Survival Analysis & the Kaplan-Meier Curve

Also known as Survival analysis · Kaplan-Meier · Censoring · Log-rank test · Cox proportional hazards · Hazard ratio · Median survival

Survival analysis for the ICU First Part: time-to-event data and censoring (right-censoring when the event is not observed), the survival function S(t) and its complement the cumulative distribution F(t), the hazard function h(t) and cumulative hazard H(t), the Kaplan-Meier estimator as a non-parametric step function of survival probability (product of conditional probabilities), the median and restricted mean survival time, the log-rank test comparing curves between groups, and Cox proportional-hazards regression yielding a hazard ratio under the assumption of proportional hazards.

medium10 referencesUpdated 26 July 202631 min readVerification in progress

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8 MCQs

Meet the patient — the survival curve on the ward round

Your consultant holds up a paper from the latest septic-shock trial. Two Kaplan-Meier curves sit on the page, one for the intervention, one for usual care. She asks: does this treatment work? The hazard ratio is 0.85, the 95 per cent confidence interval crosses 1.0, the log-rank p-value is 0.08. Before you can answer, you need to understand what a survival curve is, what censoring means, and why a single hazard ratio can mislead.^[1]

Many ICU outcomes are time-to-event data — time to death, to extubation, to discharge, to readmission. These data share a feature that ordinary averages cannot handle: censoring. Survival analysis is the set of methods built for censored data, and the Kaplan-Meier curve is its centrepiece.^[1]

References10Show

[1]Clark TG, Bradburn MJ, Love SB, Altman DG Survival analysis part I: basic concepts and first analyses Br J Cancer, 2003.PMID 12865907
[2]Bradburn MJ, Clark TG, Love SB, Altman DG Survival analysis part II: multivariate data analysis--an introduction to concepts and methods Br J Cancer, 2003.PMID 12888808
[3]Bradburn MJ, Clark TG, Love SB, Altman DG Survival analysis Part III: multivariate data analysis -- choosing a model and assessing its adequacy and fit Br J Cancer, 2003.PMID 12915864
[4]Clark TG, Bradburn MJ, Love SB, Altman DG Survival analysis part IV: further concepts and methods in survival analysis Br J Cancer, 2003.PMID 12942105
[5]Royston P, Parmar MKB Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome BMC Med Res Methodol, 2013.PMID 24314264
[6]Putter H, Fiocco M, Geskus RB Tutorial in biostatistics: competing risks and multi-state models Stat Med, 2007.PMID 17031868
[7]Bellani G, Laffey JG, Pham T, et al. Epidemiology, Patterns of Care, and Mortality for Patients With Acute Respiratory Distress Syndrome in Intensive Care Units in 50 Countries JAMA, 2016.PMID 26903337
[8]Mouncey PR, Osborn TM, Power GS, et al. Trial of early, goal-directed resuscitation for septic shock N Engl J Med, 2015.PMID 25776532
[9]Vincent JL, Moreno R, Takala J, et al The SOFA (Sepsis-related Organ Failure Assessment) score to describe organ dysfunction/failure. On behalf of the Working Group on Sepsis-Related Problems of the European Society of Intensive Care Medicine Intensive Care Med, 1996.PMID 8844239
[10]Knaus WA, Draper EA, Wagner DP, Zimmerman JE APACHE II: a severity of disease classification system Crit Care Med, 1985.PMID 3928249