Basic Biostatistics for Geneticists and Epidemiologists: A Practical Approach

Preface ix

1 Introduction: The Role and Relevance of Statistics, Genetics and Epidemiology In Medicine 3

Why Biostatistics? 3

What Exactly is (are) Statistics? 5

Reasons for Understanding Statistics 6

What Exactly is Genetics? 8

What Exactly is Epidemiology? 10

How Can a Statistician Help Geneticists and Epidemiologists? 11

Disease Prevention versus Disease Therapy 12

A Few Examples: Genetics, Epidemiology and Statistical Inference 12

Summary 14

References 15

2 Populations, Samples, and Study Design 19

The Study of Cause and Effect 19

Populations, Target Populations and Study Units 21

Probability Samples and Randomization 23

Observational Studies 25

Family Studies 27

Experimental Studies 28

Quasi-Experimental Studies 36

Summary 37

Further Reading 38

Problems 38

3 Descriptive Statistics 45

Why Do We Need Descriptive Statistics? 45

Scales of Measurement 46

Tables 47

Graphs 49

Proportions and Rates 55

Relative Measures of Disease Frequency 58

Sensitivity, Specificity and Predictive Values 61

Measures of Central Tendency 62

Measures of Spread or Variability 64

Measures of Shape 67

Summary 68

Further Reading 70

Problems 70

4 The Laws of Probability 79

Definition of Probability 79

The Probability of Either of Two Events: A or B 82

The Joint Probability of Two Events: A and B 83

Examples of Independence, Nonindependence and Genetic Counseling 86

Bayes’ Theorem 89

Likelihood Ratio 97

Summary 98

Further Reading 99

Problems 99

5 Random Variables and Distributions 107

Variability and Random Variables 107

Binomial Distribution 109

A Note about Symbols 112

Poisson Distribution 113

Uniform Distribution 114

Normal Distribution 116

Cumulative Distribution Functions 119

The Standard Normal (Gaussian) Distribution 120

Summary 122

Further Reading 123

Problems 123

6 Estimates and Confidence Limits 131

Estimates and Estimators 131

Notation for Population Parameters, Sample Estimates, and Sample Estimators 133

Properties of Estimators 134

Maximum Likelihood 135

Estimating Intervals 137

Distribution of the Sample Mean 138

Confidence Limits 140

Summary 146

Problems 148

7 Significance Tests and Tests of Hypotheses 155

Principle of Significance Testing 155

Principle of Hypothesis Testing 156

Testing a Population Mean 157

One-Sided versus Two-Sided Tests 160

Testing a Proportion 161

Testing the Equality of Two Variances 165

Testing the Equality of Two Means 167

Testing the Equality of Two Medians 169

Validity and Power 172

Summary 176

Further Reading 178

Problems 178

8 Likelihood Ratios, Bayesian Methods and Multiple Hypotheses 187

Likelihood Ratios 187

Bayesian Methods 190

Bayes’ Factors 192

Bayesian Estimates and Credible Intervals 194

The Multiple Testing Problem 195

Summary 198

Problems 199

9 The Many Uses of Chi-Square 203

The Chi-Square Distribution 203

Goodness-of-Fit Tests 206

Contingency Tables 209

Inference About the Variance 219

Combining p-Values 220

Likelihood Ratio Tests 221

Summary 223

Further Reading 225

Problems 225

10 Correlation and Regression 233

Simple Linear Regression 233

The Straight-Line Relationship When There is Inherent Variability 240

Correlation 242

Spearman’s Rank Correlation 246

Multiple Regression 246

Multiple Correlation and Partial Correlation 250

Regression toward the Mean 251

Summary 253

Further Reading 254

Problems 255

11 Analysis of Variance and Linear Models 265

Multiple Treatment Groups 265

Completely Randomized Design with a Single Classification of Treatment Groups 267

Data with Multiple Classifications 269

Analysis of Covariance 281

Assumptions Associated with the Analysis of Variance 282

Summary 283

Further Reading 284

Problems 285

12 Some Specialized Techniques 293

Multivariate Analysis 293

Discriminant Analysis 295

Logistic Regression 296

Analysis of Survival Times 299

Estimating Survival Curves 301

Permutation Tests 304

Resampling Methods 309

Summary 312

Further Reading 313

Problems 313

13 Guides to a Critical Evaluation of Published Reports 321

The Research Hypothesis 321

Variables Studied 321

The Study Design 322

Sample Size 322

Completeness of the Data 323

Appropriate Descriptive Statistics 323

Appropriate Statistical Methods for Inferences 323

Logic of the Conclusions 324

Meta-analysis 324

Summary 326

Further Reading 327

Problems 328

Epilogue 329

Review Problems 331

Answers to Odd-Numbered Problems 345

Appendix 353

Index 365