Applied Biostatistics for the Health Sciences

An authoritative, yet accessible, introduction to essential key methods used in the statistical analysis of data in the health sciences Applied Biostatistics for the Health Sciences successfully introduces readers to the basic ideas and modeling approaches used in biostatistics through both step-by-step explanations and the use of data from the latest research in the fi eld. By focusing on the correct use and interpretation of statistics rather than computation, this book covers a wide range of modern statistical methods without requiring a high level of mathematical preparation. The book promotes a primary emphasis on the correct usage, interpretation, and conceptual ideas associated with each presented concept. The author begins with a discussion of basic biostatistical methods used to describe sample data arising in biomedical or health-related studies. Subsequent chapters explore numerous modeling approaches used with biomedical and health care data, including simple and multiple regression, logistic regression, experimental design, and survival analysis. Combined with a focus on the importance of constructing and implementing well-designed sampling plans, the book outlines the importance of assessing the quality of observed data, collecting quality data, and using confi dence intervals in conjunction with hypothesis and signifi cance tests. Composed of extensively class-tested material, the book contains numerous pedagogical features that assist readers with a complete understanding of the presented concepts. Key formulae, procedures, and defi nitions are highlighted in enclosed boxes, and a glossary at the end of each chapter reviews key terminology and ideas. Worked-out examples and exercises illustrate important concepts and the proper use of statistical methods using MINITAB® output, and the examples in each section showcase the relevance of the discussed topics in modern research. A related Web site houses all of the data related to the book's case studies and exercises. Applied Biostatistics for the Health Sciences is an excellent introductory book for health science and biostatistics courses at the undergraduate and graduate levels. It is also a valuable resource for practitioners and professionals in the fields of pharmacy, biochemistry, nursing, health care informatics, and the applied health sciences.

Table of Contents:
PREFACE xi CHAPTER 1 INTRODUCTION TO BIOSTATISTICS 1 1.1 What is Biostatistics? 1 1.2 Populations, Samples, and Statistics 2 1.2.1 The Basic Biostatistical Terminology 3 1.2.2 Biomedical Studies 5 1.2.3 Observational Studies Versus Experiments 7 1.3 Clinical Trials 9 1.3.1 Safety and Ethical Considerations in a Clinical Trial 9 1.3.2 Types of Clinical Trials 10 1.3.3 The Phases of a Clinical Trial 11 1.4 Data Set Descriptions 12 1.4.1 Birth Weight Data Set 12 1.4.2 Body Fat Data Set 12 1.4.3 Coronary Heart Disease Data Set 12 1.4.4 Prostate Cancer Study Data Set 13 1.4.5 Intensive Care Unit Data Set 14 1.4.6 Mammography Experience Study Data Set 14 1.4.7 Benign Breast Disease Study 15 Glossary 17 Exercises 18 CHAPTER 2 DESCRIBING POPULATIONS 23 2.1 Populations and Variables 23 2.1.1 Qualitative Variables 24 2.1.2 Quantitative Variables 25 2.1.3 Multivariate Data 27 2.2 Population Distributions and Parameters 28 2.2.1 Distributions 29 2.2.2 Describing a Population with Parameters 33 2.2.3 Proportions and Percentiles 33 2.2.4 Parameters Measuring Centrality 35 2.2.5 Measures of Dispersion 38 2.2.6 The Coefficient of Variation 41 2.2.7 Parameters for Bivariate Populations 43 2.3 Probability 46 2.3.1 Basic Probability Rules 48 2.3.2 Conditional Probability 50 2.3.3 Independence 52 2.4 Probability Models 53 2.4.1 The Binomial Probability Model 54 2.4.2 The Normal Probability Model 57 2.4.3 Z Scores 63 Glossary 64 Exercises 65 CHAPTER 3 RANDOM SAMPLING 76 3.1 Obtaining Representative Data 76 3.1.1 The Sampling Plan 78 3.1.2 Probability Samples 78 3.2 Commonly Used Sampling Plans 80 3.2.1 Simple Random Sampling 80 3.2.2 Stratified Random Sampling 84 3.2.3 Cluster Sampling 86 3.2.4 Systematic Sampling 88 3.3 Determining the Sample Size 89 3.3.1 The Sample Size for a Simple Random Sample 89 3.3.2 The Sample Size for a Stratified Random Sample 93 3.3.3 Determining the Sample Size in a Systematic Random Sample 99 Glossary 100 Exercises 102 CHAPTER 4 SUMMARIZING RANDOM SAMPLES 109 4.1 Samples and Inferential Statistics 109 4.2 Inferential Graphical Statistics 110 4.2.1 Bar and Pie Charts 111 4.2.2 Boxplots 114 4.2.3 Histograms 120 4.2.4 Normal Probability Plots 126 4.3 Numerical Statistics for Univariate Data Sets 129 4.3.1 Estimating Population Proportions 129 4.3.2 Estimating Population Percentiles 136 4.3.3 Estimating the Mean, Median, and Mode 137 4.3.4 Estimating the Variance and Standard Deviation 143 4.3.5 Linear Transformations 148 4.3.6 The Plug-in Rule for Estimation 151 4.4 Statistics for Multivariate Data Sets 153 4.4.1 Graphical Statistics for Bivariate Data Sets 154 4.4.2 Numerical Summaries for Bivariate Data Sets 156 4.4.3 Fitting Lines to Scatterplots 161 Glossary 163 Exercises 166 CHAPTER 5 MEASURING THE RELIABILITY OF STATISTICS 181 5.1 Sampling Distributions 181 5.1.1 Unbiased Estimators 183 5.1.2 Measuring the Accuracy of an Estimator 184 5.1.3 The Bound on the Error of Estimation 186 5.2 The Sampling Distribution of a Sample Proportion 187 5.2.1 The Mean and Standard Deviation of the Sampling Distribution of  187 5.2.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation 190 5.2.3 The Central Limit Theorem for  191 5.2.4 Some Final Notes on the Sampling Distribution of  192 5.3 The Sampling Distribution of  193 5.3.1 The Mean and Standard Deviation of the Sampling Distribution of 193 5.3.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation 196 5.3.3 The Central Limit Theorem for  197 5.3.4 The t Distribution 199 5.3.5 Some Final Notes on the Sampling Distribution of  201 5.4 Comparisons Based on Two Samples 202 5.4.1 Comparing Two Population Proportions 203 5.4.2 Comparing Two Population Means 209 5.5 Bootstrapping the Sampling Distribution of a Statistic 215 Glossary 218 Exercises 219 CHAPTER 6 CONFIDENCE INTERVALS 229 6.1 Interval Estimation 229 6.2 Confidence Intervals 230 6.3 Single Sample Confidence Intervals 232 6.3.1 Confidence Intervals for Proportions 233 6.3.2 Confidence Intervals for a Mean 236 6.3.3 Large Sample Confidence Intervals for μ 237 6.3.4 Small Sample Confidence Intervals for μ 238 6.3.5 Determining the Sample Size for a Confidence Interval for the Mean 241 6.4 Bootstrap Confidence Intervals 243 6.5 Two Sample Comparative Confidence Intervals 244 6.5.1 Confidence Intervals for Comparing Two Proportions 244 6.5.2 Confidence Intervals for the Relative Risk 249 Glossary 252 Exercises 253 CHAPTER 7 TESTING STATISTICAL HYPOTHESES 265 7.1 Hypothesis Testing 265 7.1.1 The Components of a Hypothesis Test 265 7.1.2 P-Values and Significance Testing 272 7.2 Testing Hypotheses about Proportions 276 7.2.1 Single Sample Tests of a Population Proportion 276 7.2.2 Comparing Two Population Proportions 282 7.2.3 Tests of Independence 287 7.3 Testing Hypotheses about Means 295 7.3.1 t-Tests 295 7.3.2 t-Tests for the Mean of a Population 298 7.3.3 Paired Comparison t-Tests 302 7.3.4 Two Independent Sample t-Tests 307 7.4 Some Final Comments on Hypothesis Testing 313 Glossary 314 Exercises 315 CHAPTER 8 SIMPLE LINEAR REGRESSION 333 8.1 Bivariate Data, Scatterplots, and Correlation 333 8.1.1 Scatterplots 333 8.1.2 Correlation 336 8.2 The Simple Linear Regression Model 340 8.2.1 The Simple Linear Regression Model 341 8.2.2 Assumptions of the Simple Linear Regression Model 343 8.3 Fitting a Simple Linear Regression Model 344 8.4 Assessing the Assumptions and Fit of a Simple Linear Regression Model 347 8.4.1 Residuals 348 8.4.2 Residual Diagnostics 348 8.4.3 Estimating σ and Assessing the Strength of the Linear Relationship 355 8.5 Statistical Inferences based on a Fitted Model 358 8.5.1 Inferences about β0 359 8.5.2 Inferences about β1 360 8.6 Inferences about the Response Variable 363 8.6.1 Inferences About μY|X 363 8.6.2 Inferences for Predicting Values of Y 365 8.7 Some Final Comments on Simple Linear Regression 366 Glossary 369 Exercises 371 CHAPTER 9 MULTIPLE REGRESSION 383 9.1 Investigating Multivariate Relationships 385 9.2 The Multiple Linear Regression Model 387 9.2.1 The Assumptions of a Multiple Regression Model 388 9.3 Fitting a Multiple Linear Regression Model 390 9.4 Assessing the Assumptions of a Multiple Linear Regression Model 390 9.4.1 Residual Diagnostics 394 9.4.2 Detecting Multivariate Outliers and Influential Observations 399 9.5 Assessing the Adequacy of Fit of a Multiple Regression Model 401 9.5.1 Estimating σ 401 9.5.2 The Coefficient of Determination 401 9.5.3 Multiple Regression Analysis of Variance 403 9.6 Statistical Inferences-Based Multiple Regression Model 406 9.6.1 Inferences about the Regression Coefficients 406 9.6.2 Inferences about the Response Variable 408 9.7 Comparing Multiple Regression Models 410 9.8 Multiple Regression Models with Categorical Variables 413 9.8.1 Regression Models with Dummy Variables 415 9.8.2 Testing the Importance of Categorical Variables 418 9.9 Variable Selection Techniques 421 9.9.1 Model Selection Using Maximum R2adj 422 9.9.2 Model Selection using BIC 424 9.10 Some Final Comments on Multiple Regression 425 Glossary 427 Exercises 429 CHAPTER 10 LOGISTIC REGRESSION 446 10.1 Odds and Odds Ratios 447 10.2 The Logistic Regression Model 450 10.2.1 Assumptions of the Logistic Regression Model 452 10.3 Fitting a Logistic Regression Model 454 10.4 Assessing the Fit of a Logistic Regression Model 456 10.4.1 Checking the Assumptions of a Logistic Regression Model 456 10.4.2 Testing for the Goodness of Fit of a Logistic Regression Model 458 10.4.3 Model Diagnostics 459 10.5 Statistical Inferences Based on a Logistic Regression Model 465 10.5.1 Inferences about the Logistic Regression Coefficients 465 10.5.2 Comparing Models 467 10.6 Variable Selection 470 10.7 Some Final Comments on Logistic Regression 473 Glossary 474 Exercises 476 CHAPTER 11 DESIGN OF EXPERIMENTS 487 11.1 Experiments versus Observational Studies 487 11.2 The Basic Principles of Experimental Design 490 11.2.1 Terminology 490 11.2.2 Designing an Experiment 491 11.3 Experimental Designs 493 11.3.1 The Completely Randomized Design 495 11.3.2 The Randomized Block Design 498 11.4 Factorial Experiments 500 11.4.1 Two-Factor Experiments 502 11.4.2 Three-Factor Experiments 504 11.5 Models for Designed Experiments 506 11.5.1 The Model for a Completely Randomized Design 506 11.5.2 The Model for a Randomized Block Design 508 11.5.3 Models for Experimental Designs with a Factorial Treatment Structure 509 11.6 Some Final Comments of Designed Experiments 511 Glossary 511 Exercises 513 CHAPTER 12 ANALYSIS OF VARIANCE 520 12.1 Single-Factor Analysis of Variance 521 12.1.1 Partitioning the Total Experimental Variation 523 12.1.2 The Model Assumptions 524 12.1.3 The F-test 527 12.1.4 Comparing Treatment Means 528 12.2 Randomized Block Analysis of Variance 533 12.2.1 The ANOV Table for the Randomized Block Design 534 12.2.2 The Model Assumptions 536 12.2.3 The F-test 538 12.2.4 Separating the Treatment Means 539 12.3 Multifactor Analysis of Variance 542 12.3.1 Two-factor Analysis of Variance 542 12.3.2 Three-factor Analysis of Variance 550 12.4 Selecting the Number of Replicates in Analysis of Variance 555 12.4.1 Determining the Number of Replicates from the Power 555 12.4.2 Determining the Number of Replicates from D 556 12.5 Some Final Comments on Analysis of Variance 557 Glossary 558 Exercises 559 CHAPTER 13 SURVIVAL ANALYSIS 575 13.1 The Kaplan–Meier Estimate of the Survival Function 576 13.2 The Proportional Hazards Model 582 13.3 Logistic Regression and Survival Analysis 586 13.4 Some Final Comments on Survival Analysis 588 Glossary 589 Exercises 590 REFERENCES 599 APPENDIX A 605 PROBLEM SOLUTIONS 613 INDEX 643