A. Gouveia Oliveira - Biostatistics Decoded

1 Cover

2 Title Page Biostatistics Decoded Second Edition A. Gouveia Oliveira Pharmacy Department Federal University of Rio Grande do Norte Natal, Brazil

3 Copyright Page

4 Preface

5 1 Populations and Samples1.1 The Object of Biostatistics 1.2 Scales of Measurement 1.3 Central Tendency Measures 1.4 Sampling 1.5 Inferences from Samples 1.6 Measures of Location and Dispersion 1.7 The Standard Deviation 1.8 The n − 1 Divisor 1.9 Degrees of Freedom 1.10 Variance of Binary Variables 1.11 Properties of Means and Variances 1.12 Descriptive Statistics 1.13 Sampling Variation 1.14 The Normal Distribution 1.15 The Central Limit Theorem 1.16 Properties of the Normal Distribution 1.17 Probability Distribution of Sample Means 1.18 The Standard Error of the Mean 1.19 The Value of the Standard Error 1.20 Distribution of Sample Proportions 1.21 Convergence of Binomial to Normal Distribution

6 2 Descriptive Studies 2.1 Designing a Research 2.2 Study Design 2.3 Classification of Descriptive Studies 2.4 Cross‐sectional Studies 2.5 Inferences from Means 2.6 Confidence Intervals 2.7 Statistical Tables 2.8 The Case of Small Samples 2.9 Student's t Distribution 2.10 Statistical Tables of the t Distribution 2.11 Inferences from Proportions 2.12 Statistical Tables of the Binomial Distribution 2.13 Sample Size Requirements 2.14 Longitudinal Studies 2.15 Incidence Studies 2.16 Cohort Studies 2.17 Inference from Incidence Studies 2.18 Standardization 2.19 Time‐to‐Event Cohort Studies 2.20 The Actuarial Method 2.21 The Kaplan–Meier Method 2.22 Probability Sampling 2.23 Simple Random Sampling 2.24 Replacement in Sampling 2.25 Stratified Sampling 2.26 Multistage Sampling

7 3 Analytical Studies3.1 Objectives of Analytical Studies 3.2 Measures of Association 3.3 Odds, Logits, and Odds Ratios 3.4 Attributable Risk 3.5 Classification of Analytical Studies 3.6 Uncontrolled Analytical Studies 3.7 Comparative Analytical Studies 3.8 Hybrid Analytical Studies 3.9 Non‐probability Sampling in Analytical Studies 3.10 Comparison of Two Means 3.11 Comparison of Two Means from Small Samples 3.12 Comparison of Two Proportions

8 4 Statistical Tests4.1 The Null and Alternative Hypotheses 4.2 The z ‐Test 4.3 The p ‐Value 4.4 Student’s t ‐Test 4.5 The Binomial Test 4.6 The Chi‐Square Test 4.7 The Table of the Chi‐Square Distribution 4.8 Analysis of Variance 4.9 Partitioning the Sum of Squares 4.10 Statistical Tables of the F Distribution 4.11 The ANOVA Table

9 5 Aspects of Statistical Tests5.1 One‐Sided Tests 5.2 Power of a Statistical Test 5.3 Sample Size Estimation 5.4 Multiple Comparisons 5.5 Scale Transformation 5.6 Non‐parametric Tests

10 6 Cross‐sectional Studies6.1 Linear Regression 6.2 The Least Squares Method 6.3 Linear Regression Estimates 6.4 Regression and Correlation 6.5 The F ‐Test in Linear Regression 6.6 Interpretation of Regression Analysis Results 6.7 Multiple Regression 6.8 Regression Diagnostics 6.9 Selection of Predictor Variables 6.10 Independent Nominal Variables 6.11 Interaction 6.12 Nonlinear Regression

11 7 Case–Control Studies7.1 Analysis of Case–Control Studies 7.2 Logistic Regression 7.3 The Method of Maximum Likelihood 7.4 Estimation of the Logistic Regression Model 7.5 The Likelihood Ratio Test 7.6 Interpreting the Results of Logistic Regression 7.7 Regression Coefficients and Odds Ratios 7.8 Applications of Logistic Regression 7.9 The ROC Curve 7.10 Model Validation

12 8 Cohort Studies8.1 Repeated Measurements 8.2 The Paired t ‐Test 8.3 McNemar’s Test 8.4 Generalized Linear Models 8.5 The Logrank Test 8.6 The Adjusted Logrank Test 8.7 The Incidence Rate Ratio 8.8 The Cox Proportional Hazards Model 8.9 Assumptions of the Cox Model 8.10 Interpretation of Cox Regression

13 9 Measurement9.1 Construction of Clinical Questionnaires 9.2 Factor Analysis 9.3 Interpretation of Factor Analysis 9.4 Factor Rotation 9.5 Factor Scores 9.6 Reliability 9.7 Concordance 9.8 Validity 9.9 Validation of Diagnostic Tests

14 10 Experimental Studies 10.1 Main Design Features and Classification 10.2 Experimental Controls 10.3 Replicates 10.4 Classification of Experimental Designs 10.5 Completely Randomized Design 10.6 Interaction 10.7 Full Factorial Design 10.8 The Random Effects Model 10.9 Components of Variance 10.10 ANOVA Model II and Model III 10.11 Rules for the Definition of the Error Terms 10.12 ANOVA on Ranks

15 11 Blocking11.1 Randomized Block Design 11.2 Generalized Randomized Block Design 11.3 Incomplete Block Design 11.4 Factorial Design with Randomized Blocks 11.5 Latin and Greco‐Latin Square Design

16 12 Simultaneous Inference12.1 Multiple Comparisons 12.2 Generalist Methods 12.3 Multiple Comparisons of Group Means 12.4 Pairwise Comparison of Means 12.5 Different Variances 12.6 Comparison to a Control 12.7 Comparison of post hoc Tests 12.8 Complex Comparisons 12.9 Tests of Multiple Contrasts 12.10 A posteriori Contrasts 12.11 The Size of an Experiment

17 13 Factorial ANOVA13.1 The n ‐Way ANOVA 13.2 The 2 kFactorial Design 13.3 The 2 kFactorial Design with Blocking 13.4 The Fractional Factorial Design

18 14 Nested Designs14.1 Split–Plot Design 14.2 Nested (Hierarchical) Design 14.3 Mixed Model Nested ANOVA 14.4 Mixed Model Nested ANOVA with Three Sublevels 14.5 Pure Model II Nested ANOVA

19 15 Repeated Measures 15.1 Repeated Measures ANOVA 15.2 Repeated Measures ANOVA with Two Factors 15.3 ANOVA with Several Repeated Measures 15.4 Multivariate Tests

20 16 Clinical Trials16.1 Classification of Clinical Trials 16.2 The Clinical Trial Population 16.3 The Efficacy Criteria 16.4 Controlled Clinical Trials 16.5 The Control Group 16.6 Blinding 16.7 Randomization 16.8 Non‐comparative Clinical Trials 16.9 Regression Toward the Mean 16.10 Non‐randomized Controlled Clinical Trials 16.11 Classical Randomized Clinical Trial Designs 16.12 Alternative Clinical Trial Designs 16.13 Pragmatic Clinical Trials 16.14 Cluster Randomized Trials 16.15 The Size of a Clinical Trial 16.16 Non‐inferiority Clinical Trials 16.17 Adaptive Clinical Trials 16.18 Group Sequential Plans 16.19 The Alpha Spending Function 16.20 The Clinical Trial Protocol 16.21 The Data Record

21 17 Analysis of Clinical Trials17.1 General Analysis Plan 17.2 Data Preparation 17.3 Study Populations 17.4 Primary Efficacy Analysis 17.5 Analysis of Multiple Endpoints 17.6 Secondary Analyses 17.7 Safety Analysis

22 18 Meta‐analysis18.1 Purpose of Meta‐analysis 18.2 Measures of Effect 18.3 The Inverse Variance Method 18.4 The Random Effects Model 18.5 Heterogeneity 18.6 Publication Bias 18.7 The Forest Plot

23 References

24 Index

25 End User License Agreement

1 Chapter 1 Figure 1.1 Using statistics for predictions. Age‐ and sex‐specific prevalenc... Figure 1.2 Examples of commonly used ordinal scales. Figure 1.3 Difference between an ordinal and an interval scale. Figure 1.4 Comparison of the mean and the median in an asymmetrical distribu... Figure 1.5 Classical view of the purpose of sampling. Figure 1.6 Relationship between representativeness and sample size in the cl... Figure 1.7 Modern view of the purpose of sampling. The purpose of sampling i... Figure 1.8 Inference with binary attributes. Figure 1.9 Inference with interval attributes I. Figure 1.10 Inference with interval attributes II. Figure 1.11 Measures of dispersion derived from measures of location. Figure 1.12 The n divisor of the sum of squares. Figure 1.13 The n − 1 divisor of the sum of squares. Figure 1.14 Relationship between a proportion and its variance. Figure 1.15 Two random variables with uniform distribution.