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 and Somers’ D statistics measuring concordance

Parametric survival models

• Exponential
• Weibull
• Gompertz
• Lognormal
• Log-logistic
• 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

Kaplan–Meier and Nelson–Aalen

Summary tables

• Graph estimates and confidence intervals with risk tables (updated)
• List estimates and confidence intervals
• Test (log-rank, Mantel–Haenszel, Wilcoxon–Breslow, Tarone–Ware, Fleming–Harrington, Peto–Peto–Prentice)
• Test for trend
• Calculate level and confidence interval of survivor function
• Report mean survival time and confidence interval
• Cox regression-adjusted estimates

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)

Predictions

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

Marginal effects

• Marginal effects and elasticities
• Standard errors and confidence intervals
• At means or specified covariate values
• For any predicted statistic

A survival example session