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Survival analysis
Analyze duration outcomes—outcomes measuring the time to
an event such as failure or death—using Stata's
specialized tools for survival analysis. Account for the
complications inherent in this type of data such as sometimes
not observing the event (censoring), individuals entering the
study at differing times (delayed entry), and individuals who
are not continuously observed throughout the study (gaps).
You can estimate and plot the probability of survival over
time. Or model survival as a function of covariates using
Cox, Weibull, lognormal, and other regression models. Predict
hazard ratios, mean survival time, and survival probabilities.
Do you have groups of individuals in your study? Adjust for
within-group correlation using a random-effects or
shared-frailty model.
Cox proportional hazards 
- Time-varying covariates and censoring
- Continuously time-varying covariates
- Four ways to handle ties: Breslow, exact partial likelihood, exact marginal likelihood, and Efron
- Robust, cluster–robust, bootstrap, and jackknife standard errors
- Stratified estimation
- Shared frailty models
- Sampling weights and survey data
- Multiple imputation
- Martingale, efficient score, Cox–Snell, Schoenfeld, and deviance residuals
- Likelihood displacement values, LMAX values, and DFBETA influence measures
- Harrell’s C, Somers’ D, and Gönen and Heller’s K statistics measuring concordance
- Tests for proportional hazards
- Graphs of estimated survivor, failure, hazard, and cumulative hazard functions
- Goodness-of-fit plot New
Cox proportional hazards model for interval-censored data Updated
- Case II interval-censored data
- Current status or case I interval-censored data
- Time-varying covariates New
- Testing proportional-hazards assumption New
- Two ways to estimate the baseline hazard function
- Four methods to estimate standard errors Updated
- Robust and cluster–robust standard errors New
- Graphs of estimated survivor, hazard, and cumulative hazard functions Updated
- Stratified models
- Proportional-hazards assumption plots
- Goodness-of-fit plot New
- Predictions
- Hazard ratio
- Hazard contributions for interval endpoints
- Baseline survivor function for interval endpoints
- Baseline cumulative hazard function for interval endpoints
- Martingale-like residuals
- Cox–Snell-like residuals New
- Time-varying predictions New
Marginal Cox PH model for interval-censored multiple-event data StataNow
- Single-record-per-event interval-censored data
- Multiple-record-per-event interval-censored data
- Flexible model specification
- Time-varying covariates
- Testing proportional-hazards assumption
- Robust standard errors
- Powerful test for average covariate effect across all events
- Graphs of estimated survivor, hazard, and cumulative hazard functions
- Stratified models
- Proportional-hazards assumption plots
- Goodness-of-fit plot
- Predictions
- Hazard ratio
- Hazard contributions for interval endpoints
- Baseline survivor function for interval endpoints
- Baseline cumulative hazard function for interval endpoints
- Martingale-like residuals
- Cox–Snell-like residuals
- Time-varying predictions
Competing-risks regression
- Fine and Gray proportional subhazards model
- Time-varying covariates
- Robust, cluster–robust, bootstrap, and jackknife standard errors
- Multiple imputation
- Efficient score and Schoenfeld residuals
- DFBETA influence measures
- Subhazard ratios
- Cumulative subhazard and cumulative incidence graphs
Parametric survival models
- Weibull, exponential, Gompertz, lognormal, loglogistic, or generalized gamma model
- Robust, cluster–robust, bootstrap, and jackknife standard errors
- Stratified models
- Individual-level frailty
- Group-level or shared frailty
- Sampling weights and survey data
- Multiple imputation
- Martingale-like, score, Cox–Snell, and deviance residuals
- Graphs of estimated survivor, failure, hazard, and cumulative hazard functions
- Goodness-of-fit plot New
- Predictions and estimates
- Mean or median time to failure
- Mean or median log time
- Hazard
- Hazard ratios
- Survival probabilities
Interval-censored parametric survival models
- Weibull, exponential, Gompertz, lognormal, loglogistic, or generalized gamma
- Both proportional-hazards and accelerated failure-time metrics
- Robust, cluster–robust, bootstrap, and jackknife standard errors
- Stratified models
- Sampling weights and survey data
- Flexible modeling of ancillary parameters
- Martingale-like, score, and Cox–Snell residuals
- Graphs of estimated survivor, failure, hazard, and cumulative hazard functions
- Goodness-of-fit plot New
- Predictions and estimates
- Mean or median time to failure
- Mean or median log time
- Hazard
- Hazard ratios
- Survival probabilities
Bayesian parametric survival models
- Weibull, exponential, Gompertz, lognormal, loglogistic, or generalized gamma
- Both proportional-hazards and accelerated failure-time metrics
- Stratified models
- Individual-level frailty
- Group-level or shared frailty
- Flexible modeling of ancillary parameters
- Postestimation
Bayesian multilevel parametric survival models
- Weibull, exponential, lognormal, loglogistic, or gamma
- Both proportional-hazards and accelerated failure-time metrics
- Two-, three-, and higher-level models
- Nested and crossed random effects
- Random intercepts and random coefficients
- Flexible modeling of ancillary parameters
- Postestimation
Finite mixtures of parametric survival models
- Weibull, exponential, Gompertz, lognormal, loglogistic, or generalized gamma
- Both proportional-hazards and accelerated failure-time metrics
- Robust, cluster–robust, bootstrap, and jackknife standard errors
- Sampling weights and survey data
- Postestimation
Utilities
- Create nested case–control datasets
- Split and join time records
- Convert snapshot data into time-span data
Features of survival models
- Single- or multiple-failure data
- Left-truncation
- Right-censoring
- Interval-censoring
- Time-varying regressors
- Gaps
- Recurring events
- Start–stop format
- Different types of failure events
- Customized time scales allowed
Random-effects parametric survival models
- Weibull, exponential, lognormal, loglogistic, or gamma model
- Robust, cluster–robust, bootstrap, and jackknife standard errors
Multilevel mixed-effects parametric survival models
- Weibull, exponential, lognormal, loglogistic, or gamma models
- Robust and cluster–robust standard errors
- Sampling weights and survey data
- Marginal predictions and marginal means
Treatment-effects estimation for observational survival-time data
- Regression adjustment
- Inverse-probability weighting (IPW)
- Doubly robust methods
- IPW with regression adjustment
- Weighted regression adjustment
- Weibull, exponential, gamma, or lognormal outcome model
- Average treatment effects (ATEs)
- ATEs on the treated (ATETs)
- Potential-outcome means (POMs)
- Robust, bootstrap, and jackknife standard errors
Structural equation models with survival outcomes
- Latent predictors of survival outcomes
- Path models, growth curve models, and more
- Weibull, exponential, lognormal, loglogistic, or gamma models
- Survival outcomes with other outcomes
- Sampling weights and survey data
- Marginal predictions and marginal means
Graphs of survivor, failure, hazard, or cumulative hazard function Updated
- Kaplan–Meier survival or failure function
- Nelson–Aalen cumulative hazard
- Graphs and comparative graphs
- Confidence bands
- Embedded risk tables
- Adjustments for confounders
- Stratification
- Interval-censored data Updated
Postestimation Selector
- View and run all postestimation features for your command
- Automatically updated as estimation commands are run
Life tables and analysis
- Graphs and tables of estimates and confidence intervals
- Mean survival times and confidence intervals
- Cox regression adjustments
- Actuarial adjustments
- Tests of equality: log-rank, Cox, Wilcoxon–Breslow–Gehan,
Tarone–Ware, Peto–Peto–Prentice, and Fleming–Harrington
- Tests for trend
- Stratified test
Power analysis
Obtain summary statistics, confidence intervals, etc.
- Confidence intervals for incidence-rate ratio and difference
- Confidence intervals for means and percentiles of survival time
- Tabulate failure rate
- Calculate person-time (person-years), incidence rates, and
standardized mortality/morbidity ratios (SMR)
- Calculate rate ratios with the Mantel–Haenszel or Mantel–Cox method
A survival example session
Additional resources
See New in Stata 18 to learn about what was added in Stata 18.
