaggle.com/uciml). The objective is to predict based on diagnostic measurements whether a patient has diabetes.

```{r global_options, include=FALSE}
knitr::opts_chunk$set(echo=FALSE, warning=FALSE, message=FALSE)
```

```{r}
library(ggplot2)
library(dplyr)
library(gridExtra)
library(corrplot)
```

Look at the structure and the first few rows.

```{r}
diabetes <- read.csv('diabetes.csv')
dim(diabetes)
str(diabetes)
head(diabetes)
```

### Exploratory Data Analysis and Feature Selection

Check missing values 

```{r}
cat("Number of missing value:", sum(is.na(diabetes)), "\n")
```

Staitstical summary 

```{r}
summary(diabetes)
```

```{r}
diabetes$Outcome <- factor(diabetes$Outcome)
```

Histogram of numeric variables

```{r}
p1 <- ggplot(diabetes, aes(x=Pregnancies)) + ggtitle("Number of times pregnant") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 1, colour="black", fill="white") + ylab("Percentage")
p2 <- ggplot(diabetes, aes(x=Glucose)) + ggtitle("Glucose") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 5, colour="black", fill="white") + ylab("Percentage")
p3 <- ggplot(diabetes, aes(x=BloodPressure)) + ggtitle("Blood Pressure") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 2, colour="black", fill="white") + ylab("Percentage")
p4 <- ggplot(diabetes, aes(x=SkinThickness)) + ggtitle("Skin Thickness") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 2, colour="black", fill="white") + ylab("Percentage")
p5 <- ggplot(diabetes, aes(x=Insulin)) + ggtitle("Insulin") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 20, colour="black", fill="white") + ylab("Percentage")
p6 <- ggplot(diabetes, aes(x=BMI)) + ggtitle("Body Mass Index") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth = 1, colour="black", fill="white") + ylab("Percentage")
p7 <- ggplot(diabetes, aes(x=DiabetesPedigreeFunction)) + ggtitle("Diabetes Pedigree Function") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), colour="black", fill="white") + ylab("Percentage")
p8 <- ggplot(diabetes, aes(x=Age)) + ggtitle("Age") +
  geom_histogram(aes(y = 100*(..count..)/sum(..count..)), binwidth=1, colour="black", fill="white") + ylab("Percentage")
grid.arrange(p1, p2, p3, p4, p5, p6, p7, p8, ncol=2)
```

All the variables have reasonable broad distribution, therefore, will be kept for the regression analysis. 

Correlation Between Numeric Varibales

```{r}
numeric.var <- sapply(diabetes, is.numeric)
corr.matrix <- cor(diabetes[,numeric.var])
corrplot(corr.matrix, main="\n\nCorrelation Plot for Numerical Variables", order = "hclust", tl.col = "black", tl.srt=45, tl.cex=0.5, cl.cex=0.5)
```

The numeric variabls are almost not correlated. 

Correlation bewteen numeric variables and outcome. 

```{r}
attach(diabetes)
par(mfrow=c(2,4))
boxplot(Pregnancies~Outcome, main="No. of Pregnancies vs. Diabetes", 
        xlab="Outcome", ylab="Pregnancies")
boxplot(Glucose~Outcome, main="Glucose vs. Diabetes", 
        xlab="Outcome", ylab="Glucose")
boxplot(BloodPressure~Outcome, main="Blood Pressure vs. Diabetes", 
        xlab="Outcome", ylab="Blood Pressure")
boxplot(SkinThickness~Outcome, main="Skin Thickness vs. Diabetes", 
        xlab="Outcome", ylab="Skin Thickness")
boxplot(Insulin~Outcome, main="Insulin vs. Diabetes", 
        xlab="Outcome", ylab="Insulin")
boxplot(BMI~Outcome, main="BMI vs. Diabetes", 
        xlab="Outcome", ylab="BMI")
boxplot(DiabetesPedigreeFunction~Outcome, main="Diabetes Pedigree Function vs. Diabetes", xlab="Outcome", ylab="DiabetesPedigreeFunction")
boxplot(Age~Outcome, main="Age vs. Diabetes", 
        xlab="Outcome", ylab="Age")

```

Blood pressure and skin thickness show little variation with diabetes, they will be excluded from the model. Other variables show more or less correlation with diabetes, so will be kept.

### Logistic Regression 

```{r}
diabetes$BloodPressure <- NULL
diabetes$SkinThickness <- NULL
train <- diabetes[1:540,]
test <- diabetes[541:768,]

model <-glm(Outcome ~.,family=binomial(link='logit'),data=train)
summary(model)
```

The top three most relevant features are "Glucose", "BMI" and "Number of times pregnant" because of the low p-values.

"Insulin" and "Age" appear not statistically significant.

```{r}
anova(model, test="Chisq")
```

From the table of deviance, we can see that adding insulin and age have little effect on the residual deviance.

### Cross Validation

```{r}
fitted.results <- predict(model,newdata=test,type='response')
fitted.results <- ifelse(fitted.results > 0.5,1,0)
misClasificError <- mean(fitted.results != test$Outcome)
print(paste('Accuracy',1-misClasificError))
```

### Decision Tree

```{r}
library(rpart)
model2 <- rpart(Outcome ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction, data=train,method="class")
```

```{r}
plot(model2, uniform=TRUE, 
  	main="Classification Tree for Diabetes")
text(model2, use.n=TRUE, all=TRUE, cex=.8)
```

This means if a person's BMI less than 45.4 and her diabetes digree function less than 0.8745, then she is more likely to have diabetes. 

Confusion table and accuracy

```{r}
treePred <- predict(model2, test, type = 'class')
table(treePred, test$Outcome)
mean(treePred==test$Outcome)
```

In this project, I compared the performance of Logistic Regression and Decision Tree algorithms and found that Logistic Regression performed better on this standard, unaltered dataset. However, there are things we can do to improve the generalization performance in decision tree induction such as pruning. I will perform that in the future posts.