Table of Contents
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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 |
46 |
2.3.2 |
Conditional
Probability |
So |
2.3.3 |
|
52 |
2.4 |
Probability
Models |
53 |
2.4.1 |
The
Binomial Probability Model |
54 |
2.4.2 |
The |
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 |
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|Z |
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 |
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