Monte-Carlo Simulation-Based Statistical Modeling (eBook)

Professor Ding-Geng Chen is a fellow of the American Statistical Association and currently the Wallace Kuralt distinguished professor at the University of North Carolina at Chapel Hill. He was a professor at the University of Rochester and the Karl E. Peace endowed eminent scholar chair in biostatistics at Georgia Southern University. He is also a senior statistics consultant for biopharmaceuticals and government agencies with extensive expertise in clinical trial biostatistics and public health statistics. Professor Chen has written more than 150 referred professional publications and co-authored and co-edited eight books on clinical trial methodology, meta-analysis, causal-inference and public health statistics. Mr. John Dean Chen is specialized in Monte-Carlo simulations in modelling financial market risk. In his career on Wall Street, he worked in Market Risk in commodities trading, structuring notes on the Exotics Interest Rate Derivatives desk at Barclays Capital. During his career in the financial industry, he witnessed in person the unfolding of the financial crisis, and the immediate aftermath consuming much of the financial industry. In its wake, a dizzying array of regulations were made from the government, severely limiting the businesses that once made banks so profitable. Mr Chen transitioned back to the Risk side of the business working in Market and Model Risk. He is currently a Vice President at Credit Suisse specializing in regulatory stress testing with  Monte-Carlo simulations. He graduated from the University of Washington with a dual Bachelors of Science in Applied Mathematics and Economics.  

Preface 6
About the Book 13
Contents 14
Editors and Contributors 16
Part I Monte-Carlo Techniques 20
Joint Generation of Binary, Ordinal, Count, and Normal Data with Specified Marginal and Association Structures in Monte-Carlo Simulations 21
1 Introduction 22
2 Algorithm 23
3 Some Operational Details and an Illustrative Example 28
4 Future Directions 29
References 32
Improving the Efficiency of the Monte-Carlo Methods Using Ranked Simulated Approach 34
1 Introduction 34
2 Steady-State Ranked Simulated Sampling (SRSIS) 37
3 Monte-Carlo Methods for Multiple Integration Problems 39
3.1 Importance Sampling Method 39
3.2 Using Bivariate Steady-State Sampling (BVSRSIS) 40
3.3 Simulation Study 41
4 Steady-State Ranked Gibbs Sampler 44
4.1 Traditional (standard) Gibbs Sampling Method 46
4.2 Steady-State Gibbs Sampling (SSGS): The Proposed Algorithms 47
4.3 Simulation Study and Illustrations 51
References 56
Normal and Non-normal Data Simulations for the Evaluation of Two-Sample Location Tests 58
1 Introduction 59
2 Statistical Tests 60
2.1 t-Test 61
2.2 Wilcoxon Rank-Sum Test 61
2.3 Two-Stage Test 62
2.4 Permutation Test 62
3 Simulations 63
4 Results 65
4.1 Heterogeneous Variance 66
4.2 Skewness 69
4.3 Kurtosis 70
5 Discussion 72
References 73
Anatomy of Correlational Magnitude Transformations in Latency and Discretization Contexts in Monte-Carlo Studies 75
1 Introduction 76
2 Building Blocks 79
2.1 Dichotomous Case: Normality 79
2.2 Dichotomous Case: Beyond Normality 80
2.3 Polytomous Case: Normality 83
2.4 Polytomous Case: Beyond Normality 84
3 Algorithms and Illustrative Examples 85
4 Simulations in a Multivariate Setting 93
5 Discussion 95
References 98
Monte-Carlo Simulation of Correlated Binary Responses 101
1 Introduction 101
1.1 Binary Data Issues 102
2 Fully Specified Joint Probability Distributions 104
2.1 Simulating Binary Data with a Joint PDF 104
2.2 Explicit Specification of the Joint PDF 105
2.3 Derivation of the Joint PDF 105
3 Specification by Mixture Distributions 108
3.1 Mixtures Involving Discrete Distributions 108
3.2 Mixtures Involving Continuous Distributions 111
4 Simulation by Dichotomizing Variates 112
4.1 Dichotomizing Normal Variables 112
4.2 Iterated Dichotomization 113
4.3 Dichotomizing Non-normal Variables 114
5 Conditionally Specified Distributions 116
5.1 The Linear Conditional Probability Model 116
5.2 Non-linear Dynamic Conditional Probability Model 117
6 Software Discussion 119
References 120
Quantifying the Uncertainty in Optimal Experiment Schemes via Monte-Carlo Simulations 122
1 Introduction 123
2 Quantifying the Uncertainty in the Optimal Experiment Scheme 124
2.1 Comparing Experimental Schemes 125
2.2 Comparing Values of Objective Functions 125
3 Progressive Censoring with Location-Scale Family of Distributions 125
3.1 Maximum Likelihood Estimation 127
3.2 Optimal Criteria 128
3.3 Numerical Illustrations 129
3.4 Discussions 130
4 Illustrative Example 136
5 Concluding Remarks 136
References 140
Part II Monte-Carlo Methods in Missing Data 142
Markov Chain Monte-Carlo Methods for Missing Data Under Ignorability Assumptions 143
1 Introduction 143
2 Missing Data Mechanisms 144
3 Data Augmentation 145
4 Missing Response 145
4.1 Method: Multivariate Normal Model 146
4.2 Simulation 147
4.3 Prostate Specific Antigen (PSA) Data 150
5 Missing Covariates 151
5.1 Method 151
5.2 Simulation 152
5.3 BRFSS Data 154
6 Discussion 155
References 156
A Multiple Imputation Framework for Massive Multivariate Data of Different Variable Types: A Monte-Carlo Technique 157
1 Introduction 157
2 Background on RNG 160
3 Missing Data and MI 166
4 Connecting RNG and MI, Outline of a Unified MI Algorithm for Mixed Data 168
5 Some Remarks and Discussion 171
References 173
Hybrid Monte-Carlo in Multiple Missing Data Imputations with Application to a Bone Fracture Data 177
1 Introduction 177
2 The Bone Fracture Data 178
3 Imputation Modeling and Inference 180
3.1 Multiple Imputation to Missing Data Problems 180
3.2 Odds Ratio Models for Complete Data 181
3.3 Multiple Imputation Under the Framework 183
4 Hybrid Monte-Carlo 184
5 Implementing HMC for Model Fitting 186
5.1 Assigning Prior Distributions 186
5.2 Tuning Proposal Distribution 186
5.3 Starting Values 186
5.4 Determining Burn-In 187
5.5 Determining Iteration Intervals to Obtain Imputed Values 187
5.6 Determining Stopping Time 188
5.7 Output Analysis 188
6 Conclusion 191
References 192
Statistical Methodologies for Dealing with Incomplete Longitudinal Outcomes Due to Dropout Missing at Random 193
1 Introduction 194
2 Notation and Basic Concepts 195
3 Dropout Analysis Strategies in Longitudinal Continuous Data 196
3.1 Likelihood Analysis 197
3.2 Multiple Imputation (MI) 198
3.3 Illustration 199
3.4 Simulation of Missing Values 200
3.5 Results 202
4 Dropout Analysis Strategies in Longitudinal Binary Data 205
4.1 Weighted Generalized Estimating Equation (WGEE) 206
4.2 Multiple Imputation Based GEE (MI-GEE) 208
4.3 Generalized Linear Mixed Model (GLMM) 209
4.4 Simulation Study 210
4.5 Analysis 212
4.6 Application Example: Dermatophyte Onychomycosis Study 217
5 Discussion and Conclusion 219
References 221
Applications of Simulation for Missing Data Issues in Longitudinal Clinical Trials 224
1 Introduction 224
2 Generation of Study Data with a Specified MDM and Cumulative Drop-Out Rates 226
3 Tipping Point Analysis to Assess the Robustness of MMRM Analyses 231
4 Monte-Carlo Approaches for Control-Based Imputation Analysis 238
5 Discussions and Remarks 242
References 244
Application of Markov Chain Monte-Carlo Multiple Imputation Method to Deal with Missing Data from the Mechanism of MNAR in Sensitivity Analysis for a Longitudinal Clinical Trial 246
1 Introduction 246
2 Multiple Imputation to Deal with Missing Data 248
2.1 Multiple Imputation via MCMC 249
2.2 Combining Inferences from Imputed Data Sets 250
3 Example of Clinical Trial and Sample Data 251
3.1 Introduction of a Simulated Longitudinal Clinical Trial 251
3.2 Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution 252
3.3 Not Assuming Data of Primary Efficacy Endpoint to Have Normal Distribution 260
4 Discussion 265
References 265
Part III Monte-Carlo in Statistical Modellings and Applications 266
Monte-Carlo Simulation in Modeling for Hierarchical Generalized Linear Mixed Models 267
1 Introduction 267
2 Generalized Linear Model 268
3 Hierarchical Models 269
3.1 Approaches with Binary Outcomes 272
4 Three-Level Hierarchical Models 272
4.1 With Random Intercepts 273
4.2 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes 274
4.3 Nested Higher Level Logistic Regression Models 275
5 Possible Problems with Hierarchical Model 275
5.1 Issues in Hierarchical Modeling 275
5.2 Parameter Estimations 276
5.3 Convergence Issues in SAS 276
6 Simulation of Data 277
6.1 Simulation Setup 278
6.2 Simulation Results 281
7 Analysis of Data 286
7.1 Description 286
7.2 Data Analysis 287
8 Conclusions 293
References 294
Monte-Carlo Methods in Financial Modeling 296
1 Hierarchical Modeling in Market Microstructure Studies 297
1.1 The Model 298
1.2 Bayesian Inference via MCMC Algorithms 299
1.3 Simulation Study 302
1.4 Empirical Study 305
1.5 Economic Interpretation 308
1.6 Appendix 1 310
2 Monte-Carlo Strategies in Option Pricing for SABR Model 315
2.1 SABR Model and Option Pricing for the Case ?= 1 316
2.2 Approximating the Distribution of (?2, X2) 318
2.3 Numerical Experiments and Empirical Calibration of SABR 319
References 327
Simulation Studies on the Effects of the Censoring Distribution Assumption in the Analysis of Interval-Censored Failure Time Data 329
1 Introduction 330
2 Methodology 332
2.1 Case I 332
2.2 Case II 334
3 Simulation Studies 336
3.1 Case I 336
3.2 Case II 346
4 Conclusions and Discussion 351
References 355
Robust Bayesian Hierarchical Model Using Monte-Carlo Simulation 357
1 Parkinson's Disease as an Example 358
2 MLIRT Model 359
3 MLIRT Model with NI Distribution 361
3.1 NI Distribution 362
3.2 NI Distribution in MLIRT Model 363
4 Bayesian Inference and Model Selection Criteria 364
5 Monte Carlo Simulation Scheme and Some Results 366
6 Application to Trial Study Data 367
7 More Extended Modeling 370
7.1 Joint MLIRT Model 370
7.2 MLIRT Model with Skew-Normal/Independent (SNI) Distributions 372
8 Discussions 373
References 374
A Comparison of Bootstrap Confidence Intervals for Multi-level Longitudinal Data Using Monte-Carlo Simulation 377
1 Introduction 378
2 Linear Mixed Effects Model 379
2.1 Statistical Models 379
2.2 Estimation Methods 381
3 Bootstrap Methods 382
3.1 Bootstrap Estimates 383
3.2 Bootstrap Confidence Intervals 385
4 Monte-Carlo Simulation Study 387
4.1 The Simulation Design 387
4.2 Simulation Results Five Students per Classroom 389
4.3 Simulation Results 15 Students per Classroom 393
4.4 Comparison of Simulation Results for Five Students per Classroom and 15 Students per Classroom 393
5 Application 401
6 Conclusions 412
References 412
Bootstrap-Based LASSO-Type Selection to Build Generalized Additive Partially Linear Models for High-Dimensional Data 414
1 Introduction 414
2 Framework of the Procedure to Build GAPLM 416
3 Generalized Additive Partial Linear Models 417
3.1 Spline Approximation 418
3.2 Penalized Regression 419
4 Real Data Examples 419
4.1 Breast Cancer Data 420
4.2 HIV Data 424
5 A Simulation Study 428
6 Summary and Discussion 431
References 432
19 Erratum to: Monte-Carlo Simulation-Based Statistical Modeling 434
Erratum to:& #6
Index 435