Kaplan-Meier Survival Analysis

The Kaplan-Meier estimator is the most common way to estimate survival statistics. It allows researchers to visualize the probability of survival over time, even when some patients drop out of the study (censored data).

The Survival Curve

A Kaplan-Meier plot typically shows:

• X-axis: Time (days, months, years) from the start of the study.
• Y-axis: Cumulative Survival Probability (0 to 1, or 0% to 100%).
• Steps: The curve drops each time an event (e.g., death) occurs.
• Tick marks: Indicate censored patients (lost to follow-up) who have not experienced the event yet.

Where d_i is the number of events at time t_i and n_i is the number of patients at risk.

Key Statistics

Metric	Definition
Median Survival Time	The time at which 50% of the population has experienced the event. This is often the primary endpoint in cancer trials.
Log-Rank Test	A statistical test (p-value) to compare survival curves between two or more groups (e.g., Treatment vs Control).