Survival Analysis Visualizer

Understanding Survival Analysis

Survival Function S(t): Probability of surviving (not experiencing the event) beyond time t.

Kaplan-Meier Estimator: S(t) = ∏(1 - d_i/n_i) for all i where t_i ≤ t

• d_i: Number of events at time t_i
• n_i: Number at risk just before t_i (subjects who haven't had event or been censored)

Censoring: When we don't observe the event for a subject (study ended, lost to follow-up, etc.). Marked with + on curves.

Log-rank Test: Compares survival distributions between groups. Null hypothesis: no difference in survival between groups.

Key Concepts

• Median Survival Time: Time at which 50% of subjects have experienced the event
• Hazard Ratio (HR): Ratio of hazard rates between groups. HR=1 means equal hazard, HR>1 means increased risk
• Confidence Intervals: Show uncertainty in survival estimates (typically 95% CI using Greenwood's formula)
• Number at Risk: How many subjects remain in the study and haven't had the event at each time point
• Assumptions: Censoring is independent of survival probability; survival probability is same for all subjects in a group