Survival Analysis

Overview

Survival analysis studies time until an event occurs, handling censored data where events haven't happened for some subjects, enabling prediction of lifetimes and risk assessment.

Key Concepts

• Survival Time: Time until event
• Censoring: Event not observed (subject dropped out)
• Hazard: Instantaneous risk at time t
• Survival Curve: Probability of surviving past time t
• Hazard Ratio: Relative risk between groups

Common Models

• Kaplan-Meier: Non-parametric survival curves
• Cox Proportional Hazards: Semi-parametric regression
• Weibull/Exponential: Parametric models
• Log-rank Test: Comparing survival curves
• Competing Risks: Multiple event types

Implementation with Python

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from lifelines import KaplanMeierFitter, CoxPHFitter, WeibullAFTFitter
from lifelines.statistics import logrank_test
import warnings
warnings.filterwarnings('ignore')

# Generate sample survival data
np.random.seed(42)
n_patients = 200

# Time to event (in months)
event_times = np.random.exponential(scale=24, size=n_patients)
# Censoring indicator (1 = event occurred, 0 = censored)
event_observed = np.random.binomial(1, 0.7, n_patients)
# Group assignment (0 = control, 1 = treatment)
group = np.random.binomial(1, 0.5, n_patients)
# Age at baseline
age = np.random.uniform(30, 80, n_patients)
# Risk score
risk_score = np.random.uniform(0, 100, n_patients)

# Adjust event times based on group (simulate treatment effect)
event_times = event_times * (1 + group * 0.3)

df = pd.DataFrame({
    'time': event_times,
    'event': event_observed,
    'group': group,
    'age': age,
    'risk_score': risk_score,
})

print("Survival Data Summary:")
print(df.head(10))
print(f"\nTotal subjects: {len(df)}")
print(f"Events: {df['event'].sum()} ({df['event'].sum()/len(df)*100:.1f}%)")
print(f"Censored: {(1-df['event']).sum()} ({(1-df['event']).sum()/len(df)*100:.1f}%)")

# 1. Kaplan-Meier Estimation
kmf = KaplanMeierFitter()
kmf.fit(df['time'], df['event'], label='Overall')

print("\n1. Kaplan-Meier Survival Estimates:")
print(f"Median survival time: {kmf.median_survival_time_:.1f} months")
print(f"6-month survival: {kmf.predict(6):.1%}")
print(f"12-month survival: {kmf.predict(12):.1%}")
print(f"24-month survival: {kmf.predict(24):.1%}")

# 2. Group Comparison
fig, axes = plt.subplots(2, 2, figsize=(14, 10))

# Overall survival curve
ax = axes[0, 0]
kmf.plot_survival_function(ax=ax, linewidth=2)
ax.set_xlabel('Time (months)')
ax.set_ylabel('Survival Probability')
ax.set_title('Kaplan-Meier Survival Curve (Overall)')
ax.grid(True, alpha=0.3)

# Survival curves by group
ax = axes[0, 1]
for group_val in [0, 1]:
    mask = df['group'] == group_val
    kmf.fit(df[mask]['time'], df[mask]['event'],
           label=f'{"Control" if group_val == 0 else "Treatment"}')
    kmf.plot_survival_function(ax=ax, linewidth=2)

ax.set_xlabel('Time (months)')
ax.set_ylabel('Survival Probability')
ax.set_title('Kaplan-Meier Curves by Group')
ax.grid(True, alpha=0.3)

# 3. Log-Rank Test
mask_control = df['group'] == 0
mask_treatment = df['group'] == 1

results = logrank_test(
    df[mask_control]['time'],
    df[mask_treatment]['time'],
    df[mask_control]['event'],
    df[mask_treatment]['event']
)

print(f"\n3. Log-Rank Test:")
print(f"Test statistic: {results.test_statistic:.4f}
how to use survival-analysis
CursorClaude CodeClineCodexWindsurfGooseGitHub CopilotVS CodeGemini CLIKiloOpencodeKimi CLIRoo ClineAiderContinueZedBolt.newLovablev0Replit AgentSweepSmol DeveloperDevinCavemanAmpAntigravity
How to use survival-analysis on Cursor
AI-first code editor with Composer
1
Prerequisites
Before installing skills in Cursor, ensure your development environment meets these requirements:
›Cursor installed and configured on your development machine
›Node.js version 16.0+ with npm package manager (verify with node --version)
›Active project directory or workspace where you want to add survival-analysis
2
Execute installation command
Execute the skills CLI command in your project's root directory to begin installation:
$npx skills add https://github.com/aj-geddes/useful-ai-prompts --skill survival-analysiscopy
The skills CLI fetches survival-analysis from GitHub repository aj-geddes/useful-ai-prompts and configures it for Cursor.
3
Select Cursor when prompted
The CLI will show a list of available agents. Use arrow keys to navigate and space to select Cursor:
◆ Which agents do you want to install to?
│
│ ── Universal (.agents/skills) ── always included ────
│   • Amp
│   • Antigravity
│   • Cline
│   • Codex
│ ●Cursor(selected)
│   • Cursor
│   • Windsurf
4
Verify installation
Confirm successful installation by checking the skill directory location:
.cursor/skills/survival-analysis
Reload or restart Cursor to activate survival-analysis. Access the skill through slash commands (e.g., /survival-analysis) or your agent's skill management interface.
⚠
Security & Verification Notice
We perform automated surface-level scans (Gen AI Scanner, Socket, Snyk) during installation. These checks detect common vulnerabilities but do not guarantee complete security. Always review skill source code and verify the publisher's reputation before production use.
Skills execute code in your development environment. Always verify the publisher's identity, review recent commits, and test in isolated environments before production deployment.
Additional Resources
›View source code on GitHub›Skills CLI documentation›Learn more about Cursor›What are agent skills?