Analysing Survival Data from Clinical Trials and Observational Studies

by Marubini, Ettore; Valsecchi, Maria Grazia

• ISBN13: 9780471939870
• ISBN10: 0471939870
• Edition: 1st
• Format: Hardcover
• Copyright: 1995-07-05
• Publisher: Wiley

Summary

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.

Author Biography

Ettore Marubini is the author of Analysing Survival Data from Clinical Trials and Observational Studies, published by Wiley.

Maria Grazia Valsecchi is the author of Analysing Survival Data from Clinical Trials and Observational Studies, published by Wiley.

Table of Contents

Preface	xiii
Series preface	xvi
The scope of survival analysis	1	(10)
Introduction	1	(1)
Characteristics of survival data and problems in survival analysis	2	(9)
Characteristics of survival data	2	(2)
Censoring	4	(3)
Problems in survival analysis	7	(4)
Randomized clinical trials: general principles and some controversial issues	11	(30)
Introduction	11	(3)
Selection of patients and trial design	14	(3)
Randomization	17	(3)
Statistical inference	20	(1)
Randomization and ``intention to treat'' principle	21	(3)
Statistical significance and clinical relevance	24	(1)
Subset analysis	25	(4)
Interim analyses in clinical trials	29	(12)
Internal and external monitoring	29	(1)
Repeated Significance Testing and early rejection of H0	30	(4)
Asymmetric group sequential boundaries and early ``acceptance'' of H0	34	(1)
Lan-DeMets procedure	35	(1)
Stochastic curtailed sampling	36	(1)
Confidence intervals	37	(1)
Survivorship data	38	(1)
Some caveats	39	(1)
Randomization and treatment comparison	39	(2)
Estimation of survival probabilities	41	(50)
Introduction	41	(1)
The product limit estimate	42	(6)
Basic concepts	42	(4)
Formal definition of the product limit estimate	46	(2)
Life tables: fundamentals and construction	48	(8)
The life table estimate	49	(5)
Comparison of the life table and product limit estimates	54	(2)
Measures of precision of the survivorship probability estimates	56	(11)
Standard errors and confidence intervals	57	(6)
Confidence bands	63	(4)
Construction of a survival curve: some comments	67	(10)
Definition of the entry point	67	(1)
Definition of the end-point	68	(2)
Modalities of follow-up	70	(4)
Reporting and interpreting a survival curve	74	(3)
Event rates	77	(14)
Basic concepts	77	(1)
Estimate of rates and their standard errors in life tables	78	(4)
The relationship between probability and rate	82	(3)
The product limit method: theory	85	(2)
Delta method	87	(1)
Percentiles of the Kolmogorov---Smirnov statistic	88	(1)
Critical values for the Hall-Wellner confidence bands	89	(2)
Non-parametric methods for the comparison of survival curves	91	(52)
Introduction	91	(1)
The two sample Mantel-Haenzel (log-rank) test	92	(4)
Estimates of the relative hazard rate 0	96	(3)
A family of two sample rank tests	99	(5)
The inclusion of strata in the Mantel-Haenzel test	104	(9)
Formulation of the test statistic	104	(3)
Testing homogeneity of treatment effects	107	(2)
Gail and Simon test of qualitative interaction	109	(4)
Two sample comparison in presence of time-dependent covariates: the Mantel-Byar test	113	(10)
Comparison of more than two samples	123	(4)
Sample size	127	(16)
Hypergeometric distribution	132	(1)
Critical values for the Gail and Simon test	133	(1)
Freedman's procedure for sample size	134	(3)
Sample size according to Freedman	137	(6)
Distribution functions for failure time T	143	(28)
Introduction	143	(1)
T continuous	143	(2)
Relationship among f(t), S(t) and λ(t)	145	(1)
T discrete	146	(2)
Models in survival analysis	148	(5)
Specifying a parametric model	148	(1)
Estimation of the parameter	149	(2)
Variance of the estimator	151	(2)
An example	153	(1)
Regression models in survival analysis	153	(18)
The exponential regression model	154	(1)
Estimation of the regression parameters	155	(3)
Statistical tests on regression coefficients	158	(2)
An example	160	(4)
Relationship among LR, Wald and Rao score tests	164	(5)
Observed information matrix for the exponential regression model	169	(2)
The Cox regression model	171	(52)
The basic Cox model	171	(8)
Estimation of the regression parameters	179	(4)
Estimation of the baseline hazard and survival probability	183	(2)
An example	185	(8)
Computing estimates	185	(4)
Relationship between the score test and the log-rank test	189	(4)
The ``implementation'' of the Cox regression model	193	(4)
A further example	197	(4)
Adjusted survival curves	201	(5)
Extensions of the basic Cox model	206	(17)
Stratification	206	(2)
Time-dependent covariates	208	(10)
A family of proportional hazards models	218	(2)
Asymptotic variance of Λ0(t) and S0(t)	220	(3)
Validation of the proportional hazards models	223	(44)
Model selection	223	(1)
Graphical methods for checking model assumptions	224	(11)
Use of the stratified Cox model	229	(6)
Tests on the proportional hazards assumption	235	(12)
Test based on defined time-dependent covariates	235	(4)
Gill and Schumacher test	239	(2)
O'Quigley and Pessione test	241	(2)
Tests of proportional hazards against a general alternative	243	(2)
Some additional remarks	245	(2)
Residuals and regression diagnostics	247	(20)
The earlier works	249	(2)
Schoenfeld's residuals	251	(3)
Martingale based residuals	254	(1)
Model criticism in an example	255	(12)
Parametric regression models	267	(28)
Introduction	267	(1)
Some (continuous) distributions of failure time	268	(6)
Weibull distribution	268	(3)
Gamma distribution	271	(1)
Log-normal distribution	272	(1)
Log-logistic distribution	272	(2)
Parametric regression models	274	(6)
Weibull regression model	274	(2)
Log-logistic regression model and the class of proportional odds models	276	(2)
An example	278	(2)
Log-linear regression models for T	280	(3)
The class of accelerated failure time (AFT) models	281	(2)
Relationship of AFT models with proportional hazards and proportional odds models	283	(4)
An example	287	(1)
Concluding remarks	288	(7)
The gamma function	291	(1)
Generation of random failure times from a given distribution	291	(1)
Derivation of the linear form in Y = log T for the Weibull distribution	292	(3)
The study of prognostic factors and the assessment of treatment effect	295	(36)
Introduction	295	(1)
Why study prognostic factors?	295	(2)
Adjusting the estimate of treatment effect	297	(8)
In the presence of unbalanced covariates	297	(2)
In the presence of balanced covariates	299	(5)
Concluding remarks	304	(1)
The study of prognostic factors by means of regression models	305	(10)
Problems with usual strategies for variable selection	307	(1)
Recommendations and cautions in prognostic factor analysis	308	(3)
The predictive value of a prognostic model	311	(2)
The definition of risk groups	313	(2)
Evaluation of treatment effectiveness	315	(16)
Measures suitable for describing clinical trial results	318	(2)
Confidence interval of measures of effectiveness	320	(6)
Procedures for variable selection	326	(1)
Relationship between risk and hazard	327	(4)
Competing risks	331	(34)
Introduction	331	(1)
The product limit estimator in the presence of competing events	332	(3)
Cause-specific hazard function, related functions and their estimators	335	(3)
Example of computation of crude cumulative incidence	338	(1)
Variance of the crude cumulative incidence and an example	339	(5)
Latent failure times	344	(2)
Cause-specific hazards and prognostic factors	346	(7)
Investigation of the relationship between different failure types	353	(2)
Comparison of treatment effects	355	(2)
Gray's method for comparing crude cumulative incidences	357	(8)
Variance of the crude cumulative incidence	361	(4)
Meta-analysis	365	(18)
Introduction	365	(1)
Definition and goals of meta-analysis	365	(2)
Fixed effect approach	367	(4)
Binary data	369	(1)
Survival data	370	(1)
Random effect model	371	(2)
Examples	373	(5)
A promising approach	378	(5)
Estimation of σ2y by the method of moments	380	(3)
References	383	(14)
Author index	397	(8)
Subject index	405