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

 

COX PROPORTIONAL HAZARDS MODEL FOR INTERVAL-CENSORED DATA

  • Case II interval-censored data
  • Current status or case I interval-censored data
  • Time-varying covariates
  • Testing proportional-hazards assumption
  • Two ways to estimate the baseline hazard function
  • Four methods to estimate standard errors
  • Robust and cluster–robust standard errors
  • 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
  • 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
  • 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
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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

  • 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

 

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

Video – How to construct life tables

Video – How to calculate the Kaplan–Meier survivor and Nelson–Aalen cumulative hazard functions

Video – How to test the equality of survivor functions

 

POWER ANALYSIS

  • Solve for sample size, power, or effect size
  • Log-rank test of survival curves
  • Cox proportional hazards model
  • Clustered data
  • Exponential regression

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