Interactive EDA for Breast Cancer Wisconsin

Introduction

###This breast cancer databases was obtained from the University of Wisconsin Hospitals, Madison from Dr. William H. Wolberg.

###Attributes 1 through 10 have been used to represent instances. Each instance has one of 2 possible classes: benign or malignant.

###Content

###Attribute Domain: ### Sample code number id number, Clump Thickness 1 - 10, Uniformity of Cell Size 1 - 10, Uniformity of Cell Shape 1 - 10, Marginal Adhesion 1 - 10, Single Epithelial Cell Size 1 - 10, Bare Nuclei 1 - 10, Bland Chromatin 1 - 10, Normal Nucleoli 1 - 10, Mitoses 1 - 10, Class (2 for benign, 4 for malignant)

Load the required libraries

library(tidyverse)
library(ggstatsplot)
library(plotly)
library(mlbench)

Load the dataset

data(BreastCancer)
head(BreastCancer)

##        Id Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size
## 1 1000025            5         1          1             1            2
## 2 1002945            5         4          4             5            7
## 3 1015425            3         1          1             1            2
## 4 1016277            6         8          8             1            3
## 5 1017023            4         1          1             3            2
## 6 1017122            8        10         10             8            7
##   Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses     Class
## 1           1           3               1       1    benign
## 2          10           3               2       1    benign
## 3           2           3               1       1    benign
## 4           4           3               7       1    benign
## 5           1           3               1       1    benign
## 6          10           9               7       1 malignant

#DATA UNDERSTANDING

dim(BreastCancer)

## [1] 699  11

str(BreastCancer)

## 'data.frame':    699 obs. of  11 variables:
##  $ Id             : chr  "1000025" "1002945" "1015425" "1016277" ...
##  $ Cl.thickness   : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 5 5 3 6 4 8 1 2 2 4 ...
##  $ Cell.size      : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 1 1 2 ...
##  $ Cell.shape     : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 2 1 1 ...
##  $ Marg.adhesion  : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 5 1 1 3 8 1 1 1 1 ...
##  $ Epith.c.size   : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 2 7 2 3 2 7 2 2 2 2 ...
##  $ Bare.nuclei    : Factor w/ 10 levels "1","2","3","4",..: 1 10 2 4 1 10 10 1 1 1 ...
##  $ Bl.cromatin    : Factor w/ 10 levels "1","2","3","4",..: 3 3 3 3 3 9 3 3 1 2 ...
##  $ Normal.nucleoli: Factor w/ 10 levels "1","2","3","4",..: 1 2 1 7 1 7 1 1 1 1 ...
##  $ Mitoses        : Factor w/ 9 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 5 1 ...
##  $ Class          : Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 1 1 1 ...

colnames(BreastCancer)

##  [1] "Id"              "Cl.thickness"    "Cell.size"       "Cell.shape"     
##  [5] "Marg.adhesion"   "Epith.c.size"    "Bare.nuclei"     "Bl.cromatin"    
##  [9] "Normal.nucleoli" "Mitoses"         "Class"

summary(BreastCancer)

##       Id             Cl.thickness   Cell.size     Cell.shape  Marg.adhesion
##  Length:699         1      :145   1      :384   1      :353   1      :407  
##  Class :character   5      :130   10     : 67   2      : 59   2      : 58  
##  Mode  :character   3      :108   3      : 52   10     : 58   3      : 58  
##                     4      : 80   2      : 45   3      : 56   10     : 55  
##                     10     : 69   4      : 40   4      : 44   4      : 33  
##                     2      : 50   5      : 30   5      : 34   8      : 25  
##                     (Other):117   (Other): 81   (Other): 95   (Other): 63  
##   Epith.c.size  Bare.nuclei   Bl.cromatin  Normal.nucleoli    Mitoses   
##  2      :386   1      :402   2      :166   1      :443     1      :579  
##  3      : 72   10     :132   3      :165   10     : 61     2      : 35  
##  4      : 48   2      : 30   1      :152   3      : 44     3      : 33  
##  1      : 47   5      : 30   7      : 73   2      : 36     10     : 14  
##  6      : 41   3      : 28   4      : 40   8      : 24     4      : 12  
##  5      : 39   (Other): 61   5      : 34   6      : 22     7      :  9  
##  (Other): 66   NA's   : 16   (Other): 69   (Other): 69     (Other): 17  
##        Class    
##  benign   :458  
##  malignant:241  
##                 
##                 
##                 
##                 
## 

sum(is.na(BreastCancer))

## [1] 16

#DATA CLEANING

bc <- BreastCancer[, -1]

# Replace "?" with NA
bc[bc == "?"] <- NA

# Convert all to proper types (except Class)
bc$Class <- factor(bc$Class, levels = c("benign", "malignant"))
bc[ , 1:9] <- lapply(bc[ , 1:9], function(x) as.numeric(as.character(x)))

cleanbc <- na.omit(bc)

sum(is.na(cleanbc))

## [1] 0

cleanbc$Id <- NULL
cleanbc$Class <- factor(cleanbc$Class, levels = c("benign", "malignant"))

#UNIVARIATE ANALYSIS

p_ct <- ggplot(cleanbc, aes(x = Cl.thickness, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Clump Thickness by Class")
       
fig_bc <- ggplotly(p_ct, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_cs <- ggplot(cleanbc, aes(x = Cell.size, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Cell Size by Class")
       
fig_bc <- ggplotly(p_cs, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_csh <- ggplot(cleanbc, aes(x = Cell.shape, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Cell Shape by Class")
       
fig_bc <- ggplotly(p_csh, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_ma <- ggplot(cleanbc, aes(x = Marg.adhesion, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Marginal Adhesion by Class")
       
fig_bc <- ggplotly(p_ma, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_ecs <- ggplot(cleanbc, aes(x = Epith.c.size, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Single Epithelial Cell Size by Class")
       
fig_bc <- ggplotly(p_ecs, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_bn <- ggplot(cleanbc, aes(x = Bare.nuclei, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Bare Nuclei by Class")
       
fig_bc <- ggplotly(p_bn, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_bc <- ggplot(cleanbc, aes(x = Bl.cromatin, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Bland Chromatin by Class")
       
fig_bc <- ggplotly(p_bc, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_nn <- ggplot(cleanbc, aes(x = Normal.nucleoli, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Normal Nucleoli by Class")
       
fig_bc <- ggplotly(p_nn, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

p_mito <- ggplot(cleanbc, aes(x = Mitoses, fill = Class)) +
  geom_histogram(bins = 10, position = "dodge") +
  labs(title = "Distribution of Mitoses by Class")
       
fig_bc <- ggplotly(p_mito, tooltip = "text") %>%
layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

##BIVARIATE ANALYSIS ## 1. Do malignant tumors have significantly higher clump thickness than benign ones? 2. Is there a difference in the number of mitoses between benign and malignant tumors? 3. Is there a correlation between clump thickness and cell size? 4. Is there a relationship between marginal adhesion and bare nuclei? 5. How strongly are cell shape and cell size related?

# t-test
t.test(Cl.thickness ~ Class, data = cleanbc)

## 
##  Welch Two Sample t-test
## 
## data:  Cl.thickness by Class
## t = -23.927, df = 361.43, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group benign and group malignant is not equal to 0
## 95 percent confidence interval:
##  -4.571510 -3.877131
## sample estimates:
##    mean in group benign mean in group malignant 
##                2.963964                7.188285

# correlation
cor.test(cleanbc$Cell.size, cleanbc$Cell.shape)

## 
##  Pearson's product-moment correlation
## 
## data:  cleanbc$Cell.size and cleanbc$Cell.shape
## t = 56.283, df = 681, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8929850 0.9196562
## sample estimates:
##       cor 
## 0.9072282

# boxplot
library(ggplot2)
p_clumpthi <- ggplot(cleanbc, aes(x = Class, y = Cl.thickness, fill = Class)) +
  geom_boxplot() +
  labs(title = "Clump Thickness by Tumor Type")

fig_bc <- ggplotly(p_clumpthi, tooltip = "text") %>%
  layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

2. Is there a difference in the number of mitoses between benign and malignant tumors?

t.test(Mitoses ~ Class, data = cleanbc)

## 
##  Welch Two Sample t-test
## 
## data:  Mitoses by Class
## t = -9.1697, df = 248.17, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group benign and group malignant is not equal to 0
## 95 percent confidence interval:
##  -1.867370 -1.207021
## sample estimates:
##    mean in group benign mean in group malignant 
##                1.065315                2.602510

p_mitosis <- ggplot(cleanbc, aes(x = Class, y = Mitoses, fill = Class)) +
  geom_boxplot() +
  labs(title = "Mitoses by Class")

fig_bc <- ggplotly(p_mitosis, tooltip = "text") %>%
  layout(modebar = list(visible = FALSE))

# Show plot
fig_bc

3. Is there a correlation between clump thickness and cell size?

cor.test(cleanbc$Cl.thickness, cleanbc$Cell.size)

## 
##  Pearson's product-moment correlation
## 
## data:  cleanbc$Cl.thickness and cleanbc$Cell.size
## t = 21.879, df = 681, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5961976 0.6845089
## sample estimates:
##       cor 
## 0.6424815

p_ctcs <- ggplot(cleanbc, aes(x = Cl.thickness, y = Cell.size)) +
  geom_point() +
  geom_smooth(method = "lm") +
  labs(title = "Clump Thickness vs Cell Size")

fig_bc <- ggplotly(p_ctcs, tooltip = "text") %>%
  layout(modebar = list(visible = FALSE))

## `geom_smooth()` using formula = 'y ~ x'

# Show plot
fig_bc

4. Is there a relationship between marginal adhesion and bare nuclei?

cleanbc$Bare.nuclei <- as.numeric(as.character(cleanbc$Bare.nuclei)) # Ensure numeric
cor.test(cleanbc$Marg.adhesion, cleanbc$Bare.nuclei)

## 
##  Pearson's product-moment correlation
## 
## data:  cleanbc$Marg.adhesion and cleanbc$Bare.nuclei
## t = 23.594, df = 681, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6271832 0.7099493
## sample estimates:
##       cor 
## 0.6706483

p_mabn <- ggplot(cleanbc, aes(x = Marg.adhesion, y = Bare.nuclei)) +
  geom_point() +
  geom_smooth(method = "lm") +
  labs(title = "Marginal Adhesion vs Bare Nuclei")

fig_bc <- ggplotly(p_mabn, tooltip = "text") %>%
  layout(modebar = list(visible = FALSE))

## `geom_smooth()` using formula = 'y ~ x'

# Show plot
fig_bc

5. How strongly are cell shape and cell size related?

# Correlation test between Cell Shape and Cell Size
cor.test(bc$Cell.shape, bc$Cell.size)

## 
##  Pearson's product-moment correlation
## 
## data:  bc$Cell.shape and bc$Cell.size
## t = 56.818, df = 697, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8927650 0.9192197
## sample estimates:
##       cor 
## 0.9068819

# Scatter plot with regression line
library(ggplot2)
p_cleanbc <- ggplot(bc, aes(x = Cell.shape, y = Cell.size)) +
  geom_point(color = "steelblue", alpha = 0.6) +
  geom_smooth(method = "lm", se = TRUE, color = "darkred") +
  labs(
    title = "Relationship Between Cell Shape and Cell Size",
    x = "Uniformity of Cell Shape",
    y = "Uniformity of Cell Size"
  )

fig_bc <- ggplotly(p_cleanbc, tooltip = "text") %>%
  layout(modebar = list(visible = FALSE))

## `geom_smooth()` using formula = 'y ~ x'

# Show plot
fig_bc

##ggstatplot Integration

##1. Do malignant tumors have significantly higher clump thickness than benign ones?

ggbetweenstats(
  data = bc,
  x = Class,
  y = Cl.thickness,
  title = "Clump Thickness: Benign vs Malignant",
  messages = FALSE
)

##Insight:Malignant tumors have significantly higher clump thickness than benign ones (mean = 7.20 vs. 2.96, p = 7.43e-78).

2. Is there a difference in the number of mitoses between benign and malignant tumors?

ggbetweenstats(
  data = bc,
  x = Class,
  y = Mitoses,
  title = "Mitoses: Benign vs Malignant",
  messages = FALSE
)

##Insight: Malignant tumors have significantly more mitoses than benign ones (mean = 2.59 vs. 1.06, p = 1.84e-17).

##3. Is there a correlation between clump thickness and cell size?

ggscatterstats(
  data = bc,
  x = Cl.thickness,
  y = Cell.size,
  title = "Correlation: Clump Thickness vs Cell Size",
  messages = FALSE
)

## Registered S3 method overwritten by 'ggside':
##   method from   
##   +.gg   ggplot2

## `stat_xsidebin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_ysidebin()` using `bins = 30`. Pick better value with `binwidth`.

##Insight: There is a strong positive correlation between clump thickness and cell size (r = 0.64, p = 1.94e-83).

4. Is there a relationship between marginal adhesion and bare nuclei?

ggscatterstats(
  data = bc,
  x = Marg.adhesion,
  y = Bare.nuclei,
  title = "Correlation: Marginal Adhesion vs Bare Nuclei",
  messages = FALSE
)

## `stat_xsidebin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_ysidebin()` using `bins = 30`. Pick better value with `binwidth`.

##Insight: There is a strong positive relationship between marginal adhesion and bare nuclei. The Pearson correlation is 0.67, indicating that as marginal adhesion increases, bare nuclei tend to increase as well.

5. How strongly are cell shape and cell size related?

ggscatterstats(
  data = bc,
  x = Cell.shape,
  y = Cell.size,
  title = "Correlation: Cell Shape vs Cell Size",
  messages = FALSE
)

## `stat_xsidebin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_ysidebin()` using `bins = 30`. Pick better value with `binwidth`.

##Insight: Cell shape and cell size are very strongly related. The Pearson correlation is 0.91, which indicates a very strong positive relationship, meaning that as cell shape increases, cell size also tends to increase significantly.

##Analysis and Conclusion

###The exploratory data analysis reveals strong and statistically significant positive correlations between several key cellular features. Most notably, cell shape and cell size exhibit a very strong correlation (r = 0.91), while clump thickness and cell size show a moderately strong correlation (r = 0.64). In both cases, the relationships are highly significant, with p-values far below conventional thresholds, indicating that these patterns are not due to random chance.

###These findings suggest that as cell shape or clump thickness increases, cell size also tends to increase. The strong alignment of data points along the regression lines in both plots highlights consistent linear trends. This implies that the features may reflect interconnected biological processes—such as cellular growth, structure, and potential abnormality—that are important in medical diagnostics, particularly in identifying or classifying tumor cells.

###However, the presence of such strong correlations, especially between cell shape and size, also suggests potential multicollinearity if these features are used together in predictive modeling. This could affect the interpretability and performance of machine learning models. Therefore, it’s recommended to consider feature selection or dimensionality reduction techniques (e.g., PCA) during model development to avoid redundancy while retaining predictive power.

###In conclusion, the identified relationships not only highlight biologically meaningful associations in the dataset but also provide important guidance for building more robust and interpretable models in subsequent analysis.