Basic Biostatistics for Geneticists and Epidemiologists

Robert C Elston, Professor Genetic and Molecular Epidemiology Track, Department of Epidemiology and Biostatistics, School of Medicine Case Western Reserve University, USA. An internationally prominent genetic epidemiologist with many years teaching experience. William D Johnson, Medical Center, University of Mississippi, USA. An experienced human geneticist.

"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)

• Preface ix1 Introduction: The Role and Relevance of Statistics, Genetics and Epidemiology In Medicine 3Why Biostatistics? 3What Exactly is (are) Statistics? 5Reasons for Understanding Statistics 6What Exactly is Genetics? 8What Exactly is Epidemiology? 10How Can a Statistician Help Geneticists and Epidemiologists? 11Disease Prevention versus Disease Therapy 12A Few Examples: Genetics, Epidemiology and Statistical Inference 12Summary 14References 152 Populations, Samples, and Study Design 19The Study of Cause and Effect 19Populations, Target Populations and Study Units 21Probability Samples and Randomization 23Observational Studies 25Family Studies 27Experimental Studies 28Quasi-Experimental Studies 36Summary 37Further Reading 38Problems 383 Descriptive Statistics 45Why Do We Need Descriptive Statistics? 45Scales of Measurement 46Tables 47Graphs 49Proportions and Rates 55Relative Measures of Disease Frequency 58Sensitivity, Specificity and Predictive Values 61Measures of Central Tendency 62Measures of Spread or Variability 64Measures of Shape 67Summary 68Further Reading 70Problems 704 The Laws of Probability 79Definition of Probability 79The Probability of Either of Two Events: A or B 82The Joint Probability of Two Events: A and B 83Examples of Independence, Nonindependence and Genetic Counseling 86Bayes’ Theorem 89Likelihood Ratio 97Summary 98Further Reading 99Problems 995 Random Variables and Distributions 107Variability and Random Variables 107Binomial Distribution 109A Note about Symbols 112Poisson Distribution 113Uniform Distribution 114Normal Distribution 116Cumulative Distribution Functions 119The Standard Normal (Gaussian) Distribution 120Summary 122Further Reading 123Problems 1236 Estimates and Confidence Limits 131Estimates and Estimators 131Notation for Population Parameters, Sample Estimates, and Sample Estimators 133Properties of Estimators 134Maximum Likelihood 135Estimating Intervals 137Distribution of the Sample Mean 138Confidence Limits 140Summary 146Problems 1487 Significance Tests and Tests of Hypotheses 155Principle of Significance Testing 155Principle of Hypothesis Testing 156Testing a Population Mean 157One-Sided versus Two-Sided Tests 160Testing a Proportion 161Testing the Equality of Two Variances 165Testing the Equality of Two Means 167Testing the Equality of Two Medians 169Validity and Power 172Summary 176Further Reading 178Problems 1788 Likelihood Ratios, Bayesian Methods and Multiple Hypotheses 187Likelihood Ratios 187Bayesian Methods 190Bayes’ Factors 192Bayesian Estimates and Credible Intervals 194The Multiple Testing Problem 195Summary 198Problems 1999 The Many Uses of Chi-Square 203The Chi-Square Distribution 203Goodness-of-Fit Tests 206Contingency Tables 209Inference About the Variance 219Combining p-Values 220Likelihood Ratio Tests 221Summary 223Further Reading 225Problems 22510 Correlation and Regression 233Simple Linear Regression 233The Straight-Line Relationship When There is Inherent Variability 240Correlation 242Spearman’s Rank Correlation 246Multiple Regression 246Multiple Correlation and Partial Correlation 250Regression toward the Mean 251Summary 253Further Reading 254Problems 25511 Analysis of Variance and Linear Models 265Multiple Treatment Groups 265Completely Randomized Design with a Single Classification of Treatment Groups 267Data with Multiple Classifications 269Analysis of Covariance 281Assumptions Associated with the Analysis of Variance 282Summary 283Further Reading 284Problems 28512 Some Specialized Techniques 293Multivariate Analysis 293Discriminant Analysis 295Logistic Regression 296Analysis of Survival Times 299Estimating Survival Curves 301Permutation Tests 304Resampling Methods 309Summary 312Further Reading 313Problems 31313 Guides to a Critical Evaluation of Published Reports 321The Research Hypothesis 321Variables Studied 321The Study Design 322Sample Size 322Completeness of the Data 323Appropriate Descriptive Statistics 323Appropriate Statistical Methods for Inferences 323Logic of the Conclusions 324Meta-analysis 324Summary 326Further Reading 327Problems 328Epilogue 329Review Problems 331Answers to Odd-Numbered Problems 345Appendix 353Index 365