Kaplan-Meier Plotter

Survival analysis exists to handle a problem ordinary averages cannot: at the end of a study, many subjects have not yet had the event, so their true event time is unknown. The Kaplan-Meier estimator, introduced by Kaplan and Meier (1958), solves this with the product-limit method, multiplying together the conditional probabilities of surviving each successive event time. Subjects with unobserved event times are censored, counted as at risk until they leave, so their partial information is used rather than discarded.

The resulting step curve reads directly: its height at any time is the estimated probability of surviving beyond that time, it drops only at event times, and small ticks mark censored subjects. The most common summary drawn from it is the median survival, the time the curve first crosses 0.5. When most subjects remain event-free at the end of follow-up the curve never reaches 0.5, and the honest report is that median survival was not reached.

Comparing two groups needs a formal test, because two curves can cross or separate by chance. The log-rank test accumulates, at every event time, the difference between observed and expected events under the null hypothesis of identical survival, producing a chi-square statistic and a p-value. This tool computes it automatically for two-group data, so a treatment-versus-control comparison returns both the curves and the significance in one step.

Kaplan-Meier and the log-rank test are the standard unadjusted analysis; they describe survival and compare groups but cannot adjust for other variables. That is the role of Cox proportional-hazards regression, the multivariable follow-up. If your curves come from a published figure rather than raw data, digitize them first with the survival curve digitizer, and for a full time-to-event analysis with adjusted hazard ratios, the biostatistics consulting service runs the Cox models and reporting.