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Survival Analysis in R using GBSG2 Dataset

This repository contains an in-depth exploration of survival analysis techniques using the GBSG2 dataset. The analysis is implemented in R and includes statistical modeling, data visualization, and interpretation of survival patterns.

Topics

Survival Analysis Kaplan-Meier Weibull Model Log-Normal Model Cox Proportional Hazards Breast Cancer GBSG2 Dataset R Programming Data Visualization Statistical Modeling Clinical Data Survival Curves Censoring Exploratory Data Analysis

Features of this Repository

1. Dataset Overview

The GBSG2 dataset is a well-known dataset used in survival analysis studies. It includes data from a clinical trial involving patients with breast cancer, providing information on:

• time: Survival time (in days).
• cens: Censoring status:
  • 0: Censored (patients alive at the end of the study or lost to follow-up).
  • 1: Event occurred (e.g., death due to cancer or other complications).
• horTh: Hormonal therapy status.
• tsize: Tumor size.
• Additional variables include patient age, menopausal status, and other clinical factors.

2. Methods and Techniques

The analysis was conducted using the following survival analysis methods:

1. Kaplan-Meier Estimator:
   • Provides non-parametric survival curves to visualize survival probabilities over time.
   • Marks censored observations on the curve and includes confidence intervals.
2. Weibull and Log-Normal Parametric Models:
   • Enables estimation of survival probabilities and comparison of different patient subgroups.
3. Cox Proportional Hazards Model:
   • Evaluates the impact of covariates (e.g., hormonal therapy, tumor size) on survival.
4. Exploratory Data Analysis (EDA):
   • Visualizations such as histograms, bar plots, and heatmaps to explore data distributions and correlations.

3. Key Visualizations and Insights

1. Kaplan-Meier Survival Curve

The Kaplan-Meier estimator shows survival probabilities over time, accounting for censored data. It highlights how many patients remain alive at various time points.

Key Insights:

• The probability of survival decreases over time.
• Censored data is marked with red + symbols.

Visualization:

2. Weibull Survival Curve

The Weibull model is a parametric survival model that estimates survival probabilities based on a mathematical distribution.

Key Insights:

• Survival probabilities decrease over time following a Weibull distribution.
• The curve aligns closely with the Kaplan-Meier estimate for most time points.

Visualization:

3. Comparison of Weibull and Log-Normal Models

This visualization compares the Weibull and Log-Normal survival curves. It highlights differences in model predictions for long-term survival.

Key Insights:

• The Weibull model predicts shorter survival times compared to the Log-Normal model for longer periods.
• Both models align well with early survival trends.

Visualization:

4. Cox Model Survival Curves

The Cox proportional hazards model was used to estimate survival probabilities for two patient groups:

• Group 1: Smaller tumors with hormonal therapy.
• Group 2: Larger tumors without therapy.

Key Insights:

• Patients with smaller tumors and hormonal therapy have significantly higher survival probabilities over time.
• The difference between groups widens as time progresses.

Visualization:

4. Conclusions

1. Censoring is common:
   • Out of 686 observations, 387 (56%) were censored.
   • Proper handling of censored data is crucial for accurate analysis.
2. Survival patterns:
   • Hormonal therapy improves survival significantly.
   • Smaller tumors predict better survival outcomes.
3. Model comparisons:
   • The Weibull model aligns closely with Kaplan-Meier estimates, while the Log-Normal model predicts slightly longer survival times.

5. Repository Contents

• Notebooks and R Scripts: Include all code for the analysis and visualizations.
• Visualizations: Kaplan-Meier, Weibull, Log-Normal, and Cox model curves.

How to Use

1. Clone the repository:

   git clone https://github.com/your-username/survival-analysis-r.git

2. Install necessary R libraries:

   install.packages(c("survival", "survminer", "TH.data", "reshape2", "ggplot2"))

3. Open the Jupyter Notebook or run the R scripts to explore the analysis.

Dependencies

• R (version >= 4.4.0)

• Libraries: tidyverse, survival, survminer, TH.data, reshape2, ggplot2.