Biostatistics Decoded

Preface xi

1 Populations and Samples 1

1.1 The Object of Biostatistics 1

1.2 Scales of Measurement 3

1.3 Central Tendency Measures 5

1.4 Sampling 8

1.5 Inferences from Samples 11

1.6 Measures of Location and Dispersion 14

1.7 The Standard Deviation 15

1.8 The n - 1 Divisor 16

1.9 Degrees of Freedom 18

1.10 Variance of Binary Variables 19

1.11 Properties of Means and Variances 20

1.12 Descriptive Statistics 22

1.13 Sampling Variation 25

1.14 The Normal Distribution 27

1.15 The Central Limit Theorem 29

1.16 Properties of the Normal Distribution 30

1.17 Probability Distribution of Sample Means 32

1.18 The Standard Error of the Mean 33

1.19 The Value of the Standard Error 35

1.20 Distribution of Sample Proportions 37

1.21 Convergence of Binomial to Normal Distribution 39

2 Descriptive Studies 41

2.1 Designing a Research 41

2.2 Study Design 42

2.3 Classification of Descriptive Studies 44

2.4 Cross-sectional Studies 45

2.5 Inferences from Means 47

2.6 Confidence Intervals 48

2.7 Statistical Tables 49

2.8 The Case of Small Samples 51

2.9 Student’s t Distribution 54

2.10 Statistical Tables of the t Distribution 56

2.11 Inferences from Proportions 58

2.12 Statistical Tables of the Binomial Distribution 60

2.13 Sample Size Requirements 61

2.14 Longitudinal Studies 63

2.15 Incidence Studies 65

2.16 Cohort Studies 66

2.17 Inference from Incidence Studies 70

2.18 Standardization 72

2.19 Time-to-Event Cohort Studies 75

2.20 The Actuarial Method 76

2.21 The Kaplan–Meier Method 79

2.22 Probability Sampling 82

2.23 Simple Random Sampling 84

2.24 Replacement in Sampling 85

2.25 Stratified Sampling 87

2.26 Multistage Sampling 92

3 Analytical Studies 97

3.1 Objectives of Analytical Studies 97

3.2 Measures of Association 98

3.3 Odds, Logits, and Odds Ratios 99

3.4 Attributable Risk 101

3.5 Classification of Analytical Studies 103

3.6 Uncontrolled Analytical Studies 104

3.7 Comparative Analytical Studies 105

3.8 Hybrid Analytical Studies 109

3.9 Non-probability Sampling in Analytical Studies 111

3.10 Comparison of Two Means 111

3.11 Comparison of Two Means from Small Samples 114

3.12 Comparison of Two Proportions 116

4 Statistical Tests 121

4.1 The Null and Alternative Hypotheses 121

4.2 The z-Test 122

4.3 The p-Value 125

4.4 Student’s t-Test 126

4.5 The Binomial Test 128

4.6 The Chi-Square Test 130

4.7 The Table of the Chi-Square Distribution 134

4.8 Analysis of Variance 135

4.9 Partitioning the Sum of Squares 139

4.10 Statistical Tables of the F Distribution 142

4.11 The ANOVA Table 143

5 Aspects of Statistical Tests 145

5.1 One-Sided Tests 145

5.2 Power of a Statistical Test 149

5.3 Sample Size Estimation 150

5.4 Multiple Comparisons 153

5.5 Scale Transformation 155

5.6 Non-parametric Tests 156

6 Cross-sectional Studies 161

6.1 Linear Regression 161

6.2 The Least Squares Method 163

6.3 Linear Regression Estimates 166

6.4 Regression and Correlation 171

6.5 The F-Test in Linear Regression 173

6.6 Interpretation of Regression Analysis Results 176

6.7 Multiple Regression 177

6.8 Regression Diagnostics 180

6.9 Selection of Predictor Variables 184

6.10 Independent Nominal Variables 185

6.11 Interaction 188

6.12 Nonlinear Regression 190

7 Case–Control Studies 193

7.1 Analysis of Case–Control Studies 193

7.2 Logistic Regression 194

7.3 The Method of Maximum Likelihood 196

7.4 Estimation of the Logistic Regression Model 198

7.5 The Likelihood Ratio Test 201

7.6 Interpreting the Results of Logistic Regression 202

7.7 Regression Coefficients and Odds Ratios 203

7.8 Applications of Logistic Regression 204

7.9 The ROC Curve 205

7.10 Model Validation 208

8 Cohort Studies 213

8.1 Repeated Measurements 213

8.2 The Paired t-Test 213

8.3 McNemar’s Test 215

8.4 Generalized Linear Models 216

8.5 The Logrank Test 219

8.6 The Adjusted Logrank Test 222

8.7 The Incidence Rate Ratio 224

8.8 The Cox Proportional Hazards Model 225

8.9 Assumptions of the Cox Model 229

8.10 Interpretation of Cox Regression 230

9 Measurement 233

9.1 Construction of Clinical Questionnaires 233

9.2 Factor Analysis 234

9.3 Interpretation of Factor Analysis 237

9.4 Factor Rotation 239

9.5 Factor Scores 241

9.6 Reliability 242

9.7 Concordance 248

9.8 Validity 253

9.9 Validation of Diagnostic Tests 255

10 Experimental Studies 257

10.1 Main Design Features and Classification 257

10.2 Experimental Controls 260

10.3 Replicates 261

10.4 Classification of Experimental Designs 262

10.5 Completely Randomized Design 263

10.6 Interaction 268

10.7 Full Factorial Design 269

10.8 The Random Effects Model 274

10.9 Components of Variance 275

10.10 ANOVA Model II and Model III 278

10.11 Rules for the Definition of the Error Terms 282

10.12 ANOVA on Ranks 284

11 Blocking 285

11.1 Randomized Block Design 285

11.2 Generalized Randomized Block Design 288

11.3 Incomplete Block Design 291

11.4 Factorial Design with Randomized Blocks 292

11.5 Latin and Greco-Latin Square Design 293

12 Simultaneous Inference 297

12.1 Multiple Comparisons 297

12.2 Generalist Methods 298

12.3 Multiple Comparisons of Group Means 303

12.4 Pairwise Comparison of Means 304

12.5 Different Variances 312

12.6 Comparison to a Control 313

12.7 Comparison of post hoc Tests 315

12.8 Complex Comparisons 316

12.9 Tests of Multiple Contrasts 320

12.10 A posteriori Contrasts 324

12.11 The Size of an Experiment 326

13 Factorial ANOVA 329

13.1 The n-Way ANOVA 329

13.2 The 2^k Factorial Design 331

13.3 The 2^k Factorial Design with Blocking 335

13.4 The Fractional Factorial Design 337

14 Nested Designs 339

14.1 Split–Plot Design 339

14.2 Nested (Hierarchical) Design 343

14.3 Mixed Model Nested ANOVA 345

14.4 Mixed Model Nested ANOVA with Three Sublevels 349

14.5 Pure Model II Nested ANOVA 352

15 Repeated Measures 355

15.1 Repeated Measures ANOVA 355

15.2 Repeated Measures ANOVA with Two Factors 359

15.3 ANOVA with Several Repeated Measures 361

15.4 Multivariate Tests 362

16 Clinical Trials 363

16.1 Classification of Clinical Trials 363

16.2 The Clinical Trial Population 365

16.3 The Efficacy Criteria 366

16.4 Controlled Clinical Trials 367

16.5 The Control Group 369

16.6 Blinding 370

16.7 Randomization 371

16.8 Non-comparative Clinical Trials 375

16.9 Regression Toward the Mean 378

16.10 Non-randomized Controlled Clinical Trials 379

16.11 Classical Randomized Clinical Trial Designs 381

16.12 Alternative Clinical Trial Designs 385

16.13 Pragmatic Clinical Trials 387

16.14 Cluster Randomized Trials 389

16.15 The Size of a Clinical Trial 393

16.16 Non-inferiority Clinical Trials 398

16.17 Adaptive Clinical Trials 403

16.18 Group Sequential Plans 405

16.19 The Alpha Spending Function 407

16.20 The Clinical Trial Protocol 409

16.21 The Data Record 411

17 Analysis of Clinical Trials 413

17.1 General Analysis Plan 413

17.2 Data Preparation 414

17.3 Study Populations 415

17.4 Primary Efficacy Analysis 418

17.5 Analysis of Multiple Endpoints 420

17.6 Secondary Analyses 423

17.7 Safety Analysis 424

18 Meta-analysis 427

18.1 Purpose of Meta-analysis 427

18.2 Measures of Effect 428

18.3 The Inverse Variance Method 429

18.4 The Random Effects Model 435

18.5 Heterogeneity 439

18.6 Publication Bias 442

18.7 The Forest Plot 444

References 447

Index 455