Survival Analysis

A set of statistical methods for outcomes measured as TIME TO AN EVENT (death, ROSC, re-attendance), not just whether it happened. Its defining feature is handling CENSORING — patients with incomplete follow-up still contribute data up to the moment they leave. Core tools: Kaplan–Meier curves (estimate survival over time), the log-rank test (compare groups), and Cox regression (adjusted hazard ratios).

Two survival curves descending over time, with censoring ticks on each. Survival analysis captures not just HOW MANY events occurred but WHEN they occurred, and it keeps patients with partial follow-up in the analysis up to the point they were last seen.

Read the curves as a whole, not at one arbitrary point. Steps down are events; ticks are censored patients (lost to follow-up or event-free at the end), not events. The log-rank test compares whole curves; a Cox model gives an adjusted hazard ratio summarising the difference in event rate.

Events in EM and critical care happen at different times and follow-up length varies between patients. Reducing a time-to-event outcome to a single “proportion dead at day 30” throws away both the timing of events and the information carried by censored patients — survival methods use all of it.

• Kaplan–Meier estimates survival over time
• Log-rank test compares groups
• Cox regression gives adjusted hazard ratios
• Censoring keeps incomplete follow-up in play

PARAMEDIC-2 (NEJM 2018) — 8007 out-of-hospital cardiac arrests, adrenaline 1 mg vs placebo. The primary time-to-event analysis reported 30-day survival of 3.2% vs 2.4% (adjusted OR 1.47, 95% CI 1.09–1.97). Survival was tracked over time with the trial accounting for patients lost to follow-up rather than dropping them. Better 30-day survival did NOT translate into better neurology — favourable neurological outcome was 2.2% vs 1.9% (no significant difference); a survival curve says nothing about the quality of survival.

• Ignoring censoring — treating censored patients as events, or as if their data never existed.
• Informative censoring — patients leave for reasons linked to outcome, biasing the estimate.
• Reducing the analysis to a single-time-point comparison instead of using the whole curve.