Introductory Biostatistics

Chap T. Le, PhD, is Distinguished Professor of Biostatistics and Director of Biostatistics and Bioinformatics at the University of Minnesota Masonic Cancer Center. He has provided statistical consulting for a variety of biomedical research projects, and he has worked on collaborations focusing on the analyses of survival and categorical data and, currently, in the areas of cancer and tobacco research. Dr. Le is the author of Health and Numbers: A Problems-Based Introduction to Biostatistics, Third Edition; Applied Categorical Data Analysis and Translational Research, Second Edition; and Applied Survival Analysis, all published by Wiley. Lynn E. Eberly, PhD, is Associate Professor in the Division of Biostatistics at the University of Minnesota. The author of more than 100 journal articles, Dr. Eberly has been a statistical collaborator in biomedical and public health research for more than 18 years. Her current research interests include methods for and applications to correlated data in neurodegenerative conditions, endocrinology, psychiatry/psychology, and cancer research.

• Preface to the Second Edition xiiiPreface to the First Edition xvAbout the Companion Website xix1 Descriptive Methods for Categorical Data 11.1 Proportions 11.1.1 Comparative Studies 21.1.2 Screening Tests 51.1.3 Displaying Proportions 71.2 Rates 101.2.1 Changes 111.2.2 Measures of Morbidity and Mortality 131.2.3 Standardization of Rates 151.3 Ratios 181.3.1 Relative Risk 181.3.2 Odds and Odds Ratio 181.3.3 Generalized Odds for Ordered 2 × k Tables 211.3.4 Mantel–Haenszel Method 251.3.5 Standardized Mortality Ratio 281.4 Notes on Computations 30Exercises 322 Descriptive Methods for Continuous Data 552.1 Tabular and Graphical Methods 552.1.1 One‐Way Scatter Plots 552.1.2 Frequency Distribution 562.1.3 Histogram and Frequency Polygon 602.1.4 Cumulative Frequency Graph and Percentiles 642.1.5 Stem and Leaf Diagrams 682.2 Numerical Methods 692.2.1 Mean 692.2.2 Other Measures of Location 722.2.3 Measures of Dispersion 732.2.4 Box Plots 762.3 Special Case of Binary Data 772.4 Coefficients of Correlation 782.4.1 Pearson’s Correlation Coefficient 802.4.2 Nonparametric Correlation Coefficients 832.5 Notes on Computations 85Exercises 873 Probability and Probability Models 1033.1 Probability 1033.1.1 Certainty of Uncertainty 1043.1.2 Probability 1043.1.3 Statistical Relationship 1063.1.4 Using Screening Tests 1093.1.5 Measuring Agreement 1123.2 Normal Distribution 1143.2.1 Shape of the Normal Curve 1143.2.2 Areas Under the Standard Normal Curve 1163.2.3 Normal Distribution as a Probability Model 1223.3 Probability Models for Continuous Data 1243.4 Probability Models for Discrete Data 1253.4.1 Binomial Distribution 1263.4.2 Poisson Distribution 1283.5 Brief Notes on the Fundamentals 1303.5.1 Mean and Variance 1303.5.2 Pair‐Matched Case–Control Study 1303.6 Notes on Computations 132Exercises 1344 Estimation of Parameters 1414.1 Basic Concepts 1424.1.1 Statistics as Variables 1434.1.2 Sampling Distributions 1434.1.3 Introduction to Confidence Estimation 1454.2 Estimation of Means 1464.2.1 Confidence Intervals for a Mean 1474.2.2 Uses of Small Samples 1494.2.3 Evaluation of Interventions 1514.3 Estimation of Proportions 1534.4 Estimation of Odds Ratios 1574.5 Estimation of Correlation Coefficients 1604.6 Brief Notes on the Fundamentals 1634.7 Notes on Computations 165Exercises 1665 Introduction to Statistical Tests of Significance 1795.1 Basic Concepts 1805.1.1 Hypothesis Tests 1815.1.2 Statistical Evidence 1825.1.3 Errors 1825.2 Analogies 1855.2.1 Trials by Jury 1855.2.2 Medical Screening Tests 1865.2.3 Common Expectations 1865.3 Summaries and Conclusions 1875.3.1 Rejection Region 1875.3.2 p Values 1895.3.3 Relationship to Confidence Intervals 1915.4 Brief Notes on the Fundamentals 1935.4.1 Type I and Type II Errors 1935.4.2 More about Errors and p Values 194Exercises 1946 Comparison of Population Proportions 1976.1 One‐Sample Problem with Binary Data 1976.2 Analysis of Pair‐Matched Data 1996.3 Comparison of Two Proportions 2026.4 Mantel–Haenszel Method 2066.5 Inferences for General Two‐Way Tables 2116.6 Fisher’s Exact Test 2176.7 Ordered 2 × K Contingency Tables 2196.8 Notes on Computations 222Exercises 2227 Comparison of Population Means 2357.1 One‐Sample Problem with Continuous Data 2357.2 Analysis of Pair‐Matched Data 2377.3 Comparison of Two Means 2427.4 Nonparametric Methods 2467.4.1 Wilcoxon Rank‐Sum Test 2467.4.2 Wilcoxon Signed‐Rank Test 2507.5 One‐Way Analysis of Variance 2527.5.1 One‐Way Analysis of Variance Model 2537.5.2 Group Comparisons 2587.6 Brief Notes on the Fundamentals 2597.7 Notes on Computations 260Exercises 2608 Analysis of Variance 2738.1 Factorial Studies 2738.1.1 Two Crossed Factors 2738.1.2 Extensions to More Than Two Factors 2788.2 Block Designs 2808.2.1 Purpose 2808.2.2 Fixed Block Designs 2818.2.3 Random Block Designs 2848.3 Diagnostics 287Exercises 2919 Regression Analysis 2979.1 Simple Regression Analysis 2989.1.1 Correlation and Regression 2989.1.2 Simple Linear Regression Model 3019.1.3 Scatter Diagram 3029.1.4 Meaning of Regression Parameters 3029.1.5 Estimation of Parameters and Prediction 3039.1.6 Testing for Independence 3079.1.7 Analysis of Variance Approach 3099.1.8 Some Biomedical Applications 3119.2 Multiple Regression Analysis 3179.2.1 Regression Model with Several Independent Variables 3189.2.2 Meaning of Regression Parameters 3189.2.3 Effect Modifications 3199.2.4 Polynomial Regression 3199.2.5 Estimation of Parameters and Prediction 3209.2.6 Analysis of Variance Approach 3219.2.7 Testing Hypotheses in Multiple Linear Regression 3229.2.8 Some Biomedical Applications 3309.3 Graphical and Computational Aids 334Exercises 33610 Logistic Regression 35110.1 Simple Regression Analysis 35310.1.1 Simple Logistic Regression Model 35310.1.2 Measure of Association 35510.1.3 Effect of Measurement Scale 35610.1.4 Tests of Association 35810.1.5 Use of the Logistic Model for Different Designs 35810.1.6 Overdispersion 35910.2 Multiple Regression Analysis 36210.2.1 Logistic Regression Model with Several Covariates 36310.2.2 Effect Modifications 36410.2.3 Polynomial Regression 36510.2.4 Testing Hypotheses in Multiple Logistic Regression 36510.2.5 Receiver Operating Characteristic Curve 37210.2.6 ROC Curve and Logistic Regression 37410.3 Brief Notes on the Fundamentals 37510.4 Notes on Computing 377Exercises 37711 Methods for Count Data 38311.1 Poisson Distribution 38311.2 Testing Goodness of Fit 38711.3 Poisson Regression Model 38911.3.1 Simple Regression Analysis 38911.3.2 Multiple Regression Analysis 39311.3.3 Overdispersion 40211.3.4 Stepwise Regression 404Exercises 40612 Methods for Repeatedly Measured Responses 40912.1 Extending Regression Methods Beyond Independent Data 40912.2 Continuous Responses 41012.2.1 Extending Regression using the Linear Mixed Model 41012.2.2 Testing and Inference 41412.2.3 Comparing Models 41712.2.4 Special Cases: Random Block Designs and Multi‐level Sampling 41812.3 Binary Responses 42312.3.1 Extending Logistic Regression using Generalized Estimating Equations 42312.3.2 Testing and Inference 42512.4 Count Responses 42712.4.1 Extending Poisson Regression using Generalized Estimating Equations 42712.4.2 Testing and Inference 42812.5 Computational Notes 431Exercises 43213 Analysis of Survival Data and Data from Matched Studies 43913.1 Survival Data 44013.2 Introductory Survival Analyses 44313.2.1 Kaplan–Meier Curve 44413.2.2 Comparison of Survival Distributions 44613.3 Simple Regression and Correlation 45013.3.1 Model and Approach 45113.3.2 Measures of Association 45213.3.3 Tests of Association 45513.4 Multiple Regression and Correlation 45613.4.1 Proportional Hazards Model with Several Covariates 45613.4.2 Testing Hypotheses in Multiple Regression 45713.4.3 Time‐Dependent Covariates and Applications 46113.5 Pair‐Matched Case–Control Studies 46413.5.1 Model 46513.5.2 Analysis 46613.6 Multiple Matching 46813.6.1 Conditional Approach 46913.6.2 Estimation of the Odds Ratio 46913.6.3 Testing for Exposure Effect 47013.7 Conditional Logistic Regression 47213.7.1 Simple Regression Analysis 47313.7.2 Multiple Regression Analysis 478Exercises 48414 Study Designs 49314.1 Types of Study Designs 49414.2 Classification of Clinical Trials 49514.3 Designing Phase I Cancer Trials 49714.4 Sample Size Determination for Phase II Trials and Surveys 49914.5 Sample Sizes for Other Phase II Trials 50114.5.1 Continuous Endpoints 50114.5.2 Correlation Endpoints 50214.6 About Simon’s Two‐Stage Phase II Design 50314.7 Phase II Designs for Selection 50414.7.1 Continuous Endpoints 50514.7.2 Binary Endpoints 50514.8 Toxicity Monitoring in Phase II Trials 50614.9 Sample Size Determination for Phase III Trials 50814.9.1 Comparison of Two Means 50914.9.2 Comparison of Two Proportions 51114.9.3 Survival Time as the Endpoint 51314.10 Sample Size Determination for Case–Control Studies 51514.10.1 Unmatched Designs for a Binary Exposure 51614.10.2 Matched Designs for a Binary Exposure 51814.10.3 Unmatched Designs for a Continuous Exposure 520Exercises 522References 529Appendices 535Answers to Selected Exercises 541Index 585