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Survival analysis

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, hazard, and cumulative hazard functions

Competing-risks regression

  • Fine and Gray proportional subhazards model
  • Time-varying covariates
  • Robust, cluster–robust, bootstrap, and jackknife standard errors
  • Linear constraints
  • 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
  • Generalized gamma
  • Robust, cluster–robust, bootstrap, and jackknife standard errors
  • Stratified models
  • Individual-level frailty
  • Group-level or shared frailty
  • Linear constraints
  • Sampling weights and survey data
  • Multiple imputation
  • Martingale-like, score, Cox–Snell, and deviance residuals
  • Graphs of estimated survivor, hazard, and cumulative hazard functions
  • Predictions and estimates
    • Mean or median time to failure
    • Mean or median log time
    • Hazard
    • Hazard ratios
    • Survival probabilities

Features of survival models

  • Single- or multiple-failure data
  • Left truncation
  • Right-censoring
  • Time-varying regressors
  • Gaps
  • Recurring events
  • Start–stop format
  • Different types of failure events
  • Multiple time scales allowed

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

  • Solve for sample size, power, or effect size
  • Log-rank test of survival curves
  • Cox proportional hazards model
  • Exponential regression
  • Time at risk, incidence rate, number of subjects, 25th, 50th, and 75th percentiles of survival time
  • Incidence-rate ratio and difference
  • Life tables
  • Rates and SMRs by one or more categorical variables
  • Stratified rate ratios
  • See the new power and sample size features.

Utilities

  • Create nested case–control datasets
  • Split and join time records
  • Convert snapshot data into time-span data

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

Graphs of survivor, 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

A survival example session

Additional resources

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