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Joint Models for Longitudinal and Time-to-Event Data: With Applications in R

by: Rizopoulos; Dimitris

Joint Models for Longitudinal and Time-to-Event Data: With Applications in R

by: Rizopoulos; Dimitris

ISBN 13:
9781439872864
ISBN 10:
1439872864
Edition: 1st
Format: Nonspecific Binding
Copyright: 06/22/2012
Publisher: Chapman & Hall

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Summary

In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest, e.g., prostate cancer studies where longitudinal PSA level measurements are collected in conjunction with the time-to-recurrence. This book provides a full treatment of joint models (JM) for longitudinal and time-to-event data. The content will be explanatory rather than mathematically rigorous and applications will be emphasized. All illustrations put forward will be available in the R programming language via the freely available package JM written by the author.

Preface	p. vii
Introduction	p. 1
Goals	p. 1
Motivating Studies	p. 2
Primary Biliary Cirrhosis Data	p. 2
AIDS Data	p. 3
Liver Cirrhosis Data	p. 4
Aortic Valve Data	p. 6
Other Applications	p. 7
Inferential Objectives in Longitudinal Studies	p. 8
Effect of Covariates on a Single Outcome	p. 9
Association between Outcomes	p. 9
Complex Hypothesis Testing	p. 10
Prediction	p. 10
Statistical Analysis with Implicit Outcomes	p. 11
Overview	p. 11
Longitudinal Data Analysis	p. 15
Features of Longitudinal Data	p. 15
Linear Mixed-Effects Models	p. 16
Estimation	p. 18
Implementation in R	p. 21
Missing Data in Longitudinal Studies	p. 27
Missing Data Mechanisms	p. 29
Missing Not at Random Model Families	p. 32
Further Reading	p. 34
Analysis of Event Time Data	p. 35
Features of Event Time Data	p. 35
Basic Functions in Survival Analysis	p. 37
Likelihood Construction for Censored Data	p. 40
Relative Risk Regression Models	p. 41
Implementation in R	p. 42
Time-Dependent Covariates	p. 44
Extended Cox Model	p. 46
Further Reading	p. 49
Joint Models for Longitudinal and Time-to-Event Data	p. 51
The Basic Joint Model	p. 51
The Survival Submodel	p. 52
The Longitudinal Submodel	p. 54
Joint Modeling in R: A Comparison with the Extended Cox Model	p. 56
Estimation of Joint Models	p. 61
Two-Stage Approaches	p. 61
Joint Likelihood Formulation	p. 62
Standard Errors with an Unspecified Baseline Risk Function	p. 66
Optimization Control in JM	p. 67
Numerical Integration	p. 68
Numerical Integration Control in JM	p. 72
Convergence Problems	p. 74
Asymptotic Inference for Joint Models	p. 78
Hypothesis Testing	p. 78
Confidence Intervals	p. 84
Design Considerations	p. 86
Estimation of the Random Effects	p. 87
Connection with the Missing Data Framework	p. 89
Sensitivity Analysis under Joint Models	p. 92
Extensions of the Standard Joint Model	p. 97
Parameterizations	p. 97
Interaction Effects	p. 98
Lagged Effects	p. 100
Time-Dependent Slopes Parameterization	p. 103
Cumulative Effects Parameterization	p. 106
Random-Effects Parameterization	p. 111
Handling Exogenous Time-Dependent Covariates	p. 115
Stratified Relative Risk Models	p. 119
Latent Class Joint Models	p. 122
Multiple Failure Times	p. 128
Competing Risks	p. 128
Recurrent Events	p. 134
Accelerated Failure Time Models	p. 137
Joint Models for Categorical Longitudinal Outcomes	p. 139
The Generalized Linear Mixed Model (GLMM)	p. 139
Combining Discrete Repeated Measures with Survival	p. 141
Joint Models for Multiple Longitudinal Outcomes	p. 142
Joint Model Diagnostics	p. 145
Residuals for Joint Models	p. 145
Residuals for the Longitudinal Part	p. 145
Residuals for the Survival Part	p. 148
Dropout and Residuals	p. 155
Multiple Imputation Residuals	p. 158
Fixed Visit Times	p. 158
Random Visit Times	p. 162
Random-Effects Distribution	p. 169
Prediction and Accuracy in Joint Models	p. 171
Dynamic Predictions of Survival Probabilities	p. 171
Definition	p. 171
Estimation	p. 172
Implementation in R	p. 174
Dynamic Predictions for the Longitudinal Outcome	p. 182
Effect of Parameterization on Predictions	p. 186
Prospective Accuracy for Joint Models	p. 194
Discrimination Measures for Binary Outcomes	p. 195
Discrimination Measures for Survival Outcomes	p. 197
Prediction Rules for Longitudinal Markers	p. 198
Discrimination Indices	p. 200
Estimation under the Joint Modeling Framework	p. 202
Implementation in R	p. 205
A Brief Introduction to R	p. 219
Obtaining and Installing R and R Packages	p. 219
Simple Manipulations	p. 220
Basic R Objects	p. 220
Indexing	p. 222
Import and Manipulate Data Frames	p. 224
The Formula Interface	p. 226
The EM Algorithm for Joint Models	p. 229
A Short Description of the EM Algorithm	p. 229
The E-step for Joint Models	p. 230
The M-step for Joint Models	p. 231
Structure of the JM Package	p. 235
Methods for Standard Generic Functions	p. 235
Additional Functions	p. 237
References	p. 239
Index	p. 257
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Joint Models for Longitudinal and Time-to-Event Data: With Applications in R

Joint Models for Longitudinal and Time-to-Event Data: With Applications in R

9781439872864

1439872864

Summary

Author Biography

Table of Contents

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