Survival Analysis
Time-to-Event Analysis · Also known as: Kaplan-Meier analysis, Cox regression, TTE analysis
Survival analysis is a collection of statistical methods for modeling time from a defined starting point until an event of interest occurs (disease, recovery, death, equipment failure). Kaplan and Meier's nonparametric estimator (1958) and David Cox's proportional hazards model (1972) jointly enabled analysis of censored data—individuals whose event times are unknown because they left the study or were still event-free at follow-up. Indispensable in oncology, cardiology, infectious disease research, engineering reliability, and any field where time-to-event matters.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+35 more
When to use it
Use survival analysis when the outcome of interest is time to event and data contain censoring. Oncology: comparing survival between treatment arms (standard randomized trials). Cardiology: analyzing time to cardiovascular events (MI, stroke) in cohort studies. Infectious disease: time from infection to recovery or progression. Medical implants: device failure or replacement time. Industrial engineering: time to equipment failure (reliability analysis). Any longitudinal study with staggered entry and/or early withdrawal can use survival methods. If no censoring exists (all participants followed to completion), simpler methods (t-test, logistic regression) suffice, though survival analysis remains valid.
Strengths & limitations
- Correctly handles censored data without bias: exploits information from censored individuals (follow-up time) rather than discarding them.
- Flexibly estimates both univariate (Kaplan-Meier) and multivariable (Cox) associations; baseline covariates are adjusted without assuming linear effects.
- Hazard ratios are intuitive: single metric comparing event rates, easily interpreted by clinicians and communicated in publications.
- Nonproportional hazards detectable: assumption diagnostics alert researchers when treatment effects change over time; alternative models (AFT, stratification, time-varying coefficients) address violations.
- Risk stratification: predicted survival curves enable clinicians to quantify prognosis and individualize treatment decisions based on baseline characteristics.
- Proportional hazards assumption: Cox model assumes constant treatment effect over time; violations require alternative methods (accelerated failure time models, time-varying coefficients, stratification).
- Sparse data at long follow-up times: survival estimates become less stable as participants are censored; confidence intervals widen, limiting inference for late-event prediction.
- Administrative censoring: if censoring is related to prognosis (informative censoring), standard methods are biased; requires joint modeling or inverse probability weighting.
- Assumes conditional independence given covariates; unmeasured confounding threatens causal inference, particularly in observational studies.
- Small event counts reduce power and stability of Cox coefficients; generally need ≥10 events per covariate for stable estimation.
Frequently asked
What does a hazard ratio of 0.6 mean, and how is it different from relative risk?
A hazard ratio (HR) of 0.6 means the instantaneous event rate (hazard) is 60% that of the reference group at any given time, adjusting for covariates—equivalent to 40% risk reduction. HR is from survival/Cox analysis. Relative risk (RR) is from cohort or trial data: RR = [incidence in exposed] / [incidence in unexposed]. HR approximates RR when events are rare (<10%), but they diverge with common outcomes. HR specifically compares event rates accounting for censoring and follow-up time; RR does not require survival methodology. Always report which measure you use.
What is the proportional hazards assumption, and what do I do if it's violated?
The proportional hazards assumption means the treatment effect (hazard ratio) is constant over time. Test it by plotting Schoenfeld residuals against time; a trend suggests violation. Alternatively, fit a time-varying coefficient model: include an interaction between the covariate and a function of time (e.g., log time). If assumption is violated, options include: (1) stratify analysis by the problematic variable (separate baseline hazards), (2) use accelerated failure time (AFT) models, or (3) report treatment effect at specific time points (e.g., 1-year, 5-year survival) separately. Always check and report on this assumption.
How should I interpret the log-rank test p-value in my Kaplan-Meier analysis?
The log-rank test compares the observed number of events in each group to the number expected under the null hypothesis (equal survival curves). p < 0.05 indicates statistically significant difference in survival between groups. Like all p-values, it tests a point null hypothesis; a large p-value does not prove equal survival, only insufficient evidence to reject equality. Also report median survival time and survival probabilities at key timepoints (1-year, 5-year), confidence intervals, and the number at risk at each interval on the Kaplan-Meier plot.
How do I handle multiple outcomes (e.g., disease recurrence and death)?
When multiple distinct events are possible, use competing risks analysis. If you model disease recurrence with Cox regression while ignoring death, you bias estimates because death censors recurrence follow-up. Fine-Gray subdistribution hazards model separates the marginal probability of each event. Calculate cumulative incidence function (CIF) for each event type (not 1-minus-other); compare using Gray's test. This approach is essential in oncology (recurrence vs non-cancer death) and cardiology (MI vs stroke).
Sources
- Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481. DOI: 10.1080/01621459.1958.10501452 ↗
- Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society, Series B, 34(2), 187–220. DOI: 10.1111/j.2517-6161.1972.tb00899.x ↗
How to cite this page
ScholarGate. (2026, June 4). Time-to-Event Analysis. ScholarGate. https://scholargate.app/en/research-statistics/survival-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Logistic RegressionResearch Statistics↔ compare
- Multilevel ModelingResearch Statistics↔ compare
- Propensity Score MatchingResearch Statistics↔ compare