An Introduction to Survival Analysis Using Stata, Revised Third Edition (4^th Ed.)

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 versedin survival analysis but are not as dexterous in using Stata toanalyze 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 modeling
Nonparametric analysis　
Linking the three approaches

The survivor and hazard functions
The quantile function
Interpreting the cumulative hazard and hazard rate

Means and medians

Hazard models

Parametric models
Semiparametric models
Analysis time (time at risk)

Censoring

Truncation

The desired format　
Other formats
Example: Wide-form snapshot data

A short lesson on dates
Purposes of the stset command
Syntax of the stset command

Look at stset’s output
List some of your data　
Use stdescribe
Use stvary　
Perhaps use stfill　
Example: Hip-fracture data

Inadequacies of standard univariate methods　
The Kaplan–Meier estimator

The Nelson–Aalen estimator
Estimating the hazard function
Estimating mean and median survival times
Tests of hypothesis

Using stcox

Likelihood calculations

Stratified analysis

Cox models with shared frailty

Cox models with survey data

Cox model with missing data—multiple imputation

Indicator variables
Categorical variables
Continuous variables

Interactions
Time-varying variables

Modeling group effects: fixed-effects, random-effects, stratification, and clustering

Testing the proportional-hazards assumption

Residuals and diagnostic measures Reye’s syndrome data

Motivation
Classes of parametric models

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

Use of predict after streg

Using stcurve
Predictive margins and marginal effects

Frailty models

Estimating sample size

Accounting for withdrawal and accrual of subjects　

Estimating power and effect size　
Tabulating or graphing results

Cause-specific hazards
Cumulative incidence functions
Nonparametric 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.