Basic Biostatistics for Geneticists and Epidemiologists (eBook)

Robert C. Elston Department of Epidemiology and Biostatistics, Case Western Reserve University, USA. William D. Johnson Pennington Biomedical Research Center, Louisiana State University, USA.

Basic Biostatistics for Geneticists and Epidemiologists 3
CONTENTS 7
PREFACE 11
1 INTRODUCTION: THE ROLE AND RELEVANCE OF STATISTICS, GENETICS AND EPIDEMIOLOGY IN MEDICINE 15
Why Biostatistics? 15
What Exactly Is (Are) Statistics? 17
Reasons for Understanding Statistics 18
What Exactly is Genetics? 20
What Exactly is Epidemiology? 22
How Can a Statistician Help Geneticists and Epidemiologists? 23
Disease Prevention versus Disease Therapy 24
A Few Examples: Genetics, Epidemiology and Statistical Inference 24
Summary 26
References 27
2 POPULATIONS, SAMPLES, AND STUDY DESIGN 31
The Study of Cause and Effect 31
Populations, Target Populations and Study Units 33
Probability Samples and Randomization 35
Observational Studies 37
Family Studies 39
Experimental Studies 40
Quasi-Experimental Studies 48
Summary 49
Further Reading 50
Problems 50
3 DESCRIPTIVE STATISTICS 57
Why Do We Need Descriptive Statistics? 57
Scales of Measurement 58
Tables 59
Graphs 61
Proportions and Rates 67
Relative Measures of Disease Frequency 70
Sensitivity, Specificity and Predictive Values 73
Measures of Central Tendency 74
Measures of Spread or Variability 76
Measures of Shape 79
Summary 80
Further Reading 82
Problems 82
4 THE LAWS OF PROBABILITY 91
Definition of Probability 91
The Probability of Either of Two Events: A or B 94
The Joint Probability of Two Events: A and B 95
Examples of Independence, Nonindependence and Genetic Counseling 98
Bayes’ Theorem 101
Likelihood Ratio 109
Summary 110
Further Reading 111
Problems 111
5 RANDOM VARIABLES AND DISTRIBUTIONS 119
Variability and Random Variables 119
Binomial Distribution 121
A Note about Symbols 124
Poisson Distribution 125
Uniform Distribution 126
Normal Distribution 128
Cumulative Distribution Functions 131
The Standard Normal (Gaussian) Distribution 132
Summary 134
Further Reading 135
Problems 135
6 ESTIMATES AND CONFIDENCE LIMITS 143
Estimates and Estimators 143
Notation for Population Parameters, Sample Estimates, and Sample Estimators 145
Properties of Estimators 146
Maximum Likelihood 147
Estimating Intervals 149
Distribution of the Sample Mean 150
Confidence Limits 152
Summary 158
Problems 160
7 SIGNIFICANCE TESTS AND TESTS OF HYPOTHESES 167
Principle of Significance Testing 167
Principle of Hypothesis Testing 168
Testing a Population Mean 169
One-Sided versus Two-Sided Tests 172
Testing a Proportion 173
Testing the Equality of Two Variances 177
Testing the Equality of Two Means 179
Testing the Equality of Two Medians 181
Validity and Power 184
Summary 188
Further Reading 190
Problems 190
8 LIKELIHOOD RATIOS, BAYESIAN METHODS AND MULTIPLE HYPOTHESES 199
Likelihood Ratios 199
Bayesian Methods 202
Bayes’ Factors 204
Bayesian Estimates and Credible Intervals 206
The Multiple Testing Problem 207
Summary 210
Problems 211
9 THE MANY USES OF CHI-SQUARE 215
The Chi-Square Distribution 215
Goodness-of-Fit Tests 218
Contingency Tables 221
Inference About the Variance 231
Combining p-Values 232
Likelihood Ratio Tests 233
Summary 235
Further Reading 237
Problems 237
10 CORRELATION AND REGRESSION 245
Simple Linear Regression 245
The Straight-Line Relationship When There is Inherent Variability 252
Correlation 254
Spearman’s Rank Correlation 258
Multiple Regression 258
Multiple Correlation and Partial Correlation 262
Regression toward the Mean 263
Summary 265
Further Reading 266
Problems 267
11 ANALYSIS OF VARIANCE AND LINEAR MODELS 277
Multiple Treatment Groups 277
Completely Randomized Design with a Single Classification of Treatment Groups 279
Data with Multiple Classifications 281
Analysis of Covariance 293
Assumptions Associated with the Analysis of Variance 294
Summary 295
Further Reading 296
Problems 297
12 SOME SPECIALIZED TECHNIQUES 305
Multivariate Analysis 305
Discriminant Analysis 307
Logistic Regression 308
Analysis of Survival Times 311
Estimating Survival Curves 313
Permutation Tests 316
Resampling Methods 321
Summary 324
Further Reading 325
Problems 325
13 GUIDES TO A CRITICAL EVALUATION OF PUBLISHED REPORTS 333
The Research Hypothesis 333
Variables Studied 333
The Study Design 334
Sample Size 334
Completeness of the Data 335
Appropriate Descriptive Statistics 335
Appropriate Statistical Methods for Inferences 335
Logic of the Conclusions 336
Meta-analysis 336
Summary 338
Further Reading 339
Problems 340
EPILOGUE 341
REVIEW PROBLEMS 343
ANSWERS TO ODD-NUMBERED PROBLEMS 357
APPENDIX 365
INDEX 377

"The book is unusual in having less ambitious goals than the average statistics textbook. The focus is not to teach applications but, as the preface maintains, simply to enable readers to knowledgeably read the new literature, to understand the statistical methods used, and thereby to better keep abreast of new findings in epidemiology and genetics." (JAMA, September 13, 2010)

"This is a well-written and comprehensive review of the basic (and not-so-basic) concepts and techniques in biostatistics. It is understandable to biologists and clinicians, while still providing useful pointers and reminders to statisticians. It is worth a place on the bookshelves of all researchers in genetics, regardless of their statistical expertise." (Human Genetics, February 2010)

"Anyone who wishes to critically read biomedical literature will find the knowledge gained from reading [the text] of great value." (American Journal of Epidemiology, 2009)