Applied Biostatistics for the Health Sciences / Edition 1

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Overview

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 field. 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 or 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 confidence intervals in conjunction with hypothesis and significance 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 definitions 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.

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Editorial Reviews

From the Publisher
"The book is an excellent introduction to biostatistics. It is also a valuable resource for practitioners in all fields of health sciences." (Biometrical Journal, February 2011)
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Product Details

  • ISBN-13: 9780470147641
  • Publisher: Wiley
  • Publication date: 12/9/2009
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 664
  • Product dimensions: 6.90 (w) x 9.90 (h) x 1.40 (d)

Meet the Author

Richard J. Rossi, PhD, is Professor and Head of the Department of Mathematical Sciences at Montana Tech of the University of Montana. He has previously served as president of the Montana Chapter of the American Statistical Association (1996 and 2001) and as associate editor for Biometrics. Dr. Rossi has published journal articles in his areas of research interest, which include nonparametric density estimation, finite mixture models, and computational statistics.—He is the author of Theorems, Corollaries, Lemmas, and Methods of Proof, also published by Wiley.

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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 Statics 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 &pcirc; 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 &pcirc; 191

5.2.4 Some Final Notes on the Sampling Distribution of &pcirc; 192

5.3 The Sampling Distribution of &xbar; 193

5.3.1 The Mean and Standard Deviation of the Sampling Distribution of &xbar; 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 &xbar; 197

5.3.4 The t Distribution 199

5.3.5 Some Final Notes on the Sampling Distribution of &xbar; 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 ? 237

6.3.4 Small Sample Confidence Intervals for ? 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 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 ?y|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

Chapters 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 R2 adj 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

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