Cox proportional hazards

• Time-varying covariates and censoring
• Continuously time-varying covariates
• Conventional or robust estimates of variance
• Stratified estimation
• Sampling weights and survey data
• Four ways to handle ties: Breslow, exact partial likelihood, exact marginal likelihood, and Efron
• Martingale, efficient score, Cox–Snell, Schoenfeld, and deviance residuals
• Tests for proportional hazards
• Estimates of baseline survival, hazard, and cumulative hazard functions
• Shared frailty models
• Harrell’s C, Somers’ D, and Gönen and Heller’s K statistics measuring concordance
• Multiple imputation

Competing-risks regression

• Fine and Gray proportional subhazards model
• Time-varying covariates
• Cumulative-incidence graphs
• Subhazard ratios
• Multiple imputation
• Constraints

Parametric survival models

• Exponential
• Weibull
• Gompertz
• Lognormal
• Loglogistic
• Generalized log-gamma
• Sampling weights and survey data
• Martingale-like, score, Cox–Snell, Schoenfeld, and deviance residuals
• Plots of predicted survival, hazard, and cumulative hazard functions
• Individual-level frailty
• Group-level or shared frailty
• Stratified models
• Linear constraints

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
• Conventional or robust estimates of variance

Life tables and analysis

• Graphs and tables of estimates and confidence intervals
• Mean survival times and confidence intervals
• Cox regression adjustments
• Actuarial adjustments
• Tests for trend
• Tests of equality—log-rank, Mantel–Haenszel, Wilcoxon–Breslow, Tarone–Ware, Fleming–Harrington, Peto–Peto–Prentice

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

Utilities

• Create nested case–control datasets
• Split and join time records
• Convert snapshot data into time-span data
• Calculate person-time (person-years), incidence rates, and standardized mortality/morbidity ratios (SMR)

Kaplan–Meier survival curves

• Graphs and comparative graphs
• Confidence bands
• Embedded risk tables
• Adjustments for confounders
• Stratification
• Nelson–Aalen graphs of cumulative hazards

Predictions and estimates

• Mean or median time to failure
• Mean or median log time
• Hazard
• Hazard ratios
• Survival probabilities

Factor variables

• Automatically create indicators based on categorical variables
• Form interactions among discrete and continuous variables
• Include polynomial terms
• Perform contrasts of categories/levels

Marginal analysis

• Estimated marginal means
• Marginal and partial effects
• Average marginal and partial effects
• Least-squares means
• Predictive margins
• Adjusted predictions, means, and effects
• Contrasts of margins
• Pairwise comparisons of margins
• Profile plots
• Graphs of margins and marginal effects

Contrasts

• Analysis of main effects, simple effects, interaction effects, partial
interaction effects, and nested effects
• Comparisons against reference groups, of adjacent levels, or against
the grand mean
• Orthogonal polynomials
• Helmert contrasts
• Custom contrasts
• ANOVA-style tests
• Contrasts of nonlinear responses
• Multiple-comparison adjustments
• Balanced and unbalanced data
• Contrasts in odds-ratio metric
• Contrasts of means, intercepts, and slopes
• Graphs of contrasts
• Interaction plots

Pairwise comparisons

• Compare estimated means, intercepts, and slopes
• Compare marginal means, intercepts, and slopes
• Balanced and unbalanced data
• Nonlinear responses
• Multiple-comparison adjustments: Bonferroni, Šidák, Scheffé, Tukey HSD, Duncan, and Student-Newman-Keuls adjustments
• Group comparisons that are significant
• Graphs of pairwise comparisons

A survival example session

Explore more about survival analysis in Stata.