Data Analysis Project

A comprehensive collection of statistical analysis methods implemented in R, focusing on medical and healthcare datasets. This project demonstrates various data analysis techniques including clustering, factor analysis, multivariate testing, classification, regression, and survival analysis.

📁 Project Structure

data_analysis/
├── README.md
├── datasets/
│   ├── DataV.csv          # Medical dataset (COVID-related patient data)
│   ├── data_big.csv       # Cardiovascular dataset
│   └── points5.csv        # Survival analysis dataset
├── cluster.R              # Clustering analysis with decision trees
├── factor.R               # Factor analysis and PCA
├── hotelling.R            # Hotelling's T² test
├── lda.R                  # Linear Discriminant Analysis
├── regr.R                 # Multiple regression analysis
└── surv.R                 # Survival analysis

📊 Datasets

DataV.csv

• Size: 145 patients × multiple variables
• Content: COVID-related medical data with cardiovascular parameters
• Variables: Age, blood pressure, severity scores, outcomes (Russian column names)
• Used in: cluster.R, lda.R

data_big.csv

• Size: 35 patients × multiple time points
• Content: Cardiovascular and psychological parameters
• Variables: HR (Heart Rate), SBP (Systolic Blood Pressure), SV (Stroke Volume), MBP (Mean Blood Pressure)
• Used in: hotelling.R, regr.R

points5.csv

• Size: 169 observations
• Content: Survival analysis data
• Variables: Survival days, surgical status, immunoglobulin levels
• Used in: surv.R

🔬 Analysis Scripts

1. cluster.R - Clustering Analysis

Purpose: Implements clustering using decision trees and information gain methods

Key Features:

• Custom information gain functions (I_inf, D_inf, GinyDA.)
• Decision tree construction based on information theory
• Comparison between standard and information gain-based trees
• Visualization of clustering results

Methods:

• Information gain calculation
• Decision tree algorithms
• Gini impurity measures

2. factor.R - Factor Analysis & PCA

Purpose: Performs dimensionality reduction and factor analysis on medical data

Key Features:

• Principal Component Analysis (PCA)
• Eigenvalue decomposition
• Factor loadings calculation
• Comparison with built-in R functions

Methods:

• Manual PCA implementation
• princomp() function validation
• Variance explained analysis

3. hotelling.R - Multivariate Testing

Purpose: Implements Hotelling's T² test for multivariate statistical analysis

Key Features:

• Outlier detection using chi-square distribution
• Multivariate hypothesis testing
• Scatter plot visualization with p-value coloring

Methods:

• Hotelling's T² statistic
• Chi-square distribution testing
• Multivariate outlier identification

4. lda.R - Linear Discriminant Analysis

Purpose: Classification analysis using Linear Discriminant Analysis

Key Features:

• Variable selection based on standard deviation
• LDA for both factorial and metric variables
• Discriminant function visualization
• Classification accuracy assessment

Methods:

• Linear discriminant functions
• Variable importance analysis
• Classification visualization

5. regr.R - Multiple Regression Analysis

Purpose: Comprehensive regression modeling and variable selection

Key Features:

• Manual coefficient calculation using covariance matrices
• Model comparison with built-in lm() function
• Combinatorial model selection
• Stepwise regression using olsrr package

Methods:

• Multiple linear regression
• Model selection algorithms
• Coefficient significance testing

6. surv.R - Survival Analysis

Purpose: Time-to-event analysis using survival methods

Key Features:

• Kaplan-Meier survival curves
• Log-rank tests for group comparisons
• Cox proportional hazards models

Methods:

• Survival curve estimation
• Hazard ratio calculation
• Time-to-event modeling

🛠️ Required R Packages

# Core packages
install.packages(c("survival", "survminer", "olsrr"))

# Additional packages that may be required
install.packages(c("ggplot2", "dplyr", "MASS"))

🚀 Usage Instructions

Running Individual Scripts

1. Set working directory to the project folder
2. Load required packages for each script
3. Run scripts in any order (they are independent)

# Example: Running cluster analysis
setwd("path/to/data_analysis")
source("cluster.R")

Script Dependencies

• Each script loads its required datasets automatically
• Scripts are designed to be run independently
• Ensure all CSV files are in the datasets/ directory

📈 Key Methodologies

Statistical Methods Implemented

• Clustering: Information gain-based decision trees
• Dimensionality Reduction: PCA and factor analysis
• Multivariate Testing: Hotelling's T² test
• Classification: Linear Discriminant Analysis
• Regression: Multiple linear regression with model selection
• Survival Analysis: Kaplan-Meier and Cox regression

Custom Implementations

• Information gain calculation functions
• Manual PCA computation
• Covariance-based regression coefficients
• Decision tree algorithms

📋 Output Examples

Each script generates:

• Statistical summaries and test results
• Visualizations (plots, charts, survival curves)
• Model comparisons and validation metrics
• Classification/prediction results

🎯 Learning Objectives

This project demonstrates proficiency in:

• Advanced statistical analysis in R
• Custom algorithm implementation
• Medical data analysis
• Multivariate statistical methods
• Survival analysis techniques
• Model validation and comparison