Applied biostatistics for the health

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.

Author Notes

Richard J. Rossi, Ph.D. 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.

Preface	p. xi
Chapter 1 Introduction to Biostatistics	p. 1
1.1 What is Biostatistics?	p. 1
1.2 Populations, Samples, and Statistics	p. 2
1.2.1 The Basic Biostatistical Terminology	p. 3
1.2.2 Biomedical Studies	p. 5
1.2.3 Observational Studies Versus Experiments	p. 7
1.3 Clinical Trials	p. 9
1.3.1 Safety and Ethical Considerations in a Clinical Trial	p. 9
1.3.2 Types of Clinical Trials	p. 10
1.3.3 The Phases of a Clinical Trial	p. 11
1.4 Data Set Descriptions	p. 12
1.4.1 Birth Weight Data Set	p. 12
1.4.2 Body Fat Data Set	p. 12
1.4.3 Coronary Heart Disease Data Set	p. 12
1.4.4 Prostate Cancer Study Data Set	p. 13
1.4.5 Intensive Care Unit Data Set	p. 14
1.4.6 Mammography Experience Study Data Set	p. 14
1.4.7 Benign Breast Disease Study	p. 15
Glossary	p. 17
Exercises	p. 18
Chapter 2 Describing Populations	p. 23
2.1 Populations and Variables	p. 23
2.1.1 Qualitative Variables	p. 24
2.1.2 Quantitative Variables	p. 25
2.1.3 Multivariate Data	p. 27
2.2 Population Distributions and Parameters	p. 28
2.2.1 Distributions	p. 29
2.2.2 Describing a Population with Parameters	p. 33
2.2.3 Proportions and Percentiles	p. 33
2.2.4 Parameters Measuring Centrality	p. 35
2.2.5 Measures of Dispersion	p. 38
2.2.6 The Coefficient of Variation	p. 41
2.2.7 Parameters for Bivariate Populations	p. 43
2.3 Probability	p. 46
2.3.1 Basic Probability Rules	p. 48
2.3.2 Conditional Probability	p. 50
2.3.3 Independence	p. 52
2.4 Probability Models	p. 53
2.4.1 The Binomial Probability Model	p. 54
2.4.2 The Normal Probability Model	p. 57
2.4.3 Z Scores	p. 63
Glossary	p. 64
Exercises	p. 65
Chapter 3 Random Sampling	p. 76
3.1 Obtaining Representative Data	p. 76
3.1.1 The Sampling Plan	p. 78
3.1.2 Probability Samples	p. 78
3.2 Commonly Used Sampling Plans	p. 80
3.2.1 Simple Random Sampling	p. 80
3.2.2 Stratified Random Sampling	p. 84
3.2.3 Cluster Sampling	p. 86
3.2.4 Systematic Sampling	p. 88
3.3 Determining the Sample Size	p. 89
3.3.1 The Sample Size for a Simple Random Sample	p. 89
3.3.2 The Sample Size for a Stratified Random Sample	p. 93
3.3.3 Determining the Sample Size in a Systematic Random Sample	p. 99
Glossary	p. 100
Exercises	p. 102
Chapter 4 Summarizing Random Samples	p. 109
4.1 Samples and Inferential Statistics	p. 109
4.2 Inferential Graphical Statics	p. 110
4.2.1 Bar and Pie Charts	p. 111
4.2.2 Boxplots	p. 114
4.2.3 Histograms	p. 120
4.2.4 Normal Probability Plots	p. 126
4.3 Numerical Statistics for Univariate Data Sets	p. 129
4.3.1 Estimating Population Proportions	p. 129
4.3.2 Estimating Population Percentiles	p. 136
4.3.3 Estimating the Mean, Median, and Mode	p. 137
4.3.4 Estimating the Variance and Standard Deviation	p. 143
4.3.5 Linear Transformations	p. 148
4.3.6 The Plug-in Rule for Estimation	p. 151
4.4 Statistics for Multivariate Data Sets	p. 153
4.4.1 Graphical Statistics for Bivariate Data Sets	p. 154
4.4.2 Numerical Summaries for Bivariate Data Sets	p. 156
4.4.3 Fitting Lines to Scatterplots	p. 161
Glossary	p. 163
Exercises	p. 166
Chapter 5 Measuring the Reliability of Statistics	p. 181
5.1 Sampling Distributions	p. 181
5.1.1 Unbiased Estimators	p. 183
5.1.2 Measuring the Accuracy of an Estimator	p. 184
5.1.3 The Bound on the Error of Estimation	p. 186
5.2 The Sampling Distribution of a Sample Proportion	p. 187
5.2.1 The Mean and Standard Deviation of the Sampling Distribution of &pcirc;	p. 187
5.2.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation	p. 190
5.2.3 The Central Limit Theorem for &pcirc;	p. 191
5.2.4 Some Final Notes on the Sampling Distribution of &pcirc;	p. 192
5.3 The Sampling Distribution of &xbar;	p. 193
5.3.1 The Mean and Standard Deviation of the Sampling Distribution of &xbar;	p. 193
5.3.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation	p. 196
5.3.3 The Central Limit Theorem for &xbar;	p. 197
5.3.4 The t Distribution	p. 199
5.3.5 Some Final Notes on the Sampling Distribution of &xbar;	p. 201
5.4 Comparisons Based on Two Samples	p. 202
5.4.1 Comparing Two Population Proportions	p. 203
5.4.2 Comparing Two Population Means	p. 209
5.5 Bootstrapping the Sampling Distribution of a Statistic	p. 215
Glossary	p. 218
Exercises	p. 219
Chapter 6 Confidence Intervals	p. 229
6.1 Interval Estimation	p. 229
6.2 Confidence Intervals	p. 230
6.3 Single Sample Confidence Intervals	p. 232
6.3.1 Confidence Intervals for Proportions	p. 233
6.3.2 Confidence Intervals for a Mean	p. 236
6.3.3 Large Sample Confidence Intervals for µ	p. 237
6.3.4 Small Sample Confidence Intervals for µ	p. 238
6.3.5 Determining the Sample Size for a Confidence Interval for the Mean	p. 241
6.4 Bootstrap Confidence Intervals	p. 243
6.5 Two Sample Comparative Confidence Intervals	p. 244
6.5.1 Confidence Intervals for Comparing Two Proportions	p. 244
6.5.2 Confidence Intervals for the Relative Risk	p. 249
Glossary	p. 252
Exercises	p. 253
Chapter 7 Testing Statistical Hypotheses	p. 265
7.1 Hypothesis Testing	p. 265
7.1.1 The Components of a Hypothesis Test	p. 265
7.1.2 P-Values and Significance Testing	p. 272
7.2 Testing Hypotheses about Proportions	p. 276
7.2.1 Single Sample Tests of a Population Proportion	p. 276
7.2.2 Comparing Two Population Proportions	p. 282
7.2.3 Tests of Independence	p. 287
7.3 Testing Hypotheses about Means	p. 295
7.3.1 t-Tests	p. 295
7.3.2 t-Tests for the Mean of a Population	p. 298
7.3.3 Paired Comparison t-Tests	p. 302
7.3.4 Two Independent Sample t-Tests	p. 307
7.4 Some Final Comments on Hypothesis Testing	p. 313
Glossary	p. 314
Exercises	p. 315
Chapter 8 Simple Linear Regression	p. 333
8.1 Bivariate Data, Scatterplots, and Correlation	p. 333
8.1.1 Scatterplots	p. 333
8.1.2 Correlation	p. 336
8.2 The Simple Linear Regression Model	p. 340
8.2.1 The Simple Linear Regression Model	p. 341
8.2.2 Assumptions of the Simple Linear Regression Model	p. 343
8.3 Fitting a Simple Linear Regression Model	p. 344
8.4 Assessing the Assumptions and Fit of a Simple Linear Regression Model	p. 347
8.4.1 Residuals	p. 348
8.4.2 Residual Diagnostics	p. 348
8.4.3 Estimating and Assessing the Strength of the Linear Relationship	p. 355
8.5 Statistical Inferences based on a Fitted Model	p. 358
8.5.1 Inferences about ß 0	p. 359
8.5.2 Inferences about ß 1	p. 360
8.6 Inferences about the Response Variable	p. 363
8.6.1 Inferences About µy\|x	p. 363
8.6.2 Inferences for Predicting Values of Y	p. 365
8.7 Some Final Comments on Simple Linear Regression	p. 366
Glossary	p. 369
Exercises	p. 371
Chapters 9 Multiple Regression	p. 383
9.1 Investigating Multivariate Relationships	p. 385
9.2 The Multiple Linear Regression Model	p. 387
9.2.1 The Assumptions of a Multiple Regression Model	p. 388
9.3 Fitting a Multiple Linear Regression Model	p. 390
9.4 Assessing the Assumptions of a Multiple Linear Regression Model	p. 390
9.4.1 Residual Diagnostics	p. 394
9.4.2 Detecting Multivariate Outliers and Influential Observations	p. 399
9.5 Assessing the Adequacy of Fit of a Multiple Regression Model	p. 401
9.5.1 Estimating ¿	p. 401
9.5.2 The Coefficient of Determination	p. 401
9.5.3 Multiple Regression Analysis of Variance	p. 403
9.6 Statistical Inferences-Based Multiple Regression Model	p. 406
9.6.1 Inferences about the Regression Coefficients	p. 406
9.6.2 Inferences about the Response Variable	p. 408
9.7 Comparing Multiple Regression Models	p. 410
9.8 Multiple Regression Models with Categorical Variables	p. 413
9.8.1 Regression Models with Dummy Variables	p. 415
9.8.2 Testing the Importance of Categorical Variables	p. 418
9.9 Variable Selection Techniques	p. 421
9.9.1 Model Selection Using Maximum R 2 adj	p. 422
9.9.2 Model Selection using BIC	p. 424
9.10 Some Final Comments on Multiple Regression	p. 425
Glossary	p. 427
Exercises	p. 429
Chapter 10 Logistic Regression	p. 446
10.1 Odds and Odds Ratios	p. 447
10.2 The Logistic Regression Model	p. 450
10.2.1 Assumptions of the Logistic Regression Model	p. 452
10.3 Fitting a Logistic Regression Model	p. 454
10.4 Assessing the Fit of a Logistic Regression Model	p. 456
10.4.1 Checking the Assumptions of a Logistic Regression Model	p. 456
10.4.2 Testing for the Goodness of Fit of a Logistic Regression Model	p. 458
10.4.3 Model Diagnostics	p. 459
10.5 Statistical Inferences Based on a Logistic Regression Model	p. 465
10.5.1 Inferences about the Logistic Regression Coefficients	p. 465
10.5.2 Comparing Models	p. 467
10.6 Variable Selection	p. 470
10.7 Some Final Comments on Logistic Regression	p. 473
Glossary	p. 474
Exercises	p. 476
Chapter 11 Design Of Experiments	p. 487
11.1 Experiments versus Observational Studies	p. 487
11.2 The Basic Principles of Experimental Design	p. 490
11.2.1 Terminology	p. 490
11.2.2 Designing an Experiment	p. 491
11.3 Experimental Designs	p. 493
11.3.1 The Completely Randomized Design	p. 495
11.3.2 The Randomized Block Design	p. 498
11.4 Factorial Experiments	p. 500
11.4.1 Two-Factor Experiments	p. 502
11.4.2 Three-Factor Experiments	p. 504
11.5 Models for Designed Experiments	p. 506
11.5.1 The Model for a Completely Randomized Design	p. 506
11.5.2 The Model for a Randomized Block Design	p. 508
11.5.3 Models for Experimental Designs with a Factorial Treatment Structure	p. 509
11.6 Some Final Comments of Designed Experiments	p. 511
Glossary	p. 511
Exercises	p. 513
Chapter 12 Analysis Of Variance	p. 520
12.1 Single-Factor Analysis of Variance	p. 521
12.1.1 Partitioning the Total Experimental Variation	p. 523
12.1.2 The Model Assumptions	p. 524
12.1.3 The F-test	p. 527
12.1.4 Comparing Treatment Means	p. 528
12.2 Randomized Block Analysis of Variance	p. 533
12.2.1 The ANOV Table for the Randomized Block Design	p. 534
12.2.2 The Model Assumptions	p. 536
12.2.3 The F-test	p. 538
12.2.4 Separating the Treatment Means	p. 539
12.3 Multifactor Analysis of Variance	p. 542
12.3.1 Two-factor Analysis of Variance	p. 542
12.3.2 Three-factor Analysis of Variance	p. 550
12.4 Selecting the Number of Replicates in Analysis of Variance	p. 555
12.4.1 Determining the Number of Replicates from the Power	p. 555
12.4.2 Determining the Number of Replicates from D	p. 556
12.5 Some Final Comments on Analysis of Variance	p. 557
Glossary	p. 558
Exercises	p. 559
Chapter 13 Survival Analysis	p. 575
13.1 The Kaplan-Meier Estimate of the Survival Function	p. 576
13.2 The Proportional Hazards Model	p. 582
13.3 Logistic Regression and Survival Analysis	p. 586
13.4 Some Final Comments on Survival Analysis	p. 588
Glossary	p. 589
Exercises	p. 590
References	p. 599
Appendix A p. 605
Problem Solutions	p. 613
Index	p. 643

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