Breast Cancer Malignancy Prediction Using Machine Learning
Phoon Hao Xian, Nur Ariana Sofea binti Badrul Hisham, Vijaykumar Kartha Ramchandran
2025-05-23
WQD7004 Programming for Data Science
Group 07 Members
| Matric Number | Full Name |
|---|---|
| S2034194 | Phoon Hao Xian |
| 23096526 | Nur Ariana Sofea binti Badrul Hisham |
| S2033073 | Vijaykumar Kartha Ramchandran |
Methodology: CRISP-DM
1. Understand: Define the problem and understand the dataset.
2. Explore: Load and examine the dataset, identifying key attributes.
3. Prepare: Clean and preprocess the data for analysis.
4. Model: Build predictive models using machine learning techniques.
5. Evaluate: Assess model performance using relevant metrics.
6. Deploy: Present findings, forecasts and actionable recommendations.
1. Data Understanding
- Problem Definition: The goal of this project is to predict whether a breast tumor is malignant or benign based on clinical data. We aim to apply machine learning algorithms to solve this classification problem.
- Business Objectives: The outcome will assist in early diagnosis and decision-making for better treatment of breast cancer.
- Data Collection: We use the Breast Cancer Prediction dataset available on Kaggle, which includes attributes related to tumors (e.g., size, texture, perimeter) and their diagnosis (benign or malignant).
Research Questions and Objectives
Research Questions:
- How can clinical data predict whether a breast tumor is malignant or benign? (Classification)
- How accurately can a regression model predict tumor size based on available clinical data? (Regression)
Research Objectives:
- To develop a machine learning model for classifying breast cancer diagnosis based on clinical data. (Classification)
- To build a predictive model that estimates tumor size using relevant clinical data to understand growth patterns. (Regression)
2. Data Exploration (Exploring and Loading the Data)
Data Overview:
- The dataset used in this project is sourced from Kaggle and can be accessed here.
- The dataset was collected in 2015 and consists of various clinical attributes related to breast cancer diagnosis.
- Download the dataset from Kaggle manually, and then upload it to R project directory as ‘breast_cancer_data.csv’.
Initial Exploration:
Step 1: Installing Required Packages
The code first ensures that the readr package is installed, which is used to read the CSV file efficiently into R. If readr is already installed, it skips this step.
# Install required packages if not already installed
if (!requireNamespace("readr", quietly = TRUE)) install.packages("readr")Step 2: Loading the readr Package
Once readr is installed, it’s loaded into the R environment using library(readr) to make the read_csv() function available for reading the CSV file.
# Load necessary libraries
library(readr)Step 3: Reading the CSV File
The read_csv() function is used to read the file ‘breast_cancer_data.csv’ into a data frame called df. This function automatically detects the data types for each column based on the content.
# Now, read the file into R
df <- read_csv("breast_cancer_data.csv")## New names:
## • `` -> `...33`## Warning: One or more parsing issues, call `problems()` on your data frame for details,
## e.g.:
## dat <- vroom(...)
## problems(dat)## Rows: 568 Columns: 33
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): diagnosis
## dbl (31): id, radius_mean, texture_mean, perimeter_mean, area_mean, smoothne...
## lgl (1): ...33
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.3A. Data Preparation (Cleaning the Data)
Data cleaning is a critical step in the data analysis process. The raw dataset often contains errors, inconsistencies and irrelevant information. In this project, data cleaning involves handling missing values, removing duplicate entries, converting variables to appropriate formats and ensuring that the dataset is ready for further analysis. Proper data cleaning enhances the accuracy and reliability of the results obtained from data analysis and model building.
In our breast cancer dataset, we have clinical attributes that need to be processed before they can be used for classification and regression tasks. Specifically, we will:
- Handle missing data by either removing or imputing missing values.
- Remove duplicate rows that can distort the analysis and lead to overfitting.
- Convert categorical variables like diagnosis to the proper data type.
- Remove unnecessary columns that do not add value to the analysis (such as the column ‘X’).
- Ensure that all variables are correctly formatted for machine learning models.
Step 1: Load the Necessary Libraries
The first step in data cleaning is to load the necessary libraries for data manipulation and visualization. In this case, we will use dplyr for data manipulation tasks and ggplot2 for visualizations.
# Load necessary libraries
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(corrplot)## corrplot 0.95 loadedlibrary(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2By loading these libraries, we gain access to the functions and methods that allow us to perform operations like filtering, selecting and transforming the dataset. dplyr is a popular R package for efficient data manipulation, and ggplot2 helps in visualizing the cleaned dataset.
Step 2: Load the Dataset
The next step is to load the ‘breast_cancer_data.csv’ dataset into R. We will use the read.csv() function to read the dataset into a data frame.
# Load the renamed CSV file
df <- read.csv("breast_cancer_data.csv", stringsAsFactors = FALSE)
# Preview the data
head(df)# Get the dimensions of the dataset
dim(df) # Returns the number of rows and columns in the dataset## [1] 569 33This step loads the dataset into the df variable. The head() function is used to preview the first six rows of the data to understand its structure before any processing is done. By setting stringsAsFactors = FALSE, we ensure that categorical variables are not automatically converted to factors (which can interfere with analysis).
Step 3: Check the Structure of the Dataset
Now, we will check the structure of the dataset using the str() function. This allows us to see the data types of each column.
str(df)## 'data.frame': 569 obs. of 33 variables:
## $ id : int 842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
## $ diagnosis : chr "M" "M" "M" "M" ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...
## $ X : logi NA NA NA NA NA NA ...The str() function provides an overview of the dataset, including the number of observations (rows) and variables (columns), as well as the data type of each column. This is useful for identifying potential issues, such as columns that should be factors but are currently stored as characters.
Step 4: Get Statistical Summary
We use the summary() function to get a statistical summary of the dataset. This function will provide basic descriptive statistics for each numeric column.
summary(df)## id diagnosis radius_mean texture_mean
## Min. : 8670 Length:569 Min. : 6.981 Min. : 9.71
## 1st Qu.: 869218 Class :character 1st Qu.:11.700 1st Qu.:16.17
## Median : 906024 Mode :character Median :13.370 Median :18.84
## Mean : 30371831 Mean :14.127 Mean :19.29
## 3rd Qu.: 8813129 3rd Qu.:15.780 3rd Qu.:21.80
## Max. :911320502 Max. :28.110 Max. :39.28
## perimeter_mean area_mean smoothness_mean compactness_mean
## Min. : 43.79 Min. : 143.5 Min. :0.05263 Min. :0.01938
## 1st Qu.: 75.17 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492
## Median : 86.24 Median : 551.1 Median :0.09587 Median :0.09263
## Mean : 91.97 Mean : 654.9 Mean :0.09636 Mean :0.10434
## 3rd Qu.:104.10 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040
## Max. :188.50 Max. :2501.0 Max. :0.16340 Max. :0.34540
## concavity_mean concave.points_mean symmetry_mean fractal_dimension_mean
## Min. :0.00000 Min. :0.00000 Min. :0.1060 Min. :0.04996
## 1st Qu.:0.02956 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770
## Median :0.06154 Median :0.03350 Median :0.1792 Median :0.06154
## Mean :0.08880 Mean :0.04892 Mean :0.1812 Mean :0.06280
## 3rd Qu.:0.13070 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612
## Max. :0.42680 Max. :0.20120 Max. :0.3040 Max. :0.09744
## radius_se texture_se perimeter_se area_se
## Min. :0.1115 Min. :0.3602 Min. : 0.757 Min. : 6.802
## 1st Qu.:0.2324 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850
## Median :0.3242 Median :1.1080 Median : 2.287 Median : 24.530
## Mean :0.4052 Mean :1.2169 Mean : 2.866 Mean : 40.337
## 3rd Qu.:0.4789 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190
## Max. :2.8730 Max. :4.8850 Max. :21.980 Max. :542.200
## smoothness_se compactness_se concavity_se concave.points_se
## Min. :0.001713 Min. :0.002252 Min. :0.00000 Min. :0.000000
## 1st Qu.:0.005169 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638
## Median :0.006380 Median :0.020450 Median :0.02589 Median :0.010930
## Mean :0.007041 Mean :0.025478 Mean :0.03189 Mean :0.011796
## 3rd Qu.:0.008146 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710
## Max. :0.031130 Max. :0.135400 Max. :0.39600 Max. :0.052790
## symmetry_se fractal_dimension_se radius_worst texture_worst
## Min. :0.007882 Min. :0.0008948 Min. : 7.93 Min. :12.02
## 1st Qu.:0.015160 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08
## Median :0.018730 Median :0.0031870 Median :14.97 Median :25.41
## Mean :0.020542 Mean :0.0037949 Mean :16.27 Mean :25.68
## 3rd Qu.:0.023480 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72
## Max. :0.078950 Max. :0.0298400 Max. :36.04 Max. :49.54
## perimeter_worst area_worst smoothness_worst compactness_worst
## Min. : 50.41 Min. : 185.2 Min. :0.07117 Min. :0.02729
## 1st Qu.: 84.11 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720
## Median : 97.66 Median : 686.5 Median :0.13130 Median :0.21190
## Mean :107.26 Mean : 880.6 Mean :0.13237 Mean :0.25427
## 3rd Qu.:125.40 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910
## Max. :251.20 Max. :4254.0 Max. :0.22260 Max. :1.05800
## concavity_worst concave.points_worst symmetry_worst fractal_dimension_worst
## Min. :0.0000 Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.1145 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2267 Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.2722 Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3829 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :1.2520 Max. :0.29100 Max. :0.6638 Max. :0.20750
## X
## Mode:logical
## NA's:569
##
##
##
## The summary() function gives us a quick overview of the central tendencies (mean, median), range (min, max) and the spread (quartiles) for numeric columns. This step helps us understand the distribution of each attribute and detect potential outliers or data quality issues.
Step 5: Check for Missing Values
Next, we check for missing values across the dataset. This will help us identify if any columns contain NA (missing) values that need to be addressed.
colSums(is.na(df))## id diagnosis radius_mean
## 0 0 0
## texture_mean perimeter_mean area_mean
## 0 0 0
## smoothness_mean compactness_mean concavity_mean
## 0 0 0
## concave.points_mean symmetry_mean fractal_dimension_mean
## 0 0 0
## radius_se texture_se perimeter_se
## 0 0 0
## area_se smoothness_se compactness_se
## 0 0 0
## concavity_se concave.points_se symmetry_se
## 0 0 0
## fractal_dimension_se radius_worst texture_worst
## 0 0 0
## perimeter_worst area_worst smoothness_worst
## 0 0 0
## compactness_worst concavity_worst concave.points_worst
## 0 0 0
## symmetry_worst fractal_dimension_worst X
## 0 0 569The is.na() function checks for missing values in the dataset. colSums() will sum the missing values in each column. This step is crucial because missing data can impact the performance of machine learning models, so we need to decide whether to remove or impute the missing values.
Step 6: Remove Unnecessary Columns
We will remove the ‘X’ column, which is empty and not useful for our analysis.
df <- df %>% select(-X)This step uses dplyr’s select() function to remove the irrelevant column. Removing unnecessary columns ensures that our dataset only contains relevant variables for analysis, reducing the complexity of the data.
Step 7: Convert ‘diagnosis’ to Factor
Since the diagnosis column contains categorical values (Benign and Malignant), we will convert it to a factor variable.
df$diagnosis <- as.factor(df$diagnosis)
str(df$diagnosis)## Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...table(df$diagnosis)##
## B M
## 357 212Converting the diagnosis column to a factor ensures that R treats it as a categorical variable. The str() function confirms the data type, and table() shows the count of each category (Benign vs. Malignant). This is important for classification tasks.
Step 8: Check for Duplicates
We check for duplicate rows in the dataset to ensure data integrity.
sum(duplicated(df))## [1] 0The duplicated() function checks for duplicate rows. If duplicates are found, they can introduce bias or overfitting in machine learning models, so they need to be removed.
Step 9: Remove Duplicate Rows
If any duplicate rows exist, we will remove them to ensure that each observation is unique.
df <- df[!duplicated(df), ]
sum(duplicated(df))## [1] 0This step removes duplicate rows using the duplicated() function, and then rechecks for any remaining duplicates. Removing duplicates ensures that the dataset only contains unique observations.
Step 10: Save the Cleaned Dataset
Once the dataset is cleaned and preprocessed, we save it as a new CSV file. This allows us to retain a copy of the cleaned data for future use and analysis, which can be helpful for reproducibility or sharing the dataset with others.
By using a relative file path (“cleaned_breast_cancer_data.csv”), we ensure that the file will be saved in the current working directory, making it portable across different environments.
Download Link: Click here to download the cleaned dataset
3B. EDA (Exploratory Data Analysis) Section
Exploratory Data Analysis (EDA) is an essential step in data analysis that helps us uncover patterns, relationships and trends within the dataset. In the context of our project, EDA will allow us to understand the distribution of key variables and their relationships to each other. This step also involves visualizing the data to detect any potential anomalies or outliers that might affect the results.
In this section, we will:
- Perform univariate analysis to understand individual variables.
- Conduct bivariate analysis to examine relationships between pairs of variables.
- Use multivariate analysis to explore relationships between multiple variables at once.
Step 1: Univariate Analysis - Bar Plot
of Diagnosis Counts
We begin with a bar plot to visualize the distribution of
diagnoses (Benign vs. Malignant).
# Bar plot of diagnosis counts
ggplot(df, aes(x = diagnosis)) +
geom_bar(fill = c("lightblue", "salmon")) +
labs(title = "Count of Diagnosis (Benign vs Malignant)", x = "Diagnosis", y = "Count") +
theme_minimal()
Explanation for the Output of Step 1 (Bar Plot of
Diagnosis Counts)
The bar plot shown here visualizes the distribution
of the diagnosis variable, which indicates whether a tumor
is Benign (‘B’) or Malignant (‘M’). In
this case:
Key Insights from the Bar Plot:
- Benign (B) Diagnoses:
- The blue bar represents the Benign category (‘B’).
- It is clearly the larger category, with over 300 instances. This indicates that the dataset contains a higher number of benign cases compared to malignant ones.
- Malignant (M) Diagnoses:
- The red bar represents the Malignant category (‘M’).
- It is smaller in size, with slightly over 200 instances, indicating that malignant cases are fewer than benign cases in the dataset.
Conclusion:
The dataset is imbalanced with more benign tumors
compared to malignant ones. This imbalance is important because it may
affect how we train machine learning models, especially for
classification tasks. We may need to consider techniques like
oversampling, undersampling or using
weighted models to account for this imbalance during model training.
Step 2: Univariate Analysis - Boxplot
for radius_mean
We visualize the distribution of radius_mean across
diagnosis categories using a boxplot.
# Boxplot for radius_mean
ggplot(df, aes(x = diagnosis, y = radius_mean, fill = diagnosis)) +
geom_boxplot() +
labs(title = "Distribution of Radius Mean by Diagnosis", x = "Diagnosis", y = "Radius Mean") +
theme_minimal()
Explanation for the Output of Step 2 (Boxplot for
radius_mean by Diagnosis)
The boxplot shown here visualizes the distribution
of the radius_mean variable across the two diagnosis
categories: Benign (B) and Malignant
(M).
Key Observations from the Boxplot:
- Benign (B) Tumors:
- The red box represents the Benign category (‘B’).
- The interquartile range (IQR) of
radius_meanfor benign tumors is relatively narrow, with a median around 12.8. - There are a few outliers present (points above the upper whisker), which indicates some benign tumors have unusually larger radii compared to most of the other benign cases.
- Malignant (M) Tumors:
- The teal box represents the Malignant category (‘M’).
- The
radius_meanfor malignant tumors is generally higher, with a median around 17.3. - The IQR for malignant tumors is broader, suggesting greater variability in the sizes of malignant tumors.
- There are also a few outliers (points above the upper whisker), indicating that some malignant tumors have a significantly larger radius than most other malignant tumors.
Conclusion:
The radius_mean variable appears to be higher for malignant
tumors compared to benign ones. The distribution of
malignant tumor sizes is more spread out, and it has a
higher median compared to benign tumors. This
difference could be an important feature in classification
models for predicting whether a tumor is benign or
malignant.
Step 3: Univariate Analysis - Boxplot
for texture_mean
A similar boxplot for texture_mean helps compare its
distribution across diagnosis categories.
# Boxplot for texture_mean
ggplot(df, aes(x = diagnosis, y = texture_mean, fill = diagnosis)) +
geom_boxplot() +
labs(title = "Distribution of Texture Mean by Diagnosis", x = "Diagnosis", y = "Texture Mean") +
theme_minimal()
Explanation for the Output of Step 3 (Boxplot for
texture_mean by Diagnosis)
The boxplot shown here visualizes the distribution
of the texture_mean variable across the two diagnosis
categories: Benign (B) and Malignant
(M).
Key Observations from the Boxplot:
- Benign (B) Tumors:
- The red box represents the Benign category (‘B’).
- The interquartile range (IQR) for
texture_meanin benign tumors is approximately 15 to 20. - The median texture value for benign tumors is around 15.5.
- There are numerous outliers (points above the upper whisker), suggesting that some benign tumors have a significantly higher texture mean than most benign cases.
- Malignant (M) Tumors:
- The teal box represents the Malignant category (‘M’).
- The
texture_meanfor malignant tumors ranges from approximately 19 to 24. - The median for malignant tumors is slightly higher than for benign tumors, around 22.
- The malignant tumors also show outliers (points above the upper whisker), indicating that some malignant tumors have a much higher texture mean compared to others.
Conclusion:
The texture_mean variable exhibits a higher
median for malignant tumors compared to benign tumors.
Additionally, malignant tumors tend to have a wider
spread of texture values, indicating more variability
in their texture compared to benign tumors.
Step 4: Univariate Analysis -
Histogram for radius_mean
We plot a histogram to examine the distribution of
radius_mean.
# Histogram for radius_mean distribution by diagnosis
ggplot(df, aes(x = radius_mean, fill = diagnosis)) +
geom_histogram(position = "dodge", bins = 30) +
labs(title = "Distribution of Radius Mean by Diagnosis", x = "Radius Mean", y = "Count") +
theme_minimal()
Explanation for the Output of Step 4 (Histogram for
radius_mean by Diagnosis)
The histogram shown here visualizes the distribution
of the radius_mean variable, which represents the mean of
the tumor’s radius. This variable is important as it gives us an idea
about the overall size of the tumor.
Key Observations from the Histogram:
- Benign (B) Tumors (represented by red
bars):
- Most of the Benign tumors have a
radius_meanin the range of 6 to 18. The histogram shows a right-skewed distribution, indicating that the majority of benign tumors are smaller in size. - There is a peak in the histogram around
radius_mean = 10, which suggests that many benign tumors have a radius close to this value. - The number of Benign tumors decreases as the
radius_meanincreases above 12.
- Most of the Benign tumors have a
- Malignant (M) Tumors (represented by blue
bars):
- The Malignant tumors, shown in the blue bars, tend
to have a wider spread across the range of
radius_meanvalues. However, there is a great concentration in the range between 13 to 21. - There is a noticeable shift towards higher values
of
radius_meanin malignant tumors, with a long tail on the right side of the distribution. This indicates that while most malignant tumors have aradius_meansimilar to benign tumors, a few malignant tumors are significantly larger.
- The Malignant tumors, shown in the blue bars, tend
to have a wider spread across the range of
Conclusion:
The radius_mean variable exhibits a different distribution
for Benign and Malignant tumors. While
both types of tumors show some overlap in their radius_mean
values (especially between 12 and 18), malignant tumors
seem to exhibit wider variation and a tendency towards
larger tumor sizes. The histogram also reveals that the
majority of Benign tumors are smaller in size, whereas
Malignant tumors exhibit more variability and larger
values. This information is valuable for building a
classification model to distinguish between Benign and
Malignant tumors based on their radius_mean.
Step 5: Bivariate Analysis - Scatter
Plot of radius_mean vs. texture_mean
We create a scatter plot to visualize the relationship between
radius_mean and texture_mean.
# Scatter plot of radius_mean vs. texture_mean, colored by diagnosis
ggplot(df, aes(x = radius_mean, y = texture_mean, color = diagnosis)) +
geom_point() +
labs(title = "Radius Mean vs. Texture Mean by Diagnosis", x = "Radius Mean", y = "Texture Mean") +
theme_minimal()
Explanation for the Output of Step 5 (Scatter Plot of
radius_mean vs. texture_mean by
Diagnosis)
The scatter plot shown here visualizes the
relationship between two features of the dataset:
radius_mean and texture_mean. These two
features are critical in identifying characteristics of the tumors in
the dataset.
Key Observations from the Scatter Plot:
- Benign (B) Tumors (Red points):
- The Benign tumors are generally
concentrated at the lower end of the
radius_meanaxis, withradius_meanvalues mostly between 8 and 16. - The
texture_meanvalues for Benign tumors range from about 10 to 28. The red points form a relatively dense cloud, indicating that most Benign tumors have smaller radii and moderate texture values. - There is a distinct clustering in the lower part of the graph for Benign tumors.
- The Benign tumors are generally
concentrated at the lower end of the
- Malignant (M) Tumors (Blue points):
- The Malignant tumors, represented by blue points, tend to spread across the graph. While they also appear in the lower range of the radius_mean (between 10 and 25), there is a notable shift towards the right..
- Malignant tumors have more diverse texture values (ranging from about 12 to 31), and the spread is more wide and dispersed compared to Benign tumors.
- There is a separation in the higher
radius_meanandtexture_meanvalues, indicating that Malignant tumors tend to be larger and have more varied textures.
Conclusion: The scatter plot indicates that there is
a potential relationship between the
radius_mean and texture_mean of the tumors.
Malignant tumors tend to have larger
radii and more varied textures, while
Benign tumors show smaller radii and
more consistent textures. This distinction is helpful
in identifying the type of tumor and may assist in building a
classification model for tumor diagnosis based on these
features.
Step 6: Bivariate Analysis - Boxplot
for smoothness_mean by Diagnosis
We use a boxplot to visualize the distribution of
smoothness_mean for each diagnosis.
# Boxplot for smoothness_mean by diagnosis
ggplot(df, aes(x = diagnosis, y = smoothness_mean, fill = diagnosis)) +
geom_boxplot() +
labs(title = "Smoothness Mean by Diagnosis", x = "Diagnosis", y = "Smoothness Mean") +
theme_minimal()
Explanation for the Output of Step 6 (Boxplot for
smoothness_mean by Diagnosis)
The boxplot displayed here visualizes the
distribution of the smoothness_mean feature, segmented by
the diagnosis of the tumor (Benign vs. Malignant). The
smoothness_mean measures the smoothness of the tumor’s
surface, which can be indicative of the tumor’s texture and
consistency.
Key Observations from the Boxplot:
- Benign (B) Tumors (Red box):
- The Benign tumors tend to have a slightly
lower median
smoothness_mean(around 0.090**), as shown by the red box. - The interquartile range (IQR) for Benign tumors is narrower, indicating that most of the Benign tumors have a relatively consistent smoothness.
- The upper and lower whiskers for the Benign
tumors indicate that there are a few outliers
with high smoothness values, but the majority of the data is
concentrated in the lower range of the
smoothness_mean.
- The Benign tumors tend to have a slightly
lower median
- Malignant (M) Tumors (Blue box):
- The Malignant tumors, represented by the blue box, show a slightly higher median smoothness_mean (around 0.113), indicating that Malignant tumors are generally somewhat smoother.
- The interquartile range for Malignant tumors is wider, suggesting more variation in smoothness compared to Benign tumors.
- Malignant tumors also exhibit outliers, with some having much higher smoothness values, especially in the upper range, which indicates that there is greater diversity in smoothness for Malignant tumors.
Conclusion: The boxplot reveals that Benign tumors tend to have a more consistent smoothness with a lower median value, whereas Malignant tumors exhibit more variability in smoothness and have a slightly higher median. These observations can be useful in distinguishing between Benign and Malignant tumors based on smoothness, providing a useful feature for classification models.
Step 7: Multivariate Analysis - Correlation Matrix
We compute and visualize the correlation matrix to understand the relationships between numeric features.
numeric_cols <- sapply(df, is.numeric)
cor_matrix <- cor(df[, numeric_cols], use = "complete.obs")
library(corrplot)
corrplot(cor_matrix, method = "color", type = "upper", tl.col = "black", tl.cex = 0.7)
Explanation for the Output of Step 7 (Correlation Matrix)
The correlation matrix displayed here visualizes the relationships between numeric features in the dataset, particularly focusing on the correlation between various tumor-related measurements. This matrix is generated using a heatmap where the color intensity indicates the strength of the relationship between pairs of variables. The color scale at the right side of the plot indicates the strength and direction of the correlation: - Blue represents positive correlations, where both variables increase or decrease together. - Red represents negative correlations, where as one variable increases, the other decreases. - White/Light color indicates a weak or no correlation between variables.
Key Observations from the Correlation Matrix:
- High Positive Correlations:
- There are strong positive correlations between
several variables, which makes sense as many of the features are related
to each other in terms of size, shape or texture of the tumors:
radius_meanandperimeter_mean: These two features show a very strong positive correlation (actually 1), meaning that as the radius increases, the perimeter also increases. This is expected because a larger radius would typically result in a larger perimeter.area_meanandperimeter_mean: The correlation between these two features is also strong, as a larger area tends to correlate with a larger perimeter.smoothness_meanandsymmetry_mean: These features also show a positive correlation (almost 0.7), which suggests that smoother tumors tend to be more symmetrical.
- These high correlations are expected since many of these measurements are geometric features that are often related to each other.
- There are strong positive correlations between
several variables, which makes sense as many of the features are related
to each other in terms of size, shape or texture of the tumors:
- Weaker or Negative Correlations:
- Some correlations are weaker or negative, which indicates that there
isn’t a strong relationship between these pairs of features:
- For example, there is a weak correlation between
radius_meanandfractal_dimension_mean. The fractal dimension measures the irregularity or complexity of the tumor, which doesn’t necessarily increase or decrease with the radius.
- For example, there is a weak correlation between
- Some correlations are weaker or negative, which indicates that there
isn’t a strong relationship between these pairs of features:
Conclusion: The correlation matrix is a useful tool
for identifying relationships between variables. It helps us identify
redundant features (e.g., radius_mean,
perimeter_mean and area_mean are highly
correlated) and suggests which features might provide complementary
information when building predictive models. The matrix also indicates
which variables might be combined or excluded for model building based
on their correlations.
Step 8: Multivariate Analysis - Pair Plot of Selected Features
We use a pair plot to visualize the relationships between selected
features (e.g., radius_mean,
texture_mean).
library(GGally)
features_subset <- c("diagnosis", "radius_mean", "texture_mean", "perimeter_mean", "area_mean", "smoothness_mean")
ggpairs(df[, features_subset], mapping = aes(color = diagnosis), title = "Pairplot of Selected Features")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Explanation for the Output of Step 8 (Pair Plot of Selected Features)
The pair plot is a powerful visualization tool for exploring relationships between multiple features in the dataset. It provides a matrix of scatter plots, histograms and correlation coefficients to help identify patterns, trends and possible relationships between pairs of variables.
Key Observations from the Pair Plot:
- Univariate Distribution (Diagonal):
- The histograms along the diagonal show the
distribution of each feature. For example:
radius_meanandperimeter_meanshow distinct distributions for Benign and Malignant tumors, with Malignant tumors (denoted by blue) having higher values.texture_meanandarea_meanalso exhibit different distributions between Benign and Malignant cases, which suggests these features can help differentiate the two classes.
- The histograms along the diagonal show the
distribution of each feature. For example:
- Bivariate Relationships (Off-diagonal):
- The scatter plots show how two features interact with each other.
For example:
- There is a strong positive correlation between
radius_meanandperimeter_mean(as expected, since a larger radius leads to a larger perimeter). The correlation value (0.998) is displayed in the plot, which confirms this. - The relationship between
radius_meanandtexture_meanshows a weak positive correlation (0.324), suggesting that these two features do not have a strong linear relationship. - The scatter plot for
area_meanandperimeter_meanalso demonstrates a strong positive correlation (0.987), which is similar to the relationship betweenradius_meanandperimeter_mean.
- There is a strong positive correlation between
- The scatter plots show how two features interact with each other.
For example:
- Correlation Coefficients:
- The correlation values on each scatter plot show
the degree of linear relationship between pairs of features:
- Strong Positive Correlations:
radius_meanvs.perimeter_mean: 0.998 (very strong correlation, indicating that as radius increases, perimeter also increases).perimeter_meanvs.area_mean: 0.987 (strong positive correlation, as expected for geometric properties of tumors).
- Moderate Correlations:
radius_meanvs.texture_mean: 0.324 (weak positive correlation).area_meanvs.smoothness_mean: 0.177 (weak positive correlation).
- Negative Correlations:
texture_meanvs.smoothness_mean: -0.023 (small negative correlation, suggesting that higher texture values tend to correspond to lower smoothness).
- Strong Positive Correlations:
- The correlation values on each scatter plot show
the degree of linear relationship between pairs of features:
Conclusion: The pair plot visually confirms the
relationships between various features in the dataset. Some features
like radius_mean, perimeter_mean and
area_mean are strongly correlated, which can inform our
feature selection and model-building process. On the other hand,
features with weak correlations like radius_mean and
texture_mean may offer additional unique information for
classification or regression models.
4. Data Modelling
Based on exploratory data analysis (EDA) and the cleaned breast cancer dataset, we will train a machine learning model to predict the size of a tumor (measured by area_mean) using various clinical measurements. Since we already have labeled data with tumor size and diagnosis (benign or malignant), supervised learning is the appropriate choice.
We begin with Linear Regression, which is suitable for predicting continuous numerical variables using numerical input features. The objective is to find the best-fit linear relationship between the input features and the target variable.
Feature Selection
The original dataset includes many clinical features. However, for
our model, we remove those that are directly correlated with or
derivable from the target variable (area_mean), to prevent
data leakage. Specifically, we exclude features like
radius_*, perimeter_*, area_se,
and area_worst.
Target Variable:
area_mean(tumor size)
Excluded Features:
radius_mean,radius_se,radius_worstperimeter_mean,perimeter_se,perimeter_worstarea_se,area_worsttexture_mean,texture_se,texture_worst
Selected Input Features:
smoothness_compactness_concavity_concave.points_symmetry_fractal_dimension_
4A. Regression Models for Tumor Size Prediction
In this section, we build a linear regression model to predict the
average tumor area (area_mean) using several clinical
features from the breast cancer dataset. We first load the data and
inspect its structure, then carefully select input features to avoid
data leakage by excluding variables directly related to area, radius, or
perimeter. We then fit a linear model with the selected predictors and
display the summary of model coefficients and overall performance.
The steps include:
- Loading required packages and data
- Selecting relevant clinical features as predictors
- Fitting a linear regression model to predict tumor size
- Reviewing the model’s summary and interpreting the main results
# 1. Load required packages for data manipulation and analysis
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ lubridate 1.9.4 ✔ tibble 3.2.1
## ✔ purrr 1.0.4 ✔ tidyr 1.3.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors# 2. Read in the cleaned breast cancer dataset
data <- read.csv("cleaned_breast_cancer_data.csv")
# 3. Display all column names in the dataset
colnames(data)## [1] "id" "diagnosis"
## [3] "radius_mean" "texture_mean"
## [5] "perimeter_mean" "area_mean"
## [7] "smoothness_mean" "compactness_mean"
## [9] "concavity_mean" "concave.points_mean"
## [11] "symmetry_mean" "fractal_dimension_mean"
## [13] "radius_se" "texture_se"
## [15] "perimeter_se" "area_se"
## [17] "smoothness_se" "compactness_se"
## [19] "concavity_se" "concave.points_se"
## [21] "symmetry_se" "fractal_dimension_se"
## [23] "radius_worst" "texture_worst"
## [25] "perimeter_worst" "area_worst"
## [27] "smoothness_worst" "compactness_worst"
## [29] "concavity_worst" "concave.points_worst"
## [31] "symmetry_worst" "fractal_dimension_worst"# 4. Select input features (clinical variables to use as predictors)
input_features <- data %>%
select(
texture_mean, texture_se, texture_worst,
smoothness_mean, smoothness_se, smoothness_worst,
compactness_mean, compactness_se, compactness_worst,
concavity_mean, concavity_se, concavity_worst,
concave.points_mean, concave.points_se, concave.points_worst,
symmetry_mean, symmetry_se, symmetry_worst,
fractal_dimension_mean, fractal_dimension_se, fractal_dimension_worst
)
# 5. Create a new data frame that combines the target variable (area_mean) with selected predictors
model_data <- cbind(area_mean = data$area_mean, input_features)
# 6. Fit a linear regression model to predict area_mean using the selected clinical features
model <- lm(area_mean ~ ., data = model_data)
# 7. Display a summary of the model, including coefficients and overall fit statistics
summary(model)##
## Call:
## lm(formula = area_mean ~ ., data = model_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -344.16 -79.47 -4.35 60.31 737.62
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1899.863 94.586 20.086 < 2e-16 ***
## texture_mean 4.464 3.977 1.123 0.2621
## texture_se -27.704 18.233 -1.519 0.1292
## texture_worst -1.209 3.451 -0.350 0.7263
## smoothness_mean -2081.443 988.983 -2.105 0.0358 *
## smoothness_se 1178.960 3316.281 0.356 0.7223
## smoothness_worst -651.244 719.240 -0.905 0.3656
## compactness_mean 858.997 504.839 1.702 0.0894 .
## compactness_se -713.588 1089.052 -0.655 0.5126
## compactness_worst -110.845 188.287 -0.589 0.5563
## concavity_mean 181.210 488.417 0.371 0.7108
## concavity_se 1029.424 633.448 1.625 0.1047
## concavity_worst -266.272 133.468 -1.995 0.0465 *
## concave.points_mean 8265.114 905.487 9.128 < 2e-16 ***
## concave.points_se -12134.831 2448.102 -4.957 9.57e-07 ***
## concave.points_worst 870.287 445.687 1.953 0.0514 .
## symmetry_mean -493.813 368.524 -1.340 0.1808
## symmetry_se 1980.721 1328.944 1.490 0.1367
## symmetry_worst -359.753 242.540 -1.483 0.1386
## fractal_dimension_mean -21533.110 2318.737 -9.287 < 2e-16 ***
## fractal_dimension_se 14127.010 5627.863 2.510 0.0124 *
## fractal_dimension_worst 991.675 1193.376 0.831 0.4063
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 121.1 on 547 degrees of freedom
## Multiple R-squared: 0.886, Adjusted R-squared: 0.8816
## F-statistic: 202.5 on 21 and 547 DF, p-value: < 2.2e-16Linear Regression: Model Training and RMSE Evaluation
We now assess the predictive performance of our linear regression model. To do this, we randomly split the dataset into training (80%) and test (20%) sets. The model is trained on the training set and then used to predict tumor size on the test set. We use Root Mean Squared Error (RMSE) as our evaluation metric. RMSE provides an interpretable measure of the average prediction error (in the same units as the target variable), with lower values indicating better model performance.
# Split into training and test sets
set.seed(123)
index <- sample(1:nrow(model_data), 0.8 * nrow(model_data))
train <- model_data[index, ]
test <- model_data[-index, ]
# Train model
model_train <- lm(area_mean ~ ., data = train)
# Predict on test data
predictions <- predict(model_train, newdata = test)
# Calculate RMSE
rmse <- sqrt(mean((test$area_mean - predictions)^2))
print(paste("RMSE:", round(rmse, 2)))## [1] "RMSE: 121.41"Regularized Regression Models: Ridge & Lasso
We now apply Ridge and Lasso regression, which help reduce overfitting by penalizing large coefficients. Ridge regression applies L2 regularization, which shrinks coefficients toward zero without setting them exactly to zero. Lasso regression uses L1 regularization, which can shrink some coefficients all the way to zero, effectively performing feature selection.
1. Data Preparation for Regularized Regression:
We reload and preprocess the data, selecting and scaling input features to ensure fair evaluation across models.
#install.packages("glmnet")
#install.packages("caret") # for splitting
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.1-8library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## lift2. Model Training:
# Load the data
data <- read.csv("cleaned_breast_cancer_data.csv")
# Select only input features (excluding radius, area, perimeter)
features <- data %>%
select(
texture_mean, texture_se, texture_worst,
smoothness_mean, smoothness_se, smoothness_worst,
compactness_mean, compactness_se, compactness_worst,
concavity_mean, concavity_se, concavity_worst,
concave.points_mean, concave.points_se, concave.points_worst,
symmetry_mean, symmetry_se, symmetry_worst,
fractal_dimension_mean, fractal_dimension_se, fractal_dimension_worst
)
# Scale the features
scaled_features <- scale(features)
# Prepare input matrix and target
X <- as.matrix(scaled_features)
y <- data$area_mean# Split data into training and test set
set.seed(123)
trainIndex <- createDataPartition(y, p = 0.8, list = FALSE)
X_train <- X[trainIndex, ]
X_test <- X[-trainIndex, ]
y_train <- y[trainIndex]
y_test <- y[-trainIndex]3. Ridge Regression:
We fit a Ridge regression model and evaluate its RMSE on the test set.
ridge_model <- cv.glmnet(X_train, y_train, alpha = 0) # alpha = 0 for Ridge
plot(ridge_model)
# Best lambda
ridge_lambda <- ridge_model$lambda.min
# Predict and evaluate
ridge_preds <- predict(ridge_model, s = ridge_lambda, newx = X_test)
ridge_rmse <- sqrt(mean((y_test - ridge_preds)^2))
cat("Ridge RMSE:", round(ridge_rmse, 2), "\n")## Ridge RMSE: 138.614. Lasso Regression:
We fit a Lasso regression model and report the test RMSE.
lasso_model <- cv.glmnet(X_train, y_train, alpha = 1) # alpha = 1 for Lasso
plot(lasso_model)
# Best lambda
lasso_lambda <- lasso_model$lambda.min
# Predict and evaluate
lasso_preds <- predict(lasso_model, s = lasso_lambda, newx = X_test)
lasso_rmse <- sqrt(mean((y_test - lasso_preds)^2))
cat("Lasso RMSE:", round(lasso_rmse, 2), "\n")## Lasso RMSE: 125.335. Elastic Net Regression:
We fit an Elastic Net model, which blends Ridge and Lasso penalties and report the RMSE.
enet_model <- cv.glmnet(X_train, y_train, alpha = 0.5)
enet_lambda <- enet_model$lambda.min
enet_preds <- predict(enet_model, s = enet_lambda, newx = X_test)
enet_rmse <- sqrt(mean((y_test - enet_preds)^2))
cat("Elastic Net RMSE:", round(enet_rmse, 2), "\n")## Elastic Net RMSE: 133.05Performance by Diagnosis Type
We evaluate the Ridge model separately on benign and malignant tumors to check for differences in model accuracy by diagnosis class.
data$diagnosis <- ifelse(data$diagnosis == "M", 1, 0)
# Reconstruct test_data
test_data <- data[-trainIndex, ]
# Predict on test set
preds <- as.vector(predict(ridge_model, s = ridge_lambda, newx = X_test))
# Compute RMSE for benign (diagnosis == 0)
rmse_benign <- sqrt(mean((preds[test_data$diagnosis == 0] - y_test[test_data$diagnosis == 0])^2))
# Compute RMSE for malignant (diagnosis == 1)
rmse_malignant <- sqrt(mean((preds[test_data$diagnosis == 1] - y_test[test_data$diagnosis == 1])^2))
# Print
cat("RMSE (Benign):", round(rmse_benign, 2), "\n")## RMSE (Benign): 106cat("RMSE (Malignant):", round(rmse_malignant, 2), "\n")## RMSE (Malignant): 177.6The model performs better on benign cases than on malignant ones, likely due to class imbalance and higher variability in malignant tumors. Additional steps like upsampling, class-weighted loss, or separate modeling may help improve results.
K-Fold Cross-Validation
To obtain a more robust performance estimate, we use 10-fold cross-validation on the linear regression model.
# Install caret if needed
#install.packages("caret")
library(caret)
# Create model_data again (if not already in environment)
model_data <- cbind(area_mean = data$area_mean, input_features)
# Set up 10-fold cross-validation
set.seed(123)
train_control <- trainControl(method = "cv", number = 10)
# Train linear regression model using caret with cross-validation
cv_model <- train(
area_mean ~ .,
data = model_data,
method = "lm",
trControl = train_control,
metric = "RMSE"
)
# View cross-validated performance
print(cv_model)## Linear Regression
##
## 569 samples
## 21 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 512, 513, 511, 512, 512, 513, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 126.1271 0.8759337 93.27927
##
## Tuning parameter 'intercept' was held constant at a value of TRUE4B. Classification Models for Tumor Diagnosis
In this section, we use several machine learning models to predict whether a tumor is benign or malignant based on clinical features from the breast cancer dataset. We will compare models using accuracy and other classification metrics.
Data Preparation and Splitting
First, we load the required libraries, import the data, clean it and split it into training and test sets for model evaluation.
# install.packages("randomForest")
# install.packages("xgboost")
# Load required libraries
library(tidyverse)
library(caret)
library(ggplot2)
library(pROC) ## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(rpart)
library(randomForest) ## randomForest 4.7-1.2## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinelibrary(e1071)
library(xgboost)##
## Attaching package: 'xgboost'## The following object is masked from 'package:dplyr':
##
## slice# Load the dataset
data <- read.csv("cleaned_breast_cancer_data.csv")
# Remove the 'id' column as it's not relevant for prediction
data <- data %>% select(-id)
# Convert diagnosis to a factor (M = Malignant, B = Benign)
data$diagnosis <- as.factor(ifelse(data$diagnosis == "M", 1, 0))
# Check the distribution of the target variable
table(data$diagnosis)##
## 0 1
## 357 212prop.table(table(data$diagnosis))##
## 0 1
## 0.6274165 0.3725835# Set seed for reproducibility
set.seed(42)
# Split data into training (80%) and testing (20%) sets
train_index <- createDataPartition(data$diagnosis, p = 0.8, list = FALSE)
train_data <- data[train_index, ]
test_data <- data[-train_index, ]
# Check distribution in both sets
table(train_data$diagnosis)##
## 0 1
## 286 170table(test_data$diagnosis)##
## 0 1
## 71 421. Logistic Regression:
We fit a regularized logistic regression model to classify tumor diagnosis, using cross-validation for model selection.
# Train regularized logistic regression model
logit_model <- train(diagnosis ~ .,
data = train_data,
method = "glmnet",
trControl = trainControl(method = "cv", number = 5),
preProcess = c("center", "scale"),
tuneLength = 5)
# Predictions on test set
logit_pred <- predict(logit_model, newdata = test_data)
logit_prob <- predict(logit_model, newdata = test_data, type = "prob")[, "1"]
# Confusion matrix
logit_cm <- confusionMatrix(logit_pred, test_data$diagnosis, positive = "1")
print(logit_cm)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 69 0
## 1 2 42
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9625
##
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 1.0000
## Specificity : 0.9718
## Pos Pred Value : 0.9545
## Neg Pred Value : 1.0000
## Prevalence : 0.3717
## Detection Rate : 0.3717
## Detection Prevalence : 0.3894
## Balanced Accuracy : 0.9859
##
## 'Positive' Class : 1
## # Accuracy
cat("Logistic Regression's Accuracy:", round(logit_cm$overall['Accuracy'], 4), "\n")## Logistic Regression's Accuracy: 0.98232. Random Forest:
We train a random forest classifier, an ensemble method known for robustness and high accuracy.
# Train random forest model
rf_model <- train(diagnosis ~ .,
data = train_data,
method = "rf",
trControl = trainControl(method = "cv", number = 5),
importance = TRUE)
# Predictions on test set
rf_pred <- predict(rf_model, newdata = test_data)
rf_prob <- predict(rf_model, newdata = test_data, type = "prob")[,"1"]
# Confusion matrix
rf_cm <- confusionMatrix(rf_pred, test_data$diagnosis, positive = "1")
print(rf_cm)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 70 0
## 1 1 42
##
## Accuracy : 0.9912
## 95% CI : (0.9517, 0.9998)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9811
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 1.0000
## Specificity : 0.9859
## Pos Pred Value : 0.9767
## Neg Pred Value : 1.0000
## Prevalence : 0.3717
## Detection Rate : 0.3717
## Detection Prevalence : 0.3805
## Balanced Accuracy : 0.9930
##
## 'Positive' Class : 1
## # Accuracy
cat("Random Forest's Accuracy:", round(rf_cm$overall['Accuracy'], 4), "\n")## Random Forest's Accuracy: 0.99123. Support Vector Machine (SVM):
We fit a support vector machine for binary classification, extracting probabilities for ROC analysis.
# Train the SVM model with probability = TRUE
svm_model <- svm(diagnosis ~ ., data = train_data, probability = TRUE)
# Predict on test set
svm_pred <- predict(svm_model, newdata = test_data, probability = TRUE)
# Extract probabilities for class "1" (Malignant)
svm_prob <- attr(svm_pred, "probabilities")[, "1"]
# Confusion Matrix
svm_cm <- confusionMatrix(svm_pred, test_data$diagnosis, positive = "1")
print(svm_cm)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 68 0
## 1 3 42
##
## Accuracy : 0.9735
## 95% CI : (0.9244, 0.9945)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.944
##
## Mcnemar's Test P-Value : 0.2482
##
## Sensitivity : 1.0000
## Specificity : 0.9577
## Pos Pred Value : 0.9333
## Neg Pred Value : 1.0000
## Prevalence : 0.3717
## Detection Rate : 0.3717
## Detection Prevalence : 0.3982
## Balanced Accuracy : 0.9789
##
## 'Positive' Class : 1
## # Accuracy
cat("SVM's Accuracy:", round(svm_cm$overall['Accuracy'], 4), "\n")## SVM's Accuracy: 0.97354. XGBoost:
We use XGBoost, a powerful gradient boosting algorithm, for classification and report accuracy on the test set.
# Ensure diagnosis is numeric (1 = Malignant, 0 = Benign)
train_label <- as.numeric(as.character(train_data$diagnosis))
test_label <- as.numeric(as.character(test_data$diagnosis))
# Prepare model matrices
train_matrix <- model.matrix(diagnosis ~ . - 1, data = train_data)
test_matrix <- model.matrix(diagnosis ~ . - 1, data = test_data)
# Convert to xgb.DMatrix
dtrain <- xgb.DMatrix(data = train_matrix, label = train_label)
dtest <- xgb.DMatrix(data = test_matrix, label = test_label)
# Set parameters
params <- list(
objective = "binary:logistic",
eval_metric = "auc",
max_depth = 6,
eta = 0.1,
gamma = 0,
colsample_bytree = 0.8,
min_child_weight = 1,
subsample = 0.8
)
# Train XGBoost model
xgb_model <- xgb.train(
params = params,
data = dtrain,
nrounds = 100,
watchlist = list(train = dtrain, test = dtest),
print_every_n = 10,
verbose = 1
)## [1] train-auc:0.987258 test-auc:0.980382
## [11] train-auc:0.999044 test-auc:0.999665
## [21] train-auc:0.999609 test-auc:0.999665
## [31] train-auc:0.999897 test-auc:0.999329
## [41] train-auc:0.999959 test-auc:1.000000
## [51] train-auc:0.999979 test-auc:1.000000
## [61] train-auc:1.000000 test-auc:1.000000
## [71] train-auc:1.000000 test-auc:0.999665
## [81] train-auc:1.000000 test-auc:0.999665
## [91] train-auc:1.000000 test-auc:0.999665
## [100] train-auc:1.000000 test-auc:0.999665# Predictions
xgb_prob <- predict(xgb_model, dtest)
xgb_pred <- ifelse(xgb_prob > 0.5, "1", "0")
xgb_pred <- factor(xgb_pred, levels = c("0", "1"))
test_data$diagnosis <- factor(test_data$diagnosis, levels = c("0", "1"))
# Confusion matrix
xgb_cm <- confusionMatrix(xgb_pred, test_data$diagnosis, positive = "1")
print(xgb_cm)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 69 0
## 1 2 42
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6283
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9625
##
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 1.0000
## Specificity : 0.9718
## Pos Pred Value : 0.9545
## Neg Pred Value : 1.0000
## Prevalence : 0.3717
## Detection Rate : 0.3717
## Detection Prevalence : 0.3894
## Balanced Accuracy : 0.9859
##
## 'Positive' Class : 1
## # Accuracy
cat("XGBoost's Accuracy:", round(xgb_cm$overall['Accuracy'], 4), "\n")## XGBoost's Accuracy: 0.98234C. Visualizations
This section presents graphical summaries to interpret our regression and classification model results. We visualize predicted vs. actual values for the regression model and plot ROC curves to evaluate classifier performance.
1. Predicted vs Actual Plot for Regression Model:
This scatter plot compares the predicted tumor area to the actual tumor area for our test set. The dashed red line represents perfect prediction. Points closer to the line indicate more accurate predictions.
library(ggplot2)
# Create a data frame with actual and predicted values
results <- data.frame(
Actual = test$area_mean,
Predicted = predictions
)
# Plot predicted vs actual
ggplot(results, aes(x = Actual, y = Predicted)) +
geom_point(alpha = 0.6, color = "blue") +
geom_abline(intercept = 0, slope = 1, color = "red", linetype = "dashed") +
labs(
title = "Predicted vs Actual Tumor Area",
x = "Actual area_mean",
y = "Predicted area_mean"
) +
theme_minimal()
2. ROC Curves for Classification Models:
We plot the Receiver Operating Characteristic (ROC) curves for each classifier. ROC curves illustrate the trade-off between sensitivity and specificity for different thresholds. The area under the curve (AUC) quantifies overall model performance.
# Logistic Regression ROC curve
logit_roc <- suppressMessages(roc(test_data$diagnosis, logit_prob))
plot(logit_roc, main = "ROC Curve - Logistic Regression", col = "blue")
# Random Forest ROC curve
rf_roc <- suppressMessages(roc(test_data$diagnosis, rf_prob))
plot(rf_roc, main = "ROC Curve - Random Forest", col = "green")
# SVM ROC Curve
numeric_test_data <- as.numeric(as.character(test_data$diagnosis)) # Convert actual labels to numeric (for ROC)
svm_roc <- suppressMessages(roc(numeric_test_data, svm_prob))
plot(svm_roc, col = "purple", main = "ROC Curve - SVM")
# XGBoost ROC Curve
xgb_roc <- suppressMessages(roc(response = test_data$diagnosis,
predictor = xgb_prob,
levels = c("0", "1"),
direction = "<"))
plot(xgb_roc, main = "ROC Curve - XGBoost", col = "red")
5A. Classification Model Performance Comparison
This section summarizes and compares the performance of all trained classification models for breast cancer diagnosis. Models evaluated include:
Logistic Regression
Random Forest
Support Vector Machine (SVM)
XGBoost
Each model is assessed on the test set using key metrics: Accuracy, Sensitivity, Specificity and Area Under the ROC Curve (AUC). We also visualize the results for easier interpretation.
# Create a data frame to compare model performance
model_comparison <- data.frame(
Model = c("Logistic Regression", "Random Forest", "SVM", "XGBoost"),
Accuracy = c(logit_cm$overall["Accuracy"],
rf_cm$overall["Accuracy"],
svm_cm$overall["Accuracy"],
xgb_cm$overall["Accuracy"]),
Sensitivity = c(logit_cm$byClass["Sensitivity"],
rf_cm$byClass["Sensitivity"],
svm_cm$byClass["Sensitivity"],
xgb_cm$byClass["Sensitivity"]),
Specificity = c(logit_cm$byClass["Specificity"],
rf_cm$byClass["Specificity"],
svm_cm$byClass["Specificity"],
xgb_cm$byClass["Specificity"]),
AUC = c(auc(logit_roc),
auc(rf_roc),
auc(svm_roc),
auc(xgb_roc))
)
# Print the comparison table
print(model_comparison)## Model Accuracy Sensitivity Specificity AUC
## 1 Logistic Regression 0.9823009 1 0.9718310 0.9993293
## 2 Random Forest 0.9911504 1 0.9859155 0.9993293
## 3 SVM 0.9734513 1 0.9577465 1.0000000
## 4 XGBoost 0.9823009 1 0.9718310 0.9996647# Visualize model comparison
ggplot(model_comparison, aes(x = Model, y = Accuracy, fill = Model)) +
geom_bar(stat = "identity") +
geom_text(aes(label = round(Accuracy, 3)), vjust = -0.5) +
labs(title = "Model Accuracy Comparison",
y = "Accuracy",
x = "") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Plot ROC curves together
plot(logit_roc, col = "blue", main = "ROC Curves Comparison")
plot(rf_roc, col = "green", add = TRUE)
plot(svm_roc, col = "purple", add = TRUE)
plot(xgb_roc, col = "red", add = TRUE)
legend("bottomright",
legend = c(paste("Logistic Regression (AUC =", round(auc(logit_roc), 3), ")"),
paste("Random Forest (AUC =", round(auc(rf_roc), 3), ")"),
paste("SVM (AUC =", round(auc(svm_roc), 3), ")"),
paste("XGBoost (AUC =", round(auc(xgb_roc), 3), ")")),
col = c("blue", "green", "purple", "red"), lwd = 2)
5B. Regression Model Performance Comparison
This section summarizes the performance of various regression models
used to predict tumor size (area_mean). The models
evaluated include:
Linear Regression (ordinary least squares)
Ridge Regression (L2 regularization)
Lasso Regression (L1 regularization)
Elastic Net Regression (combined L1 and L2 regularization)
Each model’s performance is assessed using Root Mean Squared Error (RMSE) on a test set. Additionally, 10-fold cross-validation was used for Linear Regression to estimate its generalization ability.
| Model | RMSE (Overall) | RMSE (Benign) | RMSE (Malignant) |
|---|---|---|---|
| Linear Regression | 121.41 | — | — |
| Ridge Regression | 138.61 | 106.00 | 177.60 |
| Lasso Regression | 125.33 | — | — |
| Elastic Net | 133.05 | — | — |
| Linear Regression (10-fold CV) | 126.13 | — | — |
Key Insights:
Linear Regression yields the lowest RMSE on the test set (121.41), serving as a strong baseline.
Regularized models (Ridge, Lasso, Elastic Net) produce slightly higher RMSE values but help address overfitting.
Among regularized models, Lasso Regression achieves the lowest RMSE (125.33), providing a good balance between prediction accuracy and feature selection.
Ridge Regression is much better at predicting benign tumors (RMSE = 106.00) than malignant tumors (RMSE = 177.60), possibly due to higher variability or class imbalance in malignant cases.
10-fold cross-validation for Linear Regression supports the stability and generalizability of its performance estimate (RMSE = 126.13).
6. Conclusions and Recommendations
This project developed and evaluated a range of machine learning models to predict tumor malignancy (classification) and tumor size (regression) using the Breast Cancer Wisconsin dataset. Models such as Logistic Regression, Random Forest, SVM and XGBoost demonstrated high predictive power for diagnosing malignancy, with Random Forest achieving the top accuracy (99.12%), closely followed by Logistic Regression and XGBoost (both 98.23%). All models achieved perfect sensitivity (1.000), ensuring detection of malignant tumors, and excellent specificity, especially in Random Forest (98.59%).
Regression models for tumor size (area_mean) were
evaluated with Linear Regression,
Ridge, Lasso and Elastic
Net. Linear Regression gave the lowest test
RMSE (121.41) and a high R-squared
(0.8759). Lasso Regression was a
strong regularized alternative. These findings support both accurate
diagnosis and meaningful size prediction to guide treatment
planning.
Key Findings:
Accuracy and Sensitivity: The classification models provided high accuracy, particularly Random Forest and Logistic Regression, with perfect sensitivity. This is crucial as it ensures that malignant tumors are accurately detected, minimizing the risk of false negatives.
Model Comparisons: While Random Forest showed the best accuracy, all models demonstrated reliable performance in detecting malignant tumors, emphasizing the reliability of ensemble models like Random Forest and XGBoost. On the other hand, SVM showed slightly lower performance, which could be improved with parameter tuning.
Tumor Size Prediction: The regression models, particularly Linear Regression with an R-squared of 0.8759, effectively captured tumor size variation, which is a crucial factor for treatment planning.
Model Robustness: All models were assessed with confusion matrices, providing robust classification performance metrics. The Confusion Matrix for Logistic Regression and Random Forest showed exceptional performance with very low false positives, reflecting the model’s high predictive capability.
Improvement Potential: While the models are strong, further improvements could be made with hyperparameter tuning, feature engineering and addressing data imbalance. Specifically, Random Forest and XGBoost can be fine-tuned to enhance performance and reduce overfitting.
Model Interpretability: Models like Logistic Regression are interpretable, providing transparency on which features (such as
concave.points_meanandfractal_dimension_mean) impact predictions. In contrast, models like XGBoost and Random Forest are harder to interpret, which is a limitation in clinical applications where interpretability is important.
Limitations:
While this project provides valuable insights into breast cancer diagnosis prediction, there are a few limitations that should be considered:
Class Imbalance: The dataset is imbalanced, with a larger proportion of benign cases compared to malignant ones. This imbalance may affect the model’s ability to accurately predict malignant cases, potentially leading to biased predictions. Research indicates that imbalanced data can result in biased predictions, where the model may predict the majority class more accurately, while the minority class (malignant cases) receives less attention (Chawla et al., 2002).
Data Quality: The dataset may contain some noisy or missing values. Although preprocessing was done to handle missing values and irrelevant columns, slight inconsistencies or inaccuracies in the data might still impact model performance. Missing data, when not handled correctly, can lead to biased results and overfitting (Joel et al., 2022).
Feature Selection: The models were built using a set of features chosen based on the dataset, but there might be additional relevant features that could improve the prediction accuracy. The feature selection process was not exhaustive and could benefit from further exploration. Feature engineering is critical, as better or more informative features can significantly improve model performance (Guyon & Elisseeff, 2003).
Model Generalization: While the models performed well during training, there may still be overfitting due to the specific characteristics of the dataset. Cross-validation was applied, but it is still possible that the models might not generalize well to unseen data or different populations. Overfitting is a common issue in machine learning, where models are too complex and fail to generalize well on new data (Kuhn & Johnson, 2013).
Lack of External Validation: The dataset used for model training and testing is from a single source (the Kaggle dataset). Validation on an external dataset or in a clinical setting would be necessary to assess the real-world applicability of the models. External validation ensures that the model’s performance is consistent across different datasets and settings (Riley et al., 2016).
Recommendations for Future Work:
To improve the robustness and effectiveness of the models in predicting breast cancer malignancy, several future steps could be considered:
Address Class Imbalance: Techniques like oversampling, undersampling or using weighted loss functions should be explored to mitigate the effects of class imbalance. Synthetic data generation (e.g., using SMOTE) could also help in generating more malignant samples. These techniques have been shown to significantly improve the performance of classifiers on imbalanced datasets (He & Garcia, 2009).
Additional Feature Engineering: More in-depth feature engineering, such as creating new derived features or incorporating domain knowledge from medical experts, could enhance the models’ ability to discriminate between benign and malignant cases. Feature engineering is crucial, as it can allow models to capture more relevant patterns in the data (Domingos, 2012).
Model Selection and Tuning: Although various models like logistic regression, random forests, SVM and XGBoost were explored, further experimentation with ensemble methods, deep learning or neural networks might yield even better results. Hyperparameter optimization through grid search or random search could also enhance model performance. Ensemble methods have been shown to outperform individual models in various machine learning tasks (Dietterich, 2000).
External Validation and Real-world Testing: Testing the model on an external dataset or in collaboration with medical institutions will help in understanding how well the model performs on real-world clinical data. Collaborative efforts with hospitals could lead to more clinically relevant insights. Real-world validation is necessary to confirm the generalizability of models developed in controlled settings.
Interpretability and Explainability: To increase trust in the models, efforts should be made to improve model interpretability. Techniques like SHAP values or LIME could provide insights into how the models make their predictions and help in clinical decision-making. Explainable AI has gained significant attention in healthcare for providing transparent reasoning for predictions (Caruana et al., 2015).
References
Battineni, G., Chintalapudi, N. & Amenta, F. (2020).
Performance Analysis of Different Machine Learning Algorithms in Breast Cancer Predictions. EAI Endorsed Trans. Pervasive Health Technol., 6(e4). https://doi.org/10.4108/eai.28-5-2020.166010
The study explores how machine learning models, including Logistic Regression (LR) and Support Vector Machines (SVM), can be employed for breast cancer diagnosis. These models are evaluated for their predictive power in classifying tumors as benign or malignant, offering critical insights into model selection for our classification task (Battineni et al., 2020).Caruana, R., Gehrke, J., Koch, P., Sturm, M., & Elhadad, N. (2015).
Intelligible models for healthcare: Predicting pneumonia risk and hospital 30-day readmission. Proceedings of the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 1721-1730. https://doi.org/10.1145/2783258.2788613
This paper focuses on making machine learning models interpretable in healthcare, which is essential for clinical applications. The authors used models to predict pneumonia risk and 30-day hospital readmission, demonstrating the importance of explainability in critical healthcare predictions (Caruana et al., 2015).Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002).
SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16, 321-357. https://doi.org/10.1613/jair.953
This foundational paper introduces the SMOTE technique for handling class imbalance in machine learning datasets. SMOTE generates synthetic samples of the minority class, improving model performance for imbalanced data, which is crucial for our classification task in breast cancer prediction (Chawla et al., 2002).Chtouki, K., Rhanoui, M., Mikram, M., Amazian, K. & Yousfi, S. (2023).
Supervised Machine Learning for Breast Cancer Risk Factors Analysis and Survival Prediction. ArXiv. https://doi.org/10.48550/arXiv.2304.07299
The authors demonstrate that machine learning algorithms, including Decision Trees, Random Forest, and SVM, can effectively predict the survival of breast cancer patients. This directly supports the regression task in our project to predict tumor size and understand growth patterns based on clinical data (Chtouki et al., 2023).Dietterich, T. G. (2000).
Ensemble methods in machine learning. In Proceedings of the First International Workshop on Multiple Classifier Systems (pp. 1-15). Springer. https://doi.org/10.1007/3-540-45014-9_1
This paper provides a comprehensive discussion on ensemble learning, particularly the advantages of combining multiple models to improve prediction accuracy, an approach used in our Random Forest and XGBoost models (Dietterich, 2000).Domingos, P. (2012).
A few useful things to know about machine learning. Communications of the ACM, 55(10), 78-87. https://doi.org/10.1145/2347736.2347755
This article provides essential insights into key concepts in machine learning, emphasizing the importance of model selection and feature engineering. The concepts covered in this paper were directly applied in our feature selection and model comparison steps (Domingos, 2012).Guyon, I., & Elisseeff, A. (2003).
An introduction to variable and feature selection. Journal of Machine Learning Research, 3, 1157-1182. https://www.jmlr.org/papers/volume3/guyon03a/guyon03a.pdf
This paper outlines essential methods for feature selection, which is a critical step in reducing dimensionality and improving model performance. The authors highlight several techniques, including recursive feature elimination, which was useful for our feature selection process (Guyon & Elisseeff, 2003).He, H., & Garcia, E. A. (2009).
Learning from imbalanced data. IEEE Transactions on Knowledge and Data Engineering, 21(9), 1263-1284. https://doi.org/10.1109/TKDE.2008.239
This paper explores methods for learning from imbalanced datasets, where one class is significantly more prevalent than the other. Techniques such as SMOTE and cost-sensitive learning are discussed, both of which are highly relevant to our classification models, especially with the class imbalance in breast cancer datasets (He & Garcia, 2009).Islam, M. & Poly, T. N. (2019).
Machine Learning Models of Breast Cancer Risk Prediction. bioRxiv. https://doi.org/10.1101/723304
In this paper, the authors explore multiple machine learning techniques, such as decision trees and KNN, and compare their effectiveness in predicting breast cancer. The study reveals that KNN provides high accuracy, suggesting it as a viable candidate for the classification task in our project (Islam & Poly, 2019).Joel, L. O., Doorsamy, W., & Paul, B. S. (2022).
A review of missing data handling techniques for machine learning. International Journal of Innovative Technology & Interdisciplinary Sciences, 5(3), 971–1005. https://doi.org/10.15157/IJITIS.2022.5.3.971-1005
This paper reviews techniques for handling missing data in machine learning models, a crucial preprocessing step. Although we have handled missing values in the dataset, this reference provided insights into advanced techniques for future data processing (Joel et al., 2022).Kuhn, M., & Johnson, K. (2013).
Applied predictive modeling. Springer. https://doi.org/10.1007/978-1-4614-6849-3
This book provides comprehensive coverage of the process of building predictive models. It discusses practical aspects of model fitting, evaluation, and performance metrics, which were foundational in our model development and evaluation phases (Kuhn & Johnson, 2013).Moturi, S., Rao, S. & Vemuru, S. (2021).
Risk Prediction-Based Breast Cancer Diagnosis using Personal Health Records and Machine Learning Models. Springer. https://doi.org/10.1007/978-981-15-9516-5_37
This research examines the use of various machine learning models like Random Forest and SVM for classifying breast cancer as benign or malignant. The findings emphasize how data preprocessing and feature selection improve the accuracy of predictions, aligning with our data cleaning and feature selection steps (Moturi et al., 2021).Riley, R. D., Ensor, J., Snell, K. I., Debray, T. P., Altman, D. G., Moons, K. G., & Collins, G. S. (2016).
External validation of clinical prediction models using big datasets from e-health records or IPD meta-analysis: opportunities and challenges. BMJ (Clinical research ed.), 353, i3140. https://doi.org/10.1136/bmj.i3140
This paper discusses the challenges and opportunities of external validation for clinical prediction models. It emphasizes the importance of testing models on different datasets, which is critical for our models to generalize beyond the current dataset (Riley et al., 2016).Sudarsa, S. & Reddy, K. (2024).
Systematic Review on Breast Cancer Prediction and Classification using Machine Learning and Deep Learning Methods. In 2024 8th International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC). https://doi.org/10.1109/I-SMAC61858.2024.10714683
This review highlights various machine learning and deep learning methods for breast cancer classification and prediction, offering a comprehensive overview of methodologies that could inform our model selection and evaluation processes, especially for improving diagnostic accuracy (Sudarsa & Reddy, 2024).