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1 MEDICAL STATISTICS and COMPUTER EXPERIMENTS 2nd Edition Editor Ji-Qian Fang Sun Yat-Sen University, P R China with Yongyong Xu Fourth Military Medical University, P R China Songlin Yu Huazhong University ofscience and Technology, P R China World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI

2 Contents Preface to the Second Edition v Introduction ix About the Editors xxi Part I Basic Concepts 1, Chapter 1. Descriptive Statistics Variables and Data Frequency Table and Histogram Measurement for Average Level of a Sample Measurement for Variation of a Sample Relative Measures and Standardization Approaches Frequently Used Graphs in Statistics Computerized Experiments Practice and Experiments 41 Chapter 2. Probability and Distribution Explanation of Probability and Related Concepts Distributional Characters of Random Variables Binomial Distribution Poisson Distribution Normal Distribution Computerized Experiments Practice and Experiments 74 xi

3 xii Medical Statistics and Computer Experiments... Chapter 3. Sampling Error and Confidence Interval The Distribution of Sample Mean t Distribution The Confidence Interval for Population Mean of a Normal Distribution Four Confidence Intervals for Probability and the Difference between Two Probabilities The Sample Size for Estimation of Confidence Interval Computerized Experiments Practice and Experiments Chapter 4. Hypothesis Testing for Continuous Variables Specific Logic and Main Steps of Hypothesis Testing The t Test for One Group of Data under Completely Randomized Design The t Test for Data under Randomized Paired Design The Tests for Comparing Two Means Based on Two Groups of Data under Completely Randomized Design The F-Test for Equal Variances of Two Groups of Data under Completely Randomized Design Test for Normality The Z-Test for the Parameters of Binomial Distribution and Poisson Distribution (Large Sample) Computerized Experiments Practice and Experiments 125 Chapter 5. Chi-Square Test for Categorical Variable Chi-Square Distribution and Pearson's Goodness-of-Fit Test The x2 Test for Comparison between Two Independent Sample Proportions The x2 Tests for Binary Variable under a Paired... Design The x2 Test for R x C Contingency Table The x2 Test for Confirming a Supposed Distribution Hypothesis Testing for Two Standardized Rates Fisher's Exact Test for 2 x 2 Table 159

4 Contents xiii 5.8 Computerized Experiments Practice and Experiments Chapter 6. Further Discussion on Hypothesis Test Two Types of Error and Power The Four Elements Affecting the Power The Quantitative Relation between Power and the Four Elements Estimation of Sample Size for the Tests in Common Use Non-Inferiority Test and Equivalence Test Permutation Test Computerized Experiments Practice and Experiments 194 Chapter 7. Single-Factor Analysis of Variance One-Way Analysis of Variance: Completely Random Design Two-Way Analysis of Variance: Randomized Complete-Block Design Three-Way Analysis of Variance: The Latin-Square Design Computerized Experiments Practice and Experiments 233 Chapter 8. Nonparametric Test Based on Ranks Wilcoxon's Signed Rank Test Wilcoxon's Rank-Sum Test for Comparing the Locations of Two Distributions Hypothesis Testing for the Locations of More Than Two Populations Computerized Experiments Practice and Experiments 259 Chapter 9. Simple Linear Correlation Concept of Correlation Correlation Coefficient Inference on Correlation Coefficient 269

5 xiv Medical Statistics and Computer Experiments 9.4 Rank Correlation Caution in Analysis of Linear Correlation Computerized Experiments Practice and Experiments 278 Chapter 10. Simple Linear Regression Statistical Description of Linear Regression Statistical Inference on Regression Applications of Linear Regression and the Pre-requisites On the Basic Assumptions and Analysis of Residuals Non-linear Regression Computerized Experiments Practice and Experiments 313 Chapter 11. Statistical Principles for Design of Interventional Study The Essential Concepts of Design Statistical Principle in Clinical Trials Randomization Techniques Randomized Controlled Trial Comments on Some Medical Examples Computerized Experiments Practice and Experiments 347 Part H Multi-variate Statistics 349 Chapter 12. Multiple Regression and Correlation Basic Procedure of Multiple Regression Multiple Correlation Selection of Independent Variables Further Topics in Multiple Regression Path Analysis Computerized Experiments Practice and Experiments 380

6 Contents xv Chapter 13. Measures of Multi-variate Data and Multi-variate Analysis of Variance Multi-variate Statistical Description Comparison between Two Mean Vectors Hotelling's 72Test Comparisons among Several Multi-variate Means-Multi-variate Analysis of Variance Computerized Experiments Practice and Experiments 400 Chapter 14. Discriminant Analysis Basic Ideas of Discriminant Analysis Fisher's Discriminant Analysis Bayesian Discriminant Analysis Stepwise Discriminant Function Decision Tree Retrospective and Prospective Validation Considerations in Applications Computerized Experiments Practice and Experiments 428 Chapter 15. Logistic Regression Logistic Regression Model Conditional Logistic Regression Multinomial Logistic Regression Model Two-Level Logistic Mixed Effects Regression Model Application of Logistic Regression Computerized Experiments Practice and Experiments 462 Chapter 16. Cluster Analysis The Meaning of Clustering Hierarchical Cluster Fast Cluster. : Variable Cluster 473

7 xvi Medical Statistics and Computer Experiments 16.5 Computerized Experiments Practice and Experiments 477 Chapter 17. Principal Component Analysis The Basic Concepts of Principal Component Analysis Computation and Interpretation of Principal Components Principal Component Analysis in Regression Computerized Experiments Practice and Experiments 493 Chapter 18. Factor Analysis Factor Model Derivation of Factors Factor Pattern Plot and Factor Rotation Factor Score and Application of Factor Patterns Confirmatory Factor Analysis Computerized Experiments Practice and Experiments 515 Chapter 19. Canonical Correlation and Correspondence Analysis Canonical Correlation Correspondence Analysis Canonical Discriminant Analysis Computerized Experiments Practice and Experiments 539 Chapter 20. Survival Analysis The Basic Concept of Survival Analysis The Product-Limit Method for One Group of Survival Data The Log-Rank Test and Breslow Test for Comparing Two Survival Data Sets The Cox Regression Computerized Experiments Practice and Experiments 558

8 Contents xvii Chapter 21. Log-Linear Model for Contingency Table and Poisson Regression Log-Linear Models for Contingency Table Poisson Regression Computerized Experiments Practice and Experiments 581 Part III Design and Analysis for Medical Research 583 Chapter 22. Multi-Factor Analysis of Variance Factorial Experiments and Analysis of Variance Split-Plot Designs and Analysis of Variance Cross-Over Design and Analysis of Variance Computerized Experiments Practice and Experiments 611 Chapter 23. Analysis of Repeated Continuous-Type Measurements Examples of Repeated Measurements Imperfect Analysis and its Origins Approach with Summary Measures Analysis of Variance for Repeated Measurements Computerized Experiments Practice and Experiments 631 Chapter 24. Design and Analysis of Cross-Sectional Studies Design of the Study Sampling Methods and Estimation of Population Parameters Estimation of Sample Size The Current Life Table Computerized Experiments Practice and Experiments 659 Chapter 25. Design and Analysis of Prospective Studies Study Design Measures of Disease Occurrence 663

9 xviii Medical Statistics and Computer Experiments 25.3 Analysis of Data from Prospective Studies Computerized Experiments Practice and Experiments 692 Chapter 26. Designs and Analysis of Case-Control Studies Designs of Case-Control Studies Analysis of Data from Design for Group Comparison Analysis of Matched Data Computerized Experiments Practice and Experiments 719 Chapter 27. Design and Analysis of Diagnostic and Screening Tests Design and Data Layout Measures Frequently Used in Diagnostic Test Analysis of ROC Curve Decision Making on Diagnostic and Screening Test Computerized Experiments Practice and Experiments 742 Chapter 28. Design and Analysis of Sequential Experiments Introduction Design and Analysis of Sequential Trials Group Sequential Schemes Computerized Experiments Practice and Experiments 764 Chapter 29. Systematic Review of Medical Research and Meta-Analysis Basic Notions Statistical Methods Commonly Used in Meta-Analysis Notes Computerized Experiments Practice and Experiments 790 Chapter 30. Comparative Effectiveness Research Background 793

10 Contents xix 30.2 Definitions Examples Features and Principles Research Methods and Techniques Steps of CER Standards for Implementation and Report Summary Computerized Experiments 825 Chapter 31. Statistical Methods in Scale Development Development of Scales Adopting Scale with Foreign Language The Concept and Evaluation of Validity and Reliability Item Response Theory and Scale Evaluation Computer Experiments Exercises and Experiments 856 Chapter 32. Statistical Methods for Data from Genetic Epidemiological Study Basic Concepts Linkage Analysis Genetic Association Analysis Computerized Experiments Practice and Experiments 879 Chapter 33. Statistical Methods in Bioinformatics Sequence Alignment Methods The Data Acquisition and Standardization of Gene Expression Patterns Differentially Expressed Genes Screening Cluster Analysis of Gene Expression Analysis of Gene Regulatory Networks Computerized Experiments Summary Practice and Experiment 908

11 xx Medical Statistics and Computer Experiments Appendix I. Introduction to the Statistical Analysis System (SAS)* Appendix II. Statistical Tables 909 Appendix III. Datasets of Some Real Medical Examples 983 Appendix IV. Answers to Exercises* Appendix V. SAS Programs and Data* * Appendices I, IV and V are available at please register/sign in at the website.

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