1. Introduction
Kaplan‑Meier curves, life tables, and log‑rank tests are fundamental tools in survival analysis. They allow visualization and comparison of survival probabilities across groups.

2. Kaplan‑Meier Curve
Definition: Non‑parametric estimator of survival function.

Method: Calculates probability of survival at each event time.

Steps:

Order survival times.

Calculate survival probability at each event.

Plot stepwise curve.

Interpretation: Median survival time, differences between groups.

Advantages: Handles censoring, easy visualization.

3. Life Table
Definition: Summarizes survival data in intervals.

Method: Groups time into fixed intervals (e.g., months).

Calculations: Number at risk, number of events, survival probability.

Use: Useful for large datasets, provides summary statistics.

Limitation: Less precise than Kaplan‑Meier for small samples.

4. Log‑Rank (Mantel‑Haenszel) Test
Definition: Statistical test comparing survival curves between groups.

Hypothesis:

Null: No difference in survival between groups.

Alternative: Survival differs between groups.

Method: Compares observed vs. expected events at each time point.

Output: Chi‑square statistic and p‑value.

Interpretation: Significant p‑value indicates difference in survival.

5. Example
A cancer trial compares survival between treatment A and B. Kaplan‑Meier curves show higher survival in group A. Log‑rank test yields p=0.02, indicating significant difference. Life table summarizes survival probabilities at 6‑month intervals.

6. Applications
Oncology (time to death or relapse).

Cardiology (time to heart attack).

Neurology (time to migraine recurrence).

Public health (time to infection).

7. Limitations
Assumes proportional hazards (log‑rank).

Sensitive to censoring patterns.

Requires adequate sample size.

8. Conclusion
Kaplan‑Meier curves, life tables, and log‑rank tests are essential tools for analyzing and comparing survival data, providing both visual and statistical insights.

📝 Quiz: Survival Analysis Topics
Multiple Choice (Choose the best answer)

What is the primary outcome in survival analysis? a) Blood pressure b) Time until event occurs c) Weight change d) Lab values

What does censoring mean? a) Removing patients from study b) Event not observed during follow‑up c) Incorrect data entry d) Excluding covariates

Which function estimates probability of surviving beyond time t? a) Hazard function b) Survival function c) Regression function d) Density function

In migraine studies, the event of interest may be: a) Blood sugar level b) Migraine recurrence c) Weight gain d) Sleep duration

Which test compares survival curves between groups? a) T‑test b) ANOVA c) Log‑rank test d) Chi‑square

Kaplan‑Meier curve is: a) Linear regression model b) Stepwise survival probability plot c) Histogram of events d) Scatter plot