An Introduction to Survival Analysis Using Stata, Revised Third Edition

An Introduction to Survival Analysis Using Stata, Revised Third Edition is the ideal tutorial for professional data analysts who want to learn survival analysis for the first time or who are well versed in survival analysis but are not as dexterous in using Stata to analyze survival data. This text also serves as a valuable reference to those readers who already have experience using Stata’s survival analysis routines. The revised third edition has been updated for Stata 14, and it includes a new section on predictive margins and marginal effects, which demonstrates how to obtain and visualize marginal predictions and marginal effects using the margins and marginsplot commands after survival regression models. Survival analysis is a field of its own that requires specialized data management and analysis procedures. To meet this requirement, Stata provides the st family of commands for organizing and summarizing survival data. This book provides statistical theory, step-by-step procedures for analyzing survival data, an in-depth usage guide for Stata's most widely used st commands, and a collection of tips for using Stata to analyze survival data and to present the results. This book develops from first principles the statistical concepts unique to survival data and assumes only a knowledge of basic probability and statistics and a working knowledge of Stata. The first three chapters of the text cover basic theoretical concepts: hazard functions, cumulative hazard functions, and their interpretations; survivor functions; hazard models; and a comparison of nonparametric, semiparametric, and parametric methodologies. Chapter 4 deals with censoring and truncation. The next three chapters cover the formatting, manipulation, stsetting, and error checking involved in preparing survival data for analysis using Stata's st analysis commands. Chapter 8 covers nonparametric methods, including the Kaplan–Meier and Nelson–Aalen estimators and the various nonparametric tests for the equality of survival experience. Chapters 9–11 discuss Cox regression and include various examples of fitting a Cox model, obtaining predictions, interpreting results, building models, model diagnostics, and regression with survey data. The next four chapters cover parametric models, which are fit using Stata's streg command. These chapters include detailed derivations of all six parametric models currently supported in Stata and methods for determining which model is appropriate, as well as information on stratification, obtaining predictions, and advanced topics such as frailty models. Chapter 16 is devoted to power and sample-size calculations for survival studies. The final chapter covers survival analysis in the presence of competing risks.

The problem of survival analysis Parametric modeling Semiparametric modelingNonparametric analysis Linking the three approaches Describing the distribution of failure times The survivor and hazard functionsThe quantile functionInterpreting the cumulative hazard and hazard rate Means and medians Hazard models Parametric modelsSemiparametric modelsAnalysis time (time at risk) Censoring and truncation Censoring Truncation Recording survival data The desired format Other formatsExample: Wide-form snapshot data Using stset A short lesson on datesPurposes of the stset commandSyntax of the stset command After stset Look at stset’s outputList some of your data Use stdescribeUse stvary Perhaps use stfill Example: Hip-fracture data Nonparametric analysis Inadequacies of standard univariate methods The Kaplan–Meier estimator The Nelson–Aalen estimatorEstimating the hazard functionEstimating mean and median survival timesTests of hypothesis The Cox proportional hazards model Using stcox Likelihood calculations Stratified analysis Cox models with shared frailty Cox models with survey data Cox model with missing data—multiple imputation Model building using stcox Indicator variablesCategorical variablesContinuous variables InteractionsTime-varying variables Modeling group effects: fixed-effects, random-effects, stratification, and clustering The Cox model: Diagnostics Testing the proportional-hazards assumption Residuals and diagnostic measures Reye’s syndrome data Parametric models MotivationClasses of parametric models A survey of parametric regression models in Stata The exponential model Weibull regression Gompertz regression (PH metric)Lognormal regression (AFT metric)Loglogistic regression (AFT metric)Generalized gamma regression (AFT metric)Choosing among parametric models Postestimation commands for parametric models Use of predict after streg Using stcurvePredictive margins and marginal effects Generalizing the parametric regression model Frailty models Power and sample-size determination for survival analysis Estimating sample size Accounting for withdrawal and accrual of subjects Estimating power and effect size Tabulating or graphing results Competing risks Cause-specific hazardsCumulative incidence functionsNonparametric analysis Semiparametric analysis Parametric analysis

Mario Cleves is Professor and the Biostatistics Section Chief in the Department of Pediatrics at the University of Arkansas for Medical Sciences. William Gould is the president and head of development at StataCorp. Yulia Marchenko is a senior statistician at StataCorp. All are authors of Stata statistical software, in particular, Stata’s widely used survival analysis suite.