New Developments in Statistical Modeling Inference and Application 1st Edition by Zhezhen Jin,Mengling Liu,Xiaolong Luo 9783319425719 3319425714

Part I Theoretical Development in Statistical Modeling

Dual Model Misspecification in Generalized Linear Models with Error in Variables

1 Introduction

2 Models and Two Diagnostic Methods

2.1 Models

2.2 Remeasurement Method and Reclassification Method

3 Limiting Maximum Likelihood Estimators

3.1 Estimating Equations

3.2 Assumed and True Models

3.3 Limiting MLEs from Data with Measurement Error Only in X

3.4 Limiting MLEs Based on Reclassified Data

4 Testing Procedures

4.1 Simulation Design

4.2 Simulation Results

4.3 Sequential Tests

4.4 Directional Tests

5 Application to Real Data Examples

5.1 Framingham Heart Study

5.2 Beetle Mortality

6 Discussion

Appendix 1: Likelihood and Score Functions Referenced in Sect.3.2

Likelihood and Score Functions Under the Assumed Model

Score Estimating Equations

Likelihood Function Under the True Model

Appendix 2: Limiting Maximum Likelihood Estimators When β1=0

Appendix 3: Proof of Proposition 3.1

Appendix 4: A Counterpart Proposition of Proposition 3.1 for βc

Appendix 5: Additional Simulation Results from Sect.4

References

Joint Analysis of Longitudinal Data and Informative Observation Times with Time-Dependent Random Eff

1 Introduction

2 Notation and Models

3 Estimation Procedure

4 A Simulation Study

5 Concluding Remarks

Appendix

Proof of Theorem 1

References

A Markov Switching Model with Stochastic Regimes with Application to Business Cycle Analysis

1 Introduction

2 A Markov Switching Regression Model with Both Categorical and Continuous Regimes

2.1 Model Specification

2.2 Filtering Estimate

2.3 Smoothing Estimate

2.4 Bounded Complexity Mixture Approximation

2.5 Hyperparameter Estimation

3 Numerical Studies

3.1 Performance of Bayes and BCMIX Estimates in Frequentist Scenarios

3.2 Performance of the BCMIX Smoother Under Bayesian Scenarios

3.3 Identification Issues and Sensitivity Analysis

4 Real Data Analysis

5 Conclusion

Appendix: Proofs in Sects.2.2 and 2.3

References

Direction Estimation in a General Regression Model with Discrete Predictors

1 Introduction

2 Two Scenarios That OLS Works

2.1 OLS with Linear Link Function

2.2 OLS with the LCM Condition

3 Central Solution Space with Discrete Predictors

3.1 Beyond the LCM Condition

3.2 The Central Solution Space Estimator

4 Numerical Studies

5 Discussion

Appendix

References

Part II New Developments in Trial Design

Futility Boundary Design Based on Probability of Clinical Success Under New Drug Development Paradig

1 Introduction

1.1 A New Paradigm of Drug Development from Medical and Payer Perspective

1.2 A Motivating Example

1.3 Futility Analysis Under the New Perspective

2 Futility Analysis Design Based on Probability of Clinical Success

2.1 Probability of Clinical Success (POCS)

2.2 Relative Retention of POCS

2.3 Probability of Interim Stopping

3 Analysis of the Motivating Example Trial

4 Discussion

References

Bayesian Modeling of Time Response and Dose Response for Predictive Interim Analysis of a Clinical T

1 Introduction

2 Bayesian Predictive Interim Analysis

2.1 A Phase 2 Clinical Trial

2.2 Modeling of Time Response and Dose Response

2.2.1 Modeling Time Response for Prediction

2.2.2 Modeling Dose Response for Interim Decision

2.3 Interim Futility Decision Rule

3 Simulations Prior to Interim Analysis

4 Actual Interim Analysis

5 Analysis of Final Data

6 Discussion

References

An ROC Approach to Evaluate Interim Go/No-Go Decision-Making Quality with Application to Futility St

1 Introduction

2 ROC Curves for Interim Go/No-Go Decisions for CP, PP, and PCI Methods

2.1 Conditional Power ROC

2.2 Predictive Power ROC

2.3 Predicted Confidence Interval ROC

2.4 Equivalent Conversion of CP, PP, and PCI Methods

3 Performance Characteristics of ROC Curves

3.1 Factors Associated with the Discriminative Capacity of ROC Curves

3.2 Performance Comparisons Among the Three Methods by Simulation

4 Applications to Design Optimization in Late Phase Clinical Trials

4.1 Timing and Threshold of Interim Analysis Based on ROC Criteria

4.2 Designs with Global Optimization

4.3 An Example

5 Conclusions and Discussions

Appendix

Conditional Power Derivation in Sect.2.1

Predictive Power Derivation in Sect.2.2

Predicted Confidence Interval Derivation in Sect.2.3

References

Part III Novel Applications and Implementation

Recent Advancements in Geovisualization, with a Case Study on Chinese Religions

1 Introduction

2 Religion in China

3 Linked Micromap Plots

3.1 Preparation of Shapefiles

3.2 LM Plots of Chinese Religions

4 Interactive LM Plots and Religion Explorer

4.1 Previous Software Developments at the CDC

4.2 LM Plots in the Religion Explorer Software

5 Google Maps of Chinese Religions

6 Discussion and Outlook

References

The Efficiency of Next-Generation Gibbs-Type Samplers: An Illustration Using a Hierarchical Model in

1 Introduction

2 Bayesian Hierarchical Model for Supernova Cosmology

3 Statistical Computation

3.1 Algorithm Review

3.1.1 Ancillarity-Sufficiency Interweaving Strategy

3.1.2 Partially Collapsed Gibbs Sampler

3.2 Bayesian Fitting of the Cosmological Hierarchical Model

4 Analysis of Observed Type Ia SNe

5 Conclusion

Appendix

References

Dynamic Spatial Pattern Recognition in Count Data

1 Introduction

2 The Model

2.1 Zero-Inflated Models: A Step-by-Step Journey

2.2 Prior Specification, Posterior Computation and Model Assessment

3 Application: Analysis of the Presence and Abundance of Atlantic Cod in the Gulf of Maine-Georges B

4 Discussion

References

Bias-Corrected Estimators of Scalar Skew Normal

1 Introduction

2 Background

3 Bias Reduction Techniques for Scalar Skew Normal

3.1 Bias Correction for MLE and λ̃3

3.2 Adjusted Estimator

3.3 Jackknife and Bootstrap Bias Correction

4 Simulation Studies

5 Conclusions