What this calculator does
Survival Analysis is Module 16 of Analysis Studio. It takes a time variable and an event indicator whose event value you confirm, with an optional group variable and covariates. It reports:
- Kaplan-Meier estimates with Greenwood standard errors and log-log intervals by default
- Median survival and other quantiles, each with an interval
- A number-at-risk table under the curve, so a late step in the curve is read against how few cases remain
- Group comparisons by the log-rank test by default, with Peto-Peto as an option and Holm adjustment across pairs
- Cox proportional hazards models with Efron ties by default, hazard ratios, and the three standard tests
The Cox half carries its assumption honestly: proportional hazards is checked with scaled Schoenfeld residual tests and plots, and a violation prompts a stratification suggestion rather than silence. Under a survey design, the module fits design-based Kaplan-Meier and Cox models that match the standard survey-package implementations.
Promotion, stated with its date: through March 31, 2027, this module runs free on screen, like every module. Downloads and Copy Results stay with the subscription throughout. After the promotion, the module returns to the subscription set at $299 per year.
The method, in plain terms
The Kaplan-Meier estimate multiplies survival step by step. At each event time, the survival probability is multiplied by the share of those still at risk who did not have the event at that time:
S(t) = product over event times up to t of (1 − events at that time ÷ number at risk at that time).
Cases that leave observation without the event are censored: they count in the risk set until they leave, and then they simply stop counting. The curve assumes censoring carries no information about prognosis, which is the assumption to examine whenever a curve is interpreted.
Worked example
Eight cases, followed in months. Events at months 3, 6, 8, 12, and 18; censoring at months 5, 10, and 15.
- Month 3: eight at risk, one event. Survival = 7 ÷ 8 = 0.875
- Month 6: six at risk (one event and one censoring have left), one event. Survival = 0.875 × 5 ÷ 6 = 0.729
- Month 8: five at risk, one event. Survival = 0.729 × 4 ÷ 5 = 0.583
- Month 12: three at risk, one event. Survival = 0.583 × 2 ÷ 3 = 0.389
- Month 18: one at risk, one event. Survival = 0
Median survival is month 12, the first time the curve reaches or crosses 0.5. The number-at-risk row is the honest companion to the curve: the final step rests on a single remaining case, and the module prints that so the tail of the curve is read with the caution it deserves.
When the calculator fits, and when it does not
It fits when:
- The outcome is time to an event, follow-up varies, and some cases are censored.
- Groups need a curve-first comparison, with the log-rank test as the summary rather than the story.
- A Cox model will adjust a time-to-event comparison for covariates, with its assumption checked on the same screen.
It does not fit when:
- Events compete, meaning one event type prevents the others. Competing risks need cumulative incidence methods, which this module does not offer.
- Covariates change during follow-up. Time-varying covariates are out of scope, and the module says so.
- Nobody is censored and every time is exact. Then the question is a plain comparison of times, and simpler modules answer it.
Run it
Module 16: Survival AnalysisOpen in Analysis Studio →Load your follow-up data, confirm which value of the event variable counts as the event, and read the curve with its risk table.
Questions
What does censored mean? A censored case was last seen alive, unsubscribed, still subscribed, or otherwise event-free at its final time, and then left observation. It contributes to the risk set until that time and no longer. Censoring is information about follow-up, not a missing outcome to fill in.
How is median survival read? It is the time at which the estimated survival reaches one half: half the population is estimated to have had the event by then. If the curve never reaches one half, median survival is not reached, and the module reports that rather than extrapolating.
What does a hazard ratio of two mean? In a Cox model, the exposed group has twice the instantaneous event rate of the reference group at every point in follow-up, under the proportional hazards assumption. It is a ratio of rates, not of probabilities, and it leans on the assumption the module tests on the same screen.
Why does the curve end at zero in the example? Because the last case at risk had the event. When the final observation is censored instead, the curve ends suspended at its last value, which is the estimator declining to invent follow-up nobody observed.
Can it handle survey data? Yes. Under a declared design, curves and Cox models are computed with design-based methods, including the design-based log-rank test.