---
title: "Breast Cancer analysis"
author: "Tom Yishay"
output: 
  flexdashboard::flex_dashboard:
    orientation: rows
    vertical_layout: fill
    source_code: embed
---

```{r setup, include=FALSE}
library(ggplot2)
library(plotly)
library(plyr)
library(flexdashboard)
library(ggpubr)

# create some data
data <- read.csv("breast_cancer.csv", header= T, sep = "")
```

Descriptive Statistics
=======================================================================

Row {data-height=100}
-----------------------------------------------------------------------
###  Number of obervations
```{r}
valueBox(nrow(data))
```

###  Precentage of cancer
```{r}
rate <- round(mean(data$diagnosis == 'M') * 100 , 1)
gauge(rate, min = 0, max = 100, symbol = '%', gaugeSectors(danger = c(0, 100) ))
```

###  Mean of radius means
```{r}
valueBox(round(mean(data$radius_mean), 1))
```


Row {.tabset .tabset-fade .tabset-fade}
-------------------------------------
###  The relationship between mean texture and radius

```{r}
p1 <- ggplot(data, aes(x = radius_mean , y = texture_mean, colour = diagnosis))+
  ggplot2::geom_point() +
  theme_bw() +
  ggplot2::scale_x_continuous(name = "Radius mean") +
  ggplot2::scale_y_continuous(name = "Texture mean")
ggplotly(p1)
```

### Box plot of area mean

```{r}
p2 <- ggplot(data, aes(x = diagnosis , y = area_mean, colour = diagnosis))+
  ggplot2::geom_boxplot() +
  theme_bw() +
  ggplot2::scale_x_discrete(name = "Diagnosis") +
  ggplot2::scale_y_continuous(name = "Area mean")
ggplotly(p2)
```

### Box plot of texture mean

```{r}
p2 <- ggplot(data, aes(x = diagnosis , y = texture_mean, colour = diagnosis))+
  ggplot2::geom_boxplot() +
  theme_bw() +
  ggplot2::scale_x_discrete(name = "Radius mean") +
  ggplot2::scale_y_continuous(name = "Texture mean")
ggplotly(p2)
```


Analysis
=======================================================================

Row
-----------------------------------------------------------------------
### Components selection
The data is optimally described by 5 components according to Keizer criterion and the drop in eigen values of the standardized data:
```{r}
dataplot <- data.frame(x = 1:30, y = eigen(cor(data[,-1]))$values)
p <- ggplot(data = dataplot, aes(x = x,y = y)) +
  geom_point() +
  geom_line() +
  geom_hline(yintercept = 1, colour = "red") +
  theme_bw()

ggplotly(p)

```
Row
-----------------------------------------------------------------------
### Model selection
The model chosen is **linear discriminant analysis** used on the first five components.
As we can see the model detects cancer and no-cancer correctly 62.5% and 32.2% of the time respectively. 
```{r}
fit <- prcomp(data[,-1], scale=T)
Data <- data.frame(diag = data[,1], fit$x[,1:5])
lda.fit <-MASS::lda(diag ~ PC1+PC2+PC3+PC4+PC5, data = Data, CV = T)
Class_table <- table(real = Data$diag, predict = lda.fit$class)

prop.table(table(Reality = Data$diag, Prediction = lda.fit$class)) %>%
  round(5) %>%
  as.data.frame() %>%
  knitr::kable()
```

Row
-----------------------------------------------------------------------
###  Model's accurecy
```{r}
valueBox(round((Class_table[1,1] + Class_table[2,2]) / sum(Class_table), 2),
         "Accuracy is the fraction of correct predictions.")
```

###  Model's Precision
```{r}
valueBox(round((Class_table[1,1] + Class_table[2,1]) / sum(Class_table), 2),
         "Proportion of correct positive identifications.")
```

###  Model's Recall
```{r}
valueBox(round((Class_table[1,1] + Class_table[1,2]) / sum(Class_table), 2),
         "Proportion of correctly identified positives.")
```