Applied Biostatistics for the Health Sciences

Richard J. Rossi, PhD, is Director of the Data Science Program, former Director of the Statistics Program, and former Head of Mathematical Sciences at Montana Technical University, USA. He is author of Theorems, Corollaries, Lemmas, and Methods of Proof and Mathematical Statistics: An Introduction to Likelihood Based Inference, both published by Wiley. His research focuses on nonparametric density estimation, finite mixture models, and computational statistics.

• Preface xiChapter 1 Introduction To Biostatistics 11.1 What is Biostatistics? 11.2 Populations, Samples, and Statistics 21.2.1 The Basic Biostatistical Terminology 31.2.2 Biomedical Studies 51.2.3 Observational Studies Versus Experiments 71.3 Clinical Trials 91.3.1 Safety and Ethical Considerations in a Clinical Trial 91.3.2 Types of Clinical Trials 101.3.3 The Phases of a Clinical Trial 101.4 Data Set Descriptions 121.4.1 Birth Weight Data Set 121.4.2 Body Fat Data Set 121.4.3 Coronary Heart Disease Data Set 131.4.4 Prostate Cancer Study Data Set 131.4.5 Intensive Care Unit Data Set 141.4.6 Mammography Experience Study Data Set 141.4.7 Benign Breast Disease Study 141.4.8 Exerbike Data Sets 15Glossary 17Exercises 19Chapter 2 Describing Populations 242.1 Populations and Variables 242.1.1 Qualitative Variables 252.1.2 Quantitative Variables 262.1.3 Multivariate Data 282.2 Population Distributions and Parameters 292.2.1 Distributions 302.2.2 Describing a Population with Parameters 342.2.3 Proportions and Percentiles 352.2.4 Parameters Measuring Centrality 372.2.5 Measures of Dispersion 402.2.6 The Coefficient of Variation 432.2.7 Parameters for Bivariate Populations 452.3 Probability 482.3.1 Basic Probability Rules 502.3.2 Conditional Probability 522.3.3 Independence 542.3.4 The Relative Risk and the Odds Ratio 562.4 Probability Models 592.4.1 The Binomial Probability Model 592.4.2 The Normal Probability Model 622.4.3 Z Scores 69Glossary 69Exercises 71Chapter 3 Random Sampling 833.1 Obtaining Representative Data 833.1.1 The Sampling Plan 853.1.2 Probability Samples 853.2 Commonly Used Sampling Plans 873.2.1 Simple Random Sampling 873.2.2 Stratified Random Sampling 913.2.3 Cluster Sampling 923.2.4 Systematic Sampling 943.3 Determining the Sample Size 953.3.1 The Sample Size for Simple and Systematic Random Samples 963.3.2 The Sample Size for a Stratified Random Sample 99Glossary 105Exercises 107Chapter 4 Summarizing Random Samples 1154.1 Samples and Inferential Statistics 1154.2 Inferential Graphical Statistics 1164.2.1 Bar and Pie Charts 1164.2.2 Boxplots 1204.2.3 Histograms 1264.2.4 Normal Probability Plots 1324.3 Numerical Statistics for Univariate Data Sets 1344.3.1 Estimating Population Proportions 1354.3.2 Estimating Population Percentiles 1424.3.3 Estimating the Mean, Median, and Mode 1434.3.4 Estimating the Variance and Standard Deviation 1494.3.5 Linear Transformations 1534.3.6 The Plug-in Rule for Estimation 1564.4 Statistics for Multivariate Data Sets 1584.4.1 Graphical Statistics for Bivariate Data Sets 1584.4.2 Numerical Summaries for Bivariate Data Sets 1604.4.3 Fitting Lines to Scatterplots 166Glossary 167Exercises 170Chapter 5 Measuring The Reliability of Statistics 1865.1 Sampling Distributions 1865.1.1 Unbiased Estimators 1885.1.2 Measuring the Accuracy of an Estimator 1895.1.3 The Bound on the Error of Estimation 1915.2 The Sampling Distribution of a Sample Proportion 1925.2.1 The Mean and Standard Deviation of the Sampling Distribution of 𝑝̂ 1925.2.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation 1955.2.3 The Central Limit Theorem for p 1965.2.4 Some Final Notes on the Sampling Distribution of p 1975.3 The Sampling Distribution of x 1975.3.1 The Mean and Standard Deviation of the Sampling Distribution of x 1985.3.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation 2015.3.3 The Central Limit Theorem for x 2025.3.4 The t Distribution 204 5.3.5 Some Final Notes on the Sampling Distribution of x 2065.4 Two Sample Comparisons 2075.4.1 Comparing Two Population Proportions 2085.4.2 Comparing Two Population Means 2145.5 Bootstrapping the Sampling Distribution of a Statistic 220Glossary 223Exercises 223Chapter 6 Confidence Intervals 2356.1 Interval Estimation 2356.2 Confidence Intervals 2366.3 Single Sample Confidence Intervals 2386.3.1 Confidence Intervals for Proportions 2396.3.2 Confidence Intervals for a Mean 2426.3.3 Large Sample Confidence Intervals for 𝜇 2436.3.4 Small Sample Confidence Intervals for 𝜇 2446.3.5 Determining the Sample Size for a Confidence Interval for the Mean 2476.4 Bootstrap Confidence Intervals 2486.5 Two Sample Comparative Confidence Intervals 2506.5.1 Confidence Intervals for Comparing Two Proportions 2506.5.2 Confidence Intervals for the Relative Risk 2546.5.3 Confidence Intervals for the Odds Ratio 257Glossary 259Exercises 260Chapter 7 Testing Statistical Hypotheses 2727.1 Hypothesis Testing 2727.1.1 The Components of a Hypothesis Test 2727.1.2 P-Values and Significance Testing 2797.2 Testing Hypotheses about Proportions 2837.2.1 Single Sample Tests of a Population Proportion 2837.2.2 Comparing Two Population Proportions 2897.2.3 Tests of Independence 2937.3 Testing Hypotheses About Means 3017.3.1 t-Tests 3017.3.2 t-Tests for the Mean of a Population 3047.3.3 Paired Comparison t-Tests 3087.3.4 Two Independent Sample t-Tests 3137.4 7.4 Some Final Comments on Hypothesis Testing 318Glossary 319Exercises 320Chapter 8 Simple Linear Regression 3408.1 Bivariate Data, Scatterplots, and Correlation 3408.1.1 Scatterplots 3408.1.2 Correlation 3438.2 The Simple Linear Regression Model 3478.2.1 The Simple Linear Regression Model 3488.2.2 Assumptions of the Simple Linear Regression Model 3508.3 Fitting a Simple Linear Regression Model 3528.4 Assessing the Assumptions and Fit of a Simple Linear Regression Model 3548.4.1 Residuals 3558.4.2 Residual Diagnostics 3568.4.3 Estimating 𝜎 and Assessing the Strength of the Linear Relationship 3628.5 Statistical Inferences based on a Fitted Model 3668.5.1 Inferences About 𝛽0 3668.5.2 Inferences About 𝛽1 3688.6 Inferences about the Response Variable 3708.6.1 Inferences About 𝜇Y|X3718.6.2 Inferences for Predicting Values of Y 3728.7 Model Validation 3748.7.1 Selecting the Training and Validation Data Sets 3748.7.2 Validating a Fitted Model 3748.8 Some Final Comments on Simple Linear Regression 375Glossary 377Exercises 380Chapter 9 Multiple Regression 3969.1 Investigating Multivariate Relationships 3989.2 The Multiple Linear Regression Model 4009.2.1 The Assumptions of a Multiple Regression Model 4019.3 Fitting a Multiple Linear Regression Model 4039.4 Assessing the Assumptions of a Multiple Linear Regression Model 4039.4.1 Residual Diagnostics 4079.4.2 Detecting Multivariate Outliers and Influential Observations 4139.5 Assessing the Adequacy of Fit of a Multiple Regression Model 4149.5.1 Estimating 𝜎 4149.5.2 The Coefficient of Determination 4149.5.3 Multiple Regression Analysis of Variance 4169.6 Statistical Inferences-Based Multiple Regression Model 4199.6.1 Inferences about the Regression Coefficients 4199.6.2 Inferences About the Response Variable 4219.7 Comparing Multiple Regression Models 4239.8 Multiple Regression Models with Categorical Variables 4259.8.1 Regression Models with Dummy Variables 4289.8.2 Testing the Importance of Categorical Variables 4309.9 Variable Selection Techniques 4349.9.1 Model Selection Using Maximum R2 adj 4359.9.2 Model Selection using BIC 4369.10 Model Validation 4399.10.1 Selecting the Training and Validation Data Sets 4409.10.2 Validating a Fitted Model 4409.11 Some Final Comments on Multiple Regression 441Glossary 442Exercises 444Chapter 10 Logistic Regression 46210.1 The Logistic Regression Model 46310.1.1 Assumptions of the Logistic Regression Model 46610.2 Fitting a Logistic Regression Model 46710.3 Assessing the Fit of a Logistic Regression Model 46910.3.1 Checking the Assumptions of a Logistic Regression Model 47010.3.2 Testing for the Goodness of Fit of a Logistic Regression Model 47110.3.3 Model Diagnostics 47310.4 Statistical Inferences Based on a Logistic Regression Model 47810.4.1 Inferences about the Logistic Regression Coefficients 47910.4.2 Comparing Models 48010.5 Variable Selection 48410.6 Classification with Logistic Regression 48710.6.1 The Logistic Classifier 48710.6.2 Misclassification Errors 48810.7 Some Final Comments on Logistic Regression 489Glossary 490Exercises 492Chapter 11 Design of Experiments 50811.1 Experiments Versus Observational Studies 50811.2 The Basic Principles of Experimental Design 51111.2.1 Terminology 51111.2.2 Designing an Experiment 51211.3 Experimental Designs 51411.3.1 The Completely Randomized Design 51611.3.2 The Randomized Block Design 51911.4 Factorial Experiments 52111.4.1 Two-Factor Experiments 52311.4.2 Three-Factor Experiments 52511.5 Models for Designed Experiments 52711.5.1 The Model for a Completely Randomized Design 52711.5.2 The Model for a Randomized Block Design 52811.5.3 Models for Experimental Designs with a Factorial Treatment Structure 53011.6 Some Final Comments of Designed Experiments 531Glossary 532Exercises 534Chapter 12 Analysis of Variance 54212.1 Single-Factor Analysis of Variance 54312.1.1 Partitioning the Total Experimental Variation 54412.1.2 The Model Assumptions 54612.1.3 The F-test 54812.1.4 Comparing Treatment Means 55012.2 Randomized Block Analysis of Variance 55412.2.1 The ANOV Table for the Randomized Block Design 55512.2.2 The Model Assumptions 55712.2.3 The F-test 55912.2.4 Separating the Treatment Means 56012.3 Multi factor Analysis of Variance 56312.3.1 Two-Factor Analysis of Variance 56312.3.2 Three-Factor Analysis of Variance 57112.4 Selecting the Number of Replicates in Analysis of Variance 57512.4.1 Determining the Number of Replicates from the Power 57512.4.2 Determining the Number of Replicates from 𝐷 57612.5 Some Final Comments on Analysis of Variance 577Glossary 578Exercises 579Chapter 13 Survival Analysis 59613.1 The Kaplan–Meier Estimate of the Survival Function 59713.2 The Proportional Hazards Model 60313.3 Logistic Regression and Survival Analysis 60713.4 Some Final Comments on Survival Analysis 609Glossary 610Exercises 611References 620Appendix A 628Problem Solutions 636Index 663