Statistical Advances in the Biomedical Sciences

The Most Comprehensive and Cutting-Edge Guide to Statistical Applications in Biomedical Research With the increasing use of biotechnology in medical research and the sophisticated advances in computing, it has become essential for practitioners in the biomedical sciences to be fully educated on the role statistics plays in ensuring the accurate analysis of research findings. Statistical Advances in the Biomedical Sciences explores the growing value of statistical knowledge in the management and comprehension of medical research and, more specifically, provides an accessible introduction to the contemporary methodologies used to understand complex problems in the four major areas of modern-day biomedical science: clinical trials, epidemiology, survival analysis, and bioinformatics. Composed of contributions from eminent researchers in the field, this volume discusses the application of statistical techniques to various aspects of modern medical research and illustrates how these methods ultimately prove to be an indispensable part of proper data collection and analysis. A structural uniformity is maintained across all chapters, each beginning with an introduction that discusses general concepts and the biomedical problem under focus and is followed by specific details on the associated methods, algorithms, and applications. In addition, each chapter provides a summary of the main ideas and offers a concluding remarks section that presents novel ideas, approaches, and challenges for future research. Complete with detailed references and insight on the future directions of biomedical research, Statistical Advances in the Biomedical Sciences provides vital statistical guidance to practitioners in the biomedical sciences while also introducing statisticians to new, multidisciplinary frontiers of application. This text is an excellent reference for graduate- and PhD-level courses in various areas of biostatistics and the medical sciences and also serves as a valuable tool for medical researchers, statisticians, public health professionals, and biostatisticians.

Preface xxi Acknowledgments xxv Contributors xxvii Part I Clinical Trials 1 1. Phase I Clinical Trials 3 Anastasis Ivanova and Nancy Flournoy 1.1 Introduction, 3 1.2 Phase I Trials in Healthy Volunteers, 3 1.3 Phase I Trials with Toxic Outcomes Enrolling Patients, 5 1.4 Other Design Problems in Dose Finding, 11 1.5 Concluding Remarks, 12 2. Phase II Clinical Trials 15 Nigel Stallard 2.1 Introduction, 15 2.2 Frequentist Methods in Phase II Clinical Trials, 18 2.3 Bayesian Methods in Phase II Clinical Trials, 22 2.4 Decision-Theoretic Methods in Phase II Clinical Trials, 25 2.5 Analysis of Multiple Endpoints in Phase II Clinical Trials, 26 2.6 Outstanding Issues in Phase II Clinical Trials, 27 3. Response-Adaptive Designs in Phase III Clinical Trials 33 Atanu Biswas, Uttam Bandyopadhyay, and Rahul Bhattacharya 3.1 Introduction, 33 3.2 Adaptive Designs for Binary Treatment Responses, 34 3.3 Adaptive Designs for Binary Treatment Responses Incorporating Covariates, 40 3.4 Adaptive Designs for Categorical Responses, 41 3.5 Adaptive Designs for Continuous Responses, 42 3.6 Optimal Adaptive Designs, 43 3.7 Delayed Responses in Adaptive Designs, 44 3.8 Biased Coin Designs, 45 3.9 Real Adaptive Clinical Trials, 45 3.10 Data Study for Different Adaptive Schemes, 46 3.11 Concluding Remarks, 49 4. Inverse Sampling for Clinical Trials: A Brief Review of Theory and Practice 55 Atanu Biswas and Uttam Bandyopadhyay 4.1 Introduction, 55 4.2 Two-Sample Randomized Inverse Sampling for Clinical Trials, 59 4.3 An Example of Inverse Sampling: Boston ECMO, 62 4.4 Inverse Sampling in Adaptive Designs, 62 4.5 Concluding Remarks, 63 5. The Design and Analysis Aspects of Cluster Randomized Trials 67 Hrishikesh Chakraborty 5.1 Introduction: Cluster Randomized Trials, 67 5.2 Intracluster Correlation Coefficient and Confidence Interval, 69 5.3 Sample Size Calculation for Cluster Randomized Trials, 71 5.4 Analysis of Cluster Randomized Trial Data, 73 5.5 Concluding Remarks, 75 Part II Epidemiology 81 6. HIV Dynamics Modeling and Prediction of Clinical Outcomes in AIDS Clinical Research 83 Yangxin Huang and Hulin Wu 6.1 Introduction, 83 6.2 HIV Dynamic Model and Treatment Effect Models, 84 6.3 Statistical Methods for Predictions of Clinical Outcomes, 87 6.4 Simulation Study, 90 6.5 Clinical Data Analysis, 91 6.6 Concluding remarks, 92 7. Spatial Epidemiology 97 Lance A. Waller 7.1 Space and Disease, 97 7.2 Basic Spatial Questions and Related Data, 98 7.3 Quantifying Pattern in Point Data, 99 7.4 Predicting Spatial Observations, 107 7.5 Concluding Remarks, 118 8. Modeling Disease Dynamics: Cholera as a Case Study 123 Edward L. Ionides, Carles Bretó, and Aaron A. King 8.1 Introduction, 123 8.2 Data Analysis via Population Models, 124 8.3 Sequential Monte Carlo, 126 8.4 Modeling Cholera, 130 8.5 Concluding Remarks, 136 9. Misclassification and Measurement Error Models in Epidemiologic Studies 141 Surupa Roy and Tathagata Banerjee 9.1 Introduction, 141 9.2 A Few Examples, 143 9.3 Binary Regression Models with Two Types of Error, 144 9.4 Bivariate Binary Regression Models with Two Types of Error, 146 9.5 Models for Analyzing Mixed Misclassified Binary and Continuous Responses, 149 9.6 Atom Bomb Data Analysis, 151 9.7 Concluding Remarks, 152 Part III Survival Analysis 157 10. Semiparametric Maximum-Likelihood Inference in Survival Analysis 159 Michael R. Kosorok 10.1 Introduction, 159 10.2 Examples of Survival Models, 160 10.3 Basic Estimation and Limit Theory, 162 10.4 The Bootstrap, 163 10.5 The Profile Sampler, 166 10.6 The Piggyback Bootstrap, 168 10.7 Other Approaches, 170 10.8 Concluding Remarks, 171 11. An Overview of the Semi–Competing Risks Problem 177 Limin Peng, Hongyu Jiang, Rick J. Chappell, and Jason P. Fine 11.1 Introduction, 177 11.2 Nonparametric Inferences, 179 11.3 Semiparametric One-Sample Inference, 181 11.4 Semiparametric Regression Method, 184 11.5 Concluding Remarks, 189 12. Tests for Time-Varying Covariate Effects within Aalen’s Additive Hazards Model 193 Torben Martinussen and Thomas H. Scheike 12.1 Introduction, 193 12.2 Model Specification and Inferential Procedures, 194 12.3 Numerical Results, 199 12.4 Concluding Remarks, 204 12.5 Summary, 204 Appendix 12A, 205 13. Analysis of Outcomes Subject to Induced Dependent Censoring: A Marked Point Process Perspective 209 Yijian Huang 13.1 Introduction, 209 13.2 Induced Dependent Censoring and Associated Identifiability Issues, 210 13.3 Marked Point Process, 212 13.4 Modeling Strategy for Testing and Regression, 215 13.5 Concluding Remarks, 218 14. Analysis of Dependence in Multivariate Failure-Time Data 221 li Hsu and Zoe Moodie 14.1 Introduction, 221 14.2 Nonparametric Bivariate Survivor Function Estimation, 223 14.3 Non- and Semiparametric Estimation of Dependence Measures, 230 14.4 Concluding Remarks, 239 15. Robust Estimation for Analyzing Recurrent-Event Data in the Presence of Terminal Events 245 Rajeshwari Sundaram 15.1 Introduction, 245 15.2 Inference Procedures, 247 15.3 Large-Sample Properties, 249 15.4 Numerical Results, 252 15.5 Concluding Remarks, 259 Appendix 15A, 260 16. Tree-Based Methods for Survival Data 265 Mousumi Banerjee and Anne-Michelle Noone 16.1 Introduction, 265 16.2 Review of CART, 266 16.3 Trees for Survival Data, 268 16.4 Simulations for Comparison of Different Splitting Methods, 272 16.5 Example: Breast Cancer Prognostic Study, 274 16.6 Random Forest for Survival Data, 278 16.7 Concluding Remarks, 281 17. Bayesian Estimation of the Hazard Function with Randomly Right-Censored Data 287 Jean-François Angers and Brenda MacGibbon 17.1 Introduction, 287 17.2 Bayesian Functional Model Using Monotone Wavelet Approximation, 292 17.3 Estimation of the Subdensity F*, 295 17.4 Simulations, 296 17.5 Examples, 298 17.6 Concluding Remarks, 300 Appendix 17A, 301 Part IV Bioinformatics 307 18. The Effects of Intergene Associations on Statistical Inferences from Microarray Data 309 Kerby Shedden 18.1 Introduction, 309 18.2 Intergene Correlation, 310 18.3 Differential Expression, 314 18.4 Timecourse Experiments, 315 18.5 Meta-Analysis, 319 18.6 Concluding Remarks, 321 19. A Comparison of Methods for Meta-Analysis of Gene Expression Data 325 Hyungwon Choi and Debashis Ghosh 19.1 Introduction, 325 19.2 Background, 326 19.3 Example, 328 19.4 Cross-Comparison of Gene Signatures, 329 19.5 Best Common Mean Difference Method, 329 19.6 Effect Size Method, 331 19.7 POE Assimilation Method, 332 19.8 Comparison of Three Methods, 334 19.9 Conclusions, 336 20. Statistical Methods for Identifying Differentially Expressed Genes in Replicated Microarray Experiments: A Review 341 Lynn kuo, Fang Yu, and Yifang Zhao 20.1 Introduction, 341 20.2 Normalization, 344 20.3 Methods for Selecting Differentially Expressed Genes, 349 20.4 Simulation Study, 357 20.5 Concluding Remarks, 360 21. Clustering of Microarray Data via Mixture Models 365 Geoffrey J. McLachlan, Richard W. Bean, and Angus Ng 21.1 Introduction, 365 21.2 Clustering of Microarray Data, 367 21.3 Notation, 367 21.4 Clustering of Tissue Samples, 369 21.5 The EMMIX-GENE Clustering Procedure, 370 21.6 Clustering of Gene Profiles, 372 21.7 Emmix-wire, 373 21.8 Maximum-Likelihood Estimation via the EM Algorithm, 374 21.9 Model Selection, 376 21.10 Example: Clustering of Timecourse Data, 377 21.11 Concluding Remarks, 379 22. Censored Data Regression in High-Dimensional and Low-Sample-Size Settings for Genomic Applications 385 Hongzhe li 22.1 Introduction, 385 22.2 Censored Data Regression Models, 386 22.3 Regularized Estimation for Censored Data Regression Models, 388 22.4 Survival Ensemble Methods, 394 22.5 Nonparametric-Pathway-Based Regression Models, 395 22.6 Dimension-Reduction-Based Methods and Bayesian Variable Selection Methods, 396 22.7 Criteria for Evaluating Different Procedures, 397 22.8 Application to a Real Dataset and Comparisons, 397 22.9 Discussion and Future Research Topics, 398 22.10 Concluding Remarks, 400 23. Analysis of Case–Control Studies in Genetic Epidemiology 405 Nilanjan Chatterjee 23.1 Introduction, 405 23.2 Maximum-Likelihood Analysis of Case–Control Data with Complete Information, 406 23.3 Haplotype-based Genetic Analysis with Missing Phase Information, 410 23.4 Concluding Remarks, 415 24. Assessing Network Structure in the Presence of Measurement Error 419 Denise Scholtens, Raji Balasubramanian, and Robert Gentleman 24.1 Introduction, 419 24.2 Graphs of Biological Data, 420 24.3 Statistics on Graphs, 421 24.4 Graph-Theoretic Models, 422 24.5 Types of Measurement Error, 425 24.6 Exploratory Data Analysis, 426 24.7 Influence of Measurement Error on Graph Statistics, 429 24.8 Biological Implications, 436 24.9 Conclusions, 439 25. Prediction of RNA Splicing Signals 443 Mark R. Segal 25.1 Introduction, 443 25.2 Existing Approaches to Splice Site Identification, 445 25.3 Splice Site Recognition via Contemporary Classifiers, 450 25.4 Results, 455 25.5 Concluding Remarks, 459 26. Statistical Methods for Biomarker Discovery Using Mass Spectrometry 465 Bradley M. Broom and Kim-Anh Do 26.1. Introduction, 465 26.2 Biomarker Discovery, 470 26.3 Statistical Methods for Preprocessing, 470 26.4 Statistical Methods for Multiple Testing, Classification, and Applications, 473 26.5 Potential Statistical Developments, 481 26.6 Concluding Remarks, 483 27. Genetic Mapping of Quantitative Traits: Model-Free Sib-Pair Linkage Approaches 487 Saurabh Ghosh and Partha P. Majumder 27.1 Introduction, 487 27.2 The Basic QTL Framework For Sib-Pairs, 488 27.3 The Haseman–Elston Regression Framework, 489 27.4 Nonparametric Alternatives, 489 27.5 The Modified Nonparametric Regression, 490 27.6 Comparison With Linear Regression Methods, 492 27.7 Significance Levels and Empirical Power, 493 27.8 An Application to Real Data, 495 27.9 Concluding Remarks, 496 Part V Miscellaneous Topics 499 28. Robustness Issues in Biomedical Studies 501 Ayanendranath Basu 28.1 Introduction: The Need for Robust Procedures, 501 28.2 Standard Tools for Robustness, 502 28.3 The Robustness Question in Biomedical Studies, 506 28.4 Robust Estimation in the Logistic Regression Model, 508 28.5 Robust Estimation for Censored Survival Data, 513 28.6 Adaptive Robust Methods in Clinical Trials, 518 28.7 Concluding Remarks, 521 29. Recent Advances in the Analysis of Episodic Hormone Data 527 Timothy D. Johnson and Yuedong Wang 29.1 Introduction, 527 29.2 A General Biophysical Model, 530 29.3 Bayesian deconvolution model (BDM), 531 29.4 Nonlinear Mixed-Effects Partial-Splines Models, 537 29.5 Concluding Remarks, 542 30. Models for Carcinogenesis 547 Anup Dewanji 30.1 Introduction, 547 30.2 Statistical Models, 549 30.3 Multistage Models, 552 30.4 Two-Stage Clonal Expansion Model, 555 30.5 Physiologically Based Pharmacokinetic Models, 560 30.6 Statistical Methods, 562 30.7 Concluding Remarks, 564 Index 569