Analysing Survival Data from Clinical Trials and Observational Studies

, by Marubini, Ettore; Valsecchi, Maria Grazia

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ISBN: 9780470093412 | 0470093412
Cover: Paperback
Copyright: 7/2/2004

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A practical guide to methods of survival analysis for medical researchers with limited statistical experience. Methods and techniques described range from descriptive and exploratory analysis to multivariate regression methods. Uses illustrative data from actual clinical trials and observational studies to describe methods of analysing and reporting results. Also reviews the features and performance of statistical software available for applying the methods of analysis discussed.

Preface

xiii

Series preface

xvi

1 The scope of survival analysis

(10)

1.1 Introduction l

1.2 Characteristics of survival data and problems in survival analysis

(9)

1.2.1 Characteristics of survival data

(2)

1.2.2 Censoring

(3)

1.2.3 Problems in survival analysis

(4)

2 Randomized clinical trials: general principles and some controversial issues

(30)

2.1 Introduction

(3)

2.2 Selection of patients and trial design

(3)

2.3 Randomization

(3)

2.4 Statistical inference

(1)

2.5 Randomization and "intention to treat" principle

(3)

2.6 Statistical significance and clinical relevance

(1)

2.7 Subset analysis

(4)

2.8 Interim analyses in clinical trials

(10)

2.8.1 Internal and external monitoring

(1)

2.8.2 Repeated Significance Testing and early rejection of H()

(4)

2.8.3 Asymmetric group sequential boundaries and early "acceptance" of H()

(1)

2.8.4 Lan-DeMets procedure

(1)

2.8.5 Stochastic curtailed sampling

(1)

2.8.6 Confidence intervals

(1)

2.8.7 Survivorship data

(1)

2.8.8 Some caveats

(1)

A2.1 Randomization and treatment comparison

(2)

3 Estimation of survival probabilities

(50)

3.1 Introduction

(1)

3.2 The product limit estimate

(6)

3.2.1 Basic concepts

(4)

3.2.2 Formal definition of the product limit estimate

(2)

3.3 Life tables: fundamentals and construction

(8)

3.3.1 The life table estimate

(5)

3.3.2 Comparison of the life table and product limit estimates

(2)

3.4 Measures of precision of the survivorship probability estimates

(11)

3.4.1 Standard errors and confidence intervals

(6)

3.4.2 Confidence bands

(4)

3.5 Construction of a survival curve: some comments

(10)

3.5.1 Definition of the entry point

(1)

3.5.2 Definition of the end-point

(2)

3.5.3 Modalities of follow-up

(4)

3.5.4 Reporting and interpreting a survival curve

(3)

3.6 Event rates

(8)

3.6.1 Basic concepts

(1)

3.6.2 Estimate of rates and their standard errors in life tables

(4)

3.6.3 The relationship between probability and rate

(3)

A3.1 The product limit method: theory

(2)

A3.2 Delta method

(1)

A3.3 Percentiles of the Kolmogorov-Smirnov statistic

(1)

A3.4 Critical values for the Hall-Wellner confidence bands

(2)

4 Non-parametric methods for the comparison of survival curves

(52)

4.1 Introduction

(1)

4.2 The two sample Mantel-Haenzel (log-rank) test

(4)

4.3 Estimates of the relative hazard rate 0

(3)

4.4 A family of two sample rank tests

(5)

4.5 The inclusion of strata in the Mantel-Haenzel test

104

(9)

4.5.1 Formulation of the test statistic

104

(3)

4.5.2 Testing homogeneity of treatment effects

107

(2)

4.5.3 Gail and Simon test of qualitative interaction

109

(4)

4.6 Two sample comparison in presence of time-dependent covariates: the Mantel-Byar test

113

(10)

4.7 Comparison of more than two samples

123

(4)

4.8 Sample size

127

(16)

A4.1 Hypergeometric distribution

132

(1)

A4.2 Critical values for the Gail and Simon test

133

(1)

A4.3 Freedman's procedure for sample size

134

(3)

A4.4 Sample size according to Freedman

137

(6)

5 Distribution functions for failure time T

143

(28)

5.1 Introduction

143

(1)

5.2 T continuous

143

(2)

5.3 Relationship among f(t),S(t) and λ(t)

145

(1)

5.4 T discrete

146

(2)

5.5 Models in survival analysis

148

(5)

5.5.1 Specifying a parametric model

148

(1)

5.5.2 Estimation of the parameter

149

(2)

5.5.3 Variance of the estimator

151

(2)

5.5.4 An example

153

(1)

5.6 Regression models in survival analysis

153

(16)

5.6.1 The exponential regression model

154

(1)

5.6.2 Estimation of the regression parameters

155

(3)

5.6.3 Statistical tests on regression coefficients

158

(2)

5.6.4 An example

160

(4)

5.6.5 Relationship among LR. Wald and Rao score tests

164

(5)

A5.1 Observed information matrix for the exponential regression model

169

(2)

6 The Cox regression model

171

(52)

6.1 The basic Cox model

171

(8)

6.2 Estimation of the regression parameters

179

(4)

6.3 Estimation of the baseline hazard and survival probability

183

(2)

6.4 An example

185

(8)

6.4.1 Computing estimates

185

(4)

6.4.2 Relationship between the score test and the log-rank test

189

(4)

6.5 The "implementation" of the Cox regression model

193

(4)

6.6 A further example

197

(4)

6.7 Adjusted survival curves

201

(5)

6.8 Extensions of the basic Cox model

206

(14)

6.8.1 Stratification

206

(2)

6.8.2 Time-dependent covariates

208

(10)

6.8.3 A family of proportional hazards models

218

(2)

A6.1 Asymptotic variance of Λ0(t) and S0(t)

220

(3)

7 Validation of the proportional hazards models

223

(44)

7.1 Model selection

223

(1)

7.2 Graphical methods for checking model assumptions

224

(11)

7.2.1 Use of the stratified Cox model

229

(6)

7.3 Tests on the proportional hazards assumption

235

(12)

7.3.1 Test based on defined time-dependent covariates

235

(4)

7.3.2 Gill and Schumacher test

239

(2)

7.3.3 O'Quigley and Pessione test

241

(2)

7.3.4 Tests of proportional hazards against a general alternative

243

(2)

7.3.5 Some additional remarks

245

(2)

7.4 Residuals and regression diagnostics

247

(20)

7.4.1 The earlier works

249

(2)

7.4.2 Schoenfeld's residuals

251

(3)

7.4.3 Martingale based residuals

254

(1)

7.4.4 Model criticism in an example

255

(12)

8 Parametric regression models

267

(28)

8.1 Introduction

267

(1)

8.2 Some (continuous) distributions of failure time

268

(6)

8.2.1 Weibull distribution

268

(3)

8.2.2 Gamma distribution

271

(1)

8.2.3 Log-normal distribution

272

(1)

8.2.4 Log-logistic distribution

272

(2)

8.3 Parametric regression models

274

(6)

8.3.1 Weibull regression model

274

(2)

8.3.2 Log-logistic regression model and the class of proportional odds models

276

(2)

8.3.3 An example

278

(2)

8.4 Log-linear regression models for T

280

(3)

8.4.1 The class of accelerated failure time (AFT) models

281

(2)

8.5 Relationship of AFT models with proportional hazards and proportional odds models

283

(4)

8.6 An example

287

(1)

8.7 Concluding remarks

288

(3)

A8.1 The gamma function

291

(1)

A8.2 Generation of random failure times from a given distribution

291

(1)

A8.3 Derivation of the linear form in Y= log T for the Weibull distribution

292

(3)

9 The study of prognostic factors and the assessment of treatment effect

295

(36)

9.1 Introduction

295

(1)

9.2 Why study prognostic factors?

295

(2)

9.3 Adjusting the estimate of treatment effect

297

(8)

9.3.1 In the presence of unbalanced covariates

297

(2)

9.3.2 In the presence of balanced covariates

299

(5)

9.3.3 Concluding remarks

304

(1)

9.4 The study of prognostic factors by means of regression models

305

(10)

9.4.1 Problems with usual strategies for variable selection

307

(1)

9.4.2 Recommendations and cautions in prognostic factor analysis

308

(3)

9.4.3 The predictive value of a prognostic model

311

(2)

9.4.4 The definition of risk groups

313

(2)

9.5 Evaluation of treatment effectiveness

315

(11)

9.5.1 Measures suitable for describing clinical trial results

318

(2)

9.5.2 Confidence interval of measures of effectiveness

320

(6)

A9.1 Procedures for variable selection

326

(1)

A9.2 Relationship between risk and hazard

327

(4)

10 Competing risks

331

(34)

10.1 Introduction

331

(1)

10.2 The product limit estimator in the presence of competing events

332

(3)

10.3 Cause-specific hazard function, related functions and their estimators

335

(3)

10.4 Example of computation of crude cumulative incidence

338

(1)

10.5 Variance of the crude cumulative incidence and an example

339

(5)

10.6 Latent failure times

344

(2)

10.7 Cause-specific hazards and prognostic factors

346

(7)

10.8 Investigation of the relationship between different failure types

353

(2)

10.9 Comparison of treatment effects

355

(2)

10.10 Gray's method for comparing crude cumulative incidences

357

(4)

A10.1 Variance of the crude cumulative incidence

361

(4)

11 Meta-analysis

365

(18)

11.1 Introduction

365

(1)

11.2 Definition and goals of meta-analysis

365

(2)

11.3 Fixed effect approach

367

(4)

11.3.1 Binary data

369

(1)

11.3.2 Survival data

370

(1)

11.4 Random effect model

371

(2)

11.5 Examples

373

(5)

11.6 A promising approach

378

(2)

A11.1 Estimation of σ²/y by the method of moments

380

(3)

References

383

(14)

Author index

397

(8)

Subject index

405

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Analysing Survival Data from Clinical Trials and Observational Studies

Summary

Author Biography

Table of Contents

Supplemental Materials