ebook: Renard (2002) Multilevel & Longitudinal Models

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ebook: Renard (2002) Multilevel & Longitudinal Models

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关键词：Longitudinal Longitudina Multilevel models Renard

Contents
1 Introduction 1
1.1 Clustered Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Types of Correlated Data . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Statistical Models for Correlated Data . . . . . . . . . . . . . . . . . . 3
1.4 Organization of Subsequent Chapters . . . . . . . . . . . . . . . . . . . 6
2 Introduction to Multilevel Models 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 The 1997 Belgian Health Interview Survey . . . . . . . . . . . . . . . . 12
2.3 Linear Multilevel Models . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Nonlinear Multilevel Models . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Maximum Marginal Likelihood . . . . . . . . . . . . . . . . . . 16
2.4.2 Approximate Methods . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Weighting in Multilevel Models . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Application to the HIS . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.1 Linear Multilevel Model . . . . . . . . . . . . . . . . . . . . . . 21
2.6.2 Multilevel Logistic Model . . . . . . . . . . . . . . . . . . . . . 22
3 Pairwise Likelihood Estimation in Multilevel Probit Models 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Pseudo-Likelihood Estimation . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Pseudo-Likelihood De nition . . . . . . . . . . . . . . . . . . . 29
3.2.2 Asymptotic Properties of Pseudo-Likelihood Estimators . . . . 30
3.3 Pairwise Likelihood in the Multilevel Probit Model . . . . . . . . . . 37
3.3.1 The Multilevel Probit Model . . . . . . . . . . . . . . . . . . . 38
3.3.2 Pairwise Likelihood . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Asymptotic Relative Eciency . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Weighted Pairwise Likelihood . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Example: a Meta-Analysis of Trials in Schizophrenic Subjects . . . . . 49
3.7 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Validation of Surrogate Endpoints in Multiple Randomized Clinical
Trials with Discrete Outcomes 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Surrogate Endpoint Validation: Two Normally Distributed Endpoints 67
4.2.1 A Hierarchical Model . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.2 Trial-Level Surrogacy . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.3 Individual-Level Surrogacy . . . . . . . . . . . . . . . . . . . . 70
4.2.4 Surrogate Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.5 Computational Issues . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Surrogate Endpoint Validation: Two Binary Outcomes . . . . . . . . 73
4.3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.2 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Example: a Meta-Analysis of Trials in Schizophrenic Subjects . . . . . 78
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 Repeated-Measures Models to Evaluate a Hepatitis B Vaccination
Program 85
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Hepatitis B Vaccination Program and Scienti c Questions . . . . . . . 86
5.3 The Linear Mixed Model With Serial Correlation . . . . . . . . . . . . 89
5.4 Fractional Polynomials with Longitudinal Data . . . . . . . . . . . . . 91
5.5 Time-evolution of Antibodies . . . . . . . . . . . . . . . . . . . . . . . 93
5.6 Prediction at Year 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 Estimating Reliability Using Non-Linear Mixed Models With Re-
peated Binary Data 105
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 Estimating Reliability in Generalized Linear Mixed Models . . . . . . 107
6.2.1 General Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2.2 Probit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3 Estimating Reliability in the Probit Model with Autocorrelation . . . 110
6.3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3.2 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3.4 Application to the Schizophrenia Data . . . . . . . . . . . . . . 116
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7 Validation of a Longitudinally Measured Surrogate Marker for a Time-to-Event Endpoint 119
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2 Motivating Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.3 Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4 Application to the Advanced Prostate Cancer Data . . . . . . . . . . . 127
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8 Concluding Remarks and Further Research 133
8.1 Pairwise Likelihood Estimation . . . . . . . . . . . . . . . . . . . . . . 133
8.1.1 Model Checking and Diagnostics . . . . . . . . . . . . . . . . . 134
8.1.2 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.1.3 Crossed Random-Eects Models . . . . . . . . . . . . . . . . . 136
8.2 Evaluation of Surrogate Endpoints . . . . . . . . . . . . . . . . . . . . 138

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