BiostatisticsTier 1Medical Sciences concept

Interpreting survival/Kaplan-Meier curves from RCTs

Core concept

Kaplan-Meier (KM) curve plots cumulative probability of survival (or event-free status) over time, accounting for censoring (patients lost to follow-up or study ending before an event)
Step-down shape: each step = one or more events at that time point; vertical tick marks = censored patients (no event, but observation ended)
Comparing two curves visually shows when a treatment effect emerges/diverges -- information a single summary statistic (HR, p-value) discards

Separation of curves early vs late matters clinically: early separation suggests an acute/immediate treatment effect; late separation suggests benefit accrues only with prolonged exposure
Curves crossing at any point indicates non-proportional hazards -- a single HR across the whole study period is a misleading summary; report time-period-specific effects instead
NNT from KM data: NNT = 1 / (event rate in control - event rate in treatment) at a specified time point -- must state the time point, as NNT changes as the curves diverge or converge over follow-up

Trap: reporting "a significant p-value" from the log-rank test without looking at the curve shape -- statistical significance says the curves differ overall, not that the effect is clinically meaningful or constant over time
Reading absolute risk difference directly off the y-axis at a given time point is how to derive ARR and NNT from a KM curve -- read both curves at the same time point
ISIS-2-style interpretation: large trials can find a statistically significant but small absolute benefit -- always report the absolute difference (and resulting NNT) alongside the p-value/HR, not the p-value alone

Directly pairs with the hazard ratio - HR is the numerical summary of the whole curve; KM shows how that effect actually plays out over time
NNT calculation from a KM curve uses the same ARR logic as RRR/ARR/NNT calculation, applied at a specific time point instead of a single fixed endpoint
Censoring assumptions (censored patients assumed to have the same subsequent risk as those remaining) can be violated -- informative censoring is a recognised source of bias in survival analysis

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