Cox
proportional hazards
- time-varying covariates and censoring
- continuously time-varying covariates
- conventional or robust
estimates of variance
- stratified estimation
- sampling weights
- 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
- 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
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Kaplan–Meier and Nelson–Aalen
- graph estimates and confidence intervals
- 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
Summary
tables
- 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
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