List of tables

List of figures

Notation and typography

1 The problem of survival analysis

1.1 Parametric modeling

1.2 Semiparametric modeling

1.3 Nonparametric analysis

1.4 Linking the three approaches

2 Describing the distribution of failure times

2.1 The survivor and hazard functions

2.2 The quantile function

2.3 Interpreting the cumulative hazard and hazard rate

2.3.1 Interpreting the cumulative hazard

2.3.2 Interpreting the hazard rate

2.4 Means and medians

3 Hazard models

3.1 Parametric models

3.2 Semiparametric models

3.3 Analysis time (time at risk)

4 Censoring and truncation

4.1 Censoring

4.1.1 Right-censoring

4.1.2 Interval-censoring

4.1.3 Left-censoring

4.2 Truncation

4.2.1 Left-truncation (delayed entry)

4.2.2 Right-truncation

4.2.3 Gaps

5 Recording survival data

5.1 The desired format

5.2 Other formats

5.3 Example: Wide-form snapshot data

6 Using stset

6.1 A short lesson on dates

6.2 Purposes of the stset command

6.3 Syntax of the stset command

6.3.1 Specifying analysis time

6.3.2 Variables defined by stset

6.3.3 Specifying what constitutes failure

6.3.4 Specifying when subjects exit from the analysis

6.3.5 Specifying when subjects enter the analysis

6.3.6 Specifying the subject-ID variable

6.3.7 Specifying the begin-of-span variable

6.3.8 Convenience options

7 After stset

7.1 Look at stset’s output

7.2 List some of your data

7.3 Use stdescribe

7.4 Use stvary

7.5 Perhaps use stfill

7.6 Example: Hip-fracture data

8 Nonparametric analysis

8.1 Inadequacies of standard univariate methods

8.2 The Kaplan–Meier estimator

8.2.1 Calculation

8.2.2 Censoring

8.2.3 Left-truncation (delayed entry)

8.2.4 Gaps

8.2.5 Relationship to the empirical distribution function

8.2.6 Other uses of sts list

8.2.7 Graphing the Kaplan–Meier estimate

8.3 The Nelson–Aalen estimator

8.4 Estimating the hazard function

8.5 Estimating mean and median survival times

8.6 Tests of hypothesis

8.6.1 The log-rank test

8.6.2 The Wilcoxon test

8.6.3 Other tests

8.6.4 Stratified tests

9 The Cox proportional hazards model

9.1 Using stcox

9.1.1 The Cox model has no intercept

9.1.2 Interpreting coefficients

9.1.3 The effect of units on coefficients

9.1.4 Estimating the baseline cumulative hazard and survivor functions

9.1.5 Estimating the baseline hazard function

9.1.6 The effect of units on the baseline functions

9.2 Likelihood calculations

9.2.1 No tied failures

9.2.2 Tied failures

The marginal calculation

The partial calculation

The Breslow approximation

The Efron approximation

9.2.3 Summary

9.3 Stratified analysis

9.3.1 Obtaining coefficient estimates

9.3.2 Obtaining estimates of baseline functions

9.4 Cox models with shared frailty

9.4.1 Parameter estimation

9.4.2 Obtaining estimates of baseline functions

9.5 Cox models with survey data

9.5.1 Declaring survey characteristics

9.5.2 Fitting a Cox model with survey data

9.5.3 Some caveats of analyzing survival data from complex survey designs

9.6 Cox model with missing data—multiple imputation

9.6.1 Imputing missing values

9.6.2 Multiple-imputation inference

10 Model building using stcox

10.1 Indicator variables

10.2 Categorical variables

10.3 Continuous variables

10.3.1 Fractional polynomials

10.4 Interactions

10.5 Time-varying variables

10.5.1 Using stcox, tvc() texp()

10.5.2 Using stsplit

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

11 The Cox model: Diagnostics

11.1 Testing the proportional-hazards assumption

11.1.1 Tests based on reestimation

11.1.2 Test based on Schoenfeld residuals

11.1.3 Graphical methods

11.2 Residuals and diagnostic measures

Reye’s syndrome data

11.2.1 Determining functional form

11.2.2 Goodness of fit

11.2.3 Outliers and influential points

12 Parametric models

12.1 Motivation

12.2 Classes of parametric models

12.2.1 Parametric proportional hazards models

12.2.2 Accelerated failure-time models

12.2.3 Comparing the two parameterizations

13 A survey of parametric regression models in Stata

13.1 The exponential model

13.1.1 Exponential regression in the PH metric

13.1.2 Exponential regression in the AFT metric

13.2 Weibull regression

13.2.1 Weibull regression in the PH metric

Fitting null models

13.2.2 Weibull regression in the AFT metric

13.3 Gompertz regression (PH metric)

13.4 Lognormal regression (AFT metric)

13.5 Loglogistic regression (AFT metric)

13.6 Generalized gamma regression (AFT metric)

13.7 Choosing among parametric models

13.7.1 Nested models

13.7.2 Nonnested models

14 Postestimation commands for parametric models

14.1 Use of predict after streg

14.1.1 Predicting the time of failure

14.1.2 Predicting the hazard and related functions

14.1.3 Calculating residuals

14.2 Using stcurve

14.3 Predictive margins and marginal effects

14.3.1 Predictive margins

Marginal mean survival time

Marginal survival probabilities

Multiple-record data

14.3.2 Marginal effects

15 Generalizing the parametric regression model

15.0.3 Using the ancillary() option

15.0.4 Stratified models

15.1 Frailty models

15.1.1 Unshared-frailty models

15.1.2 Example: Kidney data

15.1.3 Testing for heterogeneity

15.1.4 Shared-frailty models

16 Power and sample-size determination for survival analysis

16.1 Estimating sample size

16.1.1 Multiple-myeloma data

16.1.2 Comparing two survivor functions nonparametrically

16.1.3 Comparing two exponential survivor functions

16.1.4 Cox regression models

16.2 Accounting for withdrawal and accrual of subjects

16.2.1 The effect of withdrawal or loss to follow-up

16.2.2 The effect of accrual

16.2.3 Examples

16.3 Estimating power and effect size

16.4 Tabulating or graphing results

17 Competing risks

17.1 Cause-specific hazards

17.2 Cumulative incidence functions

17.3 Nonparametric analysis

17.3.1 Breast cancer data

17.3.2 Cause-specific hazards

17.3.3 Cumulative incidence functions

17.4 Semiparametric analysis

17.4.1 Cause-specific hazards

Simultaneous regressions for cause-specific hazards

17.4.2 Cumulative incidence functions

Using stcrreg

Using stcox

17.5 Parametric analysis

References