🧬 R Survival Analysis – Kaplan-Meier and Cox Regression with Examples

---

🧲 Introduction – What is Survival Analysis in R?

Survival analysis deals with time-to-event data—like how long a patient survives after treatment, or time until a machine fails. Unlike standard regression, it handles censored data, where the event hasn’t occurred by the end of observation.

R provides powerful packages such as survival and survminer to:

• Model and analyze survival time
• Create Kaplan-Meier survival curves
• Compare groups using log-rank tests
• Fit Cox Proportional Hazards Models

🎯 In this guide, you’ll learn:

• How to create survival objects
• Plot Kaplan-Meier curves
• Perform log-rank tests
• Use Cox regression for time-to-event modeling

---

📦 1. Load Required Packages

library(survival)
library(survminer)

---

📊 2. Prepare Data – Survival Object

Use the built-in lung dataset:

data(lung)
head(lung)

✅ Create a Survival Object

surv_obj <- Surv(time = lung$time, event = lung$status)

🔍 Explanation:

• time: Survival time in days
• status: 1 = event occurred (death), 0 = censored
• Surv() creates a time-to-event object

---

📈 3. Kaplan-Meier Survival Curve

fit_km <- survfit(surv_obj ~ sex, data = lung)
ggsurvplot(fit_km, data = lung, pval = TRUE, conf.int = TRUE,
           risk.table = TRUE, legend.labs = c("Male", "Female"))

🔍 Features:

• KM curve shows survival probability over time
• pval = TRUE shows significance of group difference
• risk.table adds number at risk at each time point

---

🔁 4. Compare Groups – Log-Rank Test

survdiff(surv_obj ~ sex, data = lung)

🔍 Output:

• A Chi-squared test statistic
• If p < 0.05, survival differs significantly between groups

---

📉 5. Cox Proportional Hazards Model

cox_model <- coxph(surv_obj ~ age + sex + ph.ecog, data = lung)
summary(cox_model)

🔍 Output Includes:

• coef: Log hazard ratios
• exp(coef): Hazard ratios
• p-values for each predictor

---

📊 6. Visualize Cox Model

ggforest(cox_model, data = lung)

🧠 Shows hazard ratios with confidence intervals

---

🧪 7. Interpret the Cox Model

Term	Meaning
exp(coef)	Hazard Ratio (HR)
HR > 1	Higher hazard (shorter survival)
HR < 1	Lower hazard (longer survival)
p-value	Statistical significance

Example:
If HR = 1.5 for age, each additional year increases death risk by 50%

---

📌 Summary – Recap & Next Steps

Survival analysis helps understand how long until an event occurs and whether variables impact survival time. R makes it easy to analyze, plot, and model time-to-event data.

🔍 Key Takeaways:

• Use Surv() to create survival objects
• Plot KM curves using survfit() + ggsurvplot()
• Use coxph() for regression modeling
• Interpret hazard ratios and significance

⚙️ Real-World Relevance:
Widely used in clinical trials, manufacturing failure, customer churn analysis, employee retention, and time-to-purchase modeling.

---

❓ FAQs – Survival Analysis in R

❓ What does “censored” mean in survival analysis?
✅ A censored observation means the event didn’t occur during the study period (e.g., still alive at last follow-up).

❓ What’s the difference between Kaplan-Meier and Cox regression?
✅ Kaplan-Meier is non-parametric and estimates survival curves. Cox regression is semi-parametric and evaluates the effect of predictors.

❓ What does hazard ratio (HR) mean?
✅ HR > 1 = increased risk, HR < 1 = decreased risk.
Example: HR = 2 means twice the hazard compared to baseline.

❓ Can I include categorical predictors in Cox model?
✅ Yes, factors like sex, treatment group, etc., can be included.

❓ How to plot survival curves with confidence intervals?
✅ Use ggsurvplot() with conf.int = TRUE.

---

Share Now :