Applied biostatistics for the health sciences

✍ Scribed by Richard J. Rossi

• Year: 2022
• Tongue: English
• Leaves: 685
• Edition: Second
• Category: Library

✦ Table of Contents

APPLIED BIOSTATISTICS FOR THE HEALTH SCIENCES
PREFACE
Contents
CHAPTER 1 INTRODUCTION TO BIOSTATISTICS
1.1 What is Biostatistics
1.2 Populations, Samples, and Statistics
1.2.1 The Basic Biostatistical Terminology
1.2.2 Biomedical Studies
1.2.3 Observational Studies Versus Experiments
1.3 Clinical Trials
1.3.1 Safety and Ethical Considerations in a Clinical Trial
1.3.2 Types of Clinical Trials
1.3.3 The Phases of a Clinical Trial
1.4 Data Set Descriptions
1.4.1 Birth Weight Data Set
1.4.2 Body Fat Data Set
1.4.3 Coronary Heart Disease Data Set
1.4.4 Prostate Cancer Study Data Set
1.4.5 Intensive Care Unit Data Set
1.4.6 Mammography Experience Study Data Set
1.4.7 Benign Breast Disease Study
1.4.8 Exerbike Data Sets
Glossary
Exercises
CHAPTER 2 DESCRIBING POPULATIONS
2.1 Populations and Variables
2.1.1 Qualitative Variables
2.1.2 Quantitative Variables
2.1.3 Multivariate Data
2.2 Population Distributions and Parameters
2.2.1 Distributions
2.2.2 Describing a Population with Parameters
2.2.3 Proportions and Percentiles
2.2.4 Parameters Measuring Centrality
2.2.5 Measures of Dispersion
2.2.6 The Coefficient of Variation
2.2.7 Parameters for Bivariate Populations
2.3 Probability
2.3.1 Basic Probability Rules
2.3.2 Conditional Probability
2.3.3 Independence
2.3.4 The Relative Risk and the Odds Ratio
2.4 Probability Models
2.4.1 The Binomial Probability Model
2.4.2 The Normal Probability Model
2.4.3 Z Scores
Glossary
Exercises
CHAPTER 3 RANDOM SAMPLING
3.1 Obtaining Representative Data
3.1.1 The Sampling Plan
3.1.2 Probability Samples
3.2 Commonly Used Sampling Plans
3.2.1 Simple Random Sampling
3.2.2 Stratified Random Sampling
3.2.3 Cluster Sampling
3.2.4 Systematic Sampling
3.3 Determining the Sample Size
3.3.1 The Sample Size for Simple and Systematic Random Samples
3.3.2 The Sample Size for a Stratified Random Sample
Glossary
Exercises
CHAPTER 4 SUMMARIZING RANDOM SAMPLES
4.1 Samples and Inferential Statistics
4.2 Inferential Graphical Statistics
4.2.1 Bar and Pie Charts
4.2.2 Boxplots
4.2.3 Histograms
4.2.4 Normal Probability Plots
4.3 Numerical Statistics for Univariate Data Sets
4.3.1 Estimating Population Proportions
4.3.2 Estimating Population Percentiles
4.3.3 Estimating the Mean, Median, and Mode
4.3.4 Estimating the Variance and Standard Deviation
4.3.5 Linear Transformations
4.3.6 The Plug-in Rule for Estimation
4.4 Statistics for Multivariate Data Sets
4.4.1 Graphical Statistics for Bivariate Data Sets
4.4.2 Numerical Summaries for Bivariate Data Sets
4.4.3 Fitting Lines to Scatterplots
Glossary
Exercises
CHAPTER 5 MEASURING THE RELIABILITY OF STATISTICS
5.1 Sampling Distributions
5.1.1 Unbiased Estimators
5.1.2 Measuring the Accuracy of an Estimator
5.1.3 The Bound on the Error of Estimation
5.2 The Sampling Distribution of a Sample Proportion
5.2.1 The Mean and Standard Deviation of the Sampling Distribution of ˆ𝑝
5.2.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation
5.2.3 The Central Limit Theorem for ˆp
5.2.4 Some Final Notes on the Sampling Distribution of ˆp
5.3 The Sampling Distribution of 𝑥
5.3.1 The Mean and Standard Deviation of the Sampling Distribution of 𝑥
5.3.2 Determining the Sample Size for a Prespecified Value of the Bound on the Error Estimation
5.3.3 The Central Limit Theorem for 𝑥
5.3.4 The t Distribution
5.3.5 Some Final Notes on the Sampling Distribution of 𝑥
5.4 Two Sample Comparisons
5.4.1 Comparing Two Population Proportions
5.4.2 Comparing Two Population Means
5.5 Bootstrapping the Sampling Distribution of a Statistic
Glossary
Exercises
CHAPTER 6 CONFIDENCE INTERVALS
6.1 Interval Estimation
6.2 Confidence Intervals
6.3 Single Sample Confidence Intervals
6.3.1 Confidence Intervals for Proportions
6.3.2 Confidence Intervals for a Mean
6.3.3 Large Sample Confidence Intervals for 𝜇
6.3.4 Small Sample Confidence Intervals for 𝜇
6.3.5 Determining the Sample Size for a Confidence Interval for the Mean
6.4 Bootstrap Confidence Intervals
6.5 Two Sample Comparative Confidence Intervals
6.5.1 Confidence Intervals for Comparing Two Proportions
6.5.2 Confidence Intervals for the Relative Risk
6.5.3 Confidence Intervals for the Odds Ratio
Glossary
Exercises
CHAPTER 7 TESTING STATISTICAL HYPOTHESES
7.1 Hypothesis Testing
7.1.1 The Components of a Hypothesis Test
7.1.2 P-Values and Significance Testing
7.2 Testing Hypotheses about Proportions
7.2.1 Single Sample Tests of a Population Proportion
7.2.2 Comparing Two Population Proportions
7.2.3 Tests of Independence
7.3 Testing Hypotheses About Means
7.3.1 t-Tests
7.3.2 t-Tests for the Mean of a Population
7.3.3 Paired Comparison t-Tests
7.3.4 Two Independent Sample t-Tests
7.4 7.4 Some Final Comments on Hypothesis Testing
Glossary
Exercises
CHAPTER 8 SIMPLE LINEAR REGRESSION
8.1 Bivariate Data, Scatterplots, and Correlation
8.1.1 Scatterplots
8.1.2 Correlation
8.2 The Simple Linear Regression Model
8.2.1 The Simple Linear Regression Model
8.2.2 Assumptions of the Simple Linear Regression Model
8.3 Fitting a Simple Linear Regression Model
8.4 Assessing the Assumptions and Fit of a Simple Linear Regression Model
8.4.1 Residuals
8.4.2 Residual Diagnostics
8.4.3 Estimating 𝜎 and Assessing the Strength of the Linear Relationship
8.5 Statistical Inferences based on a Fitted Model
8.5.1 Inferences About 𝛽𝟎
8.5.2 Inferences About 𝛽𝟏
8.6 Inferences about the Response Variable
8.6.1 Inferences About 𝜇Y|X
8.6.2 Inferences for Predicting Values of Y
8.7 Model Validation
8.7.1 Selecting the Training and Validation Data Sets
8.7.2 Validating a Fitted Model
8.8 Some Final Comments on Simple Linear Regression
Glossary
Exercises
CHAPTER 9 MULTIPLE REGRESSION
9.1 Investigating Multivariate Relationships
9.2 The Multiple Linear Regression Model
9.2.1 The Assumptions of a Multiple Regression Model
9.3 Fitting a Multiple Linear Regression Model
9.4 Assessing the Assumptions of a Multiple Linear Regression Model
9.4.1 Residual Diagnostics
9.4.2 Detecting Multivariate Outliers and Influential Observations
9.5 Assessing the Adequacy of Fit of a Multiple Regression Model
9.5.1 Estimating 𝜎
9.5.2 The Coefficient of Determination
9.5.3 Multiple Regression Analysis of Variance
9.6 Statistical Inferences-Based Multiple Regression Model
9.6.1 Inferences about the Regression Coefficients
9.6.2 Inferences About the Response Variable
9.7 Comparing Multiple Regression Models
9.8 Multiple Regression Models with Categorical Variables
9.8.1 Regression Models with Dummy Variables
9.8.2 Testing the Importance of Categorical Variables
9.9 Variable Selection Techniques
9.9.1 Model Selection Using Maximum 𝑅2
adj
9.9.2 Model Selection using BIC
9.10 Model Validation
9.10.1 Selecting the Training and Validation Data Sets
9.10.2 Validating a Fitted Model
9.11 Some Final Comments on Multiple Regression
Glossary
Exercises
CHAPTER 10 LOGISTIC REGRESSION
10.1 The Logistic Regression Model
10.1.1 Assumptions of the Logistic Regression Model
10.1.1 Assumptions of the Logistic
Regression Model
10.2 Fitting a Logistic Regression Model
10.3 Assessing the Fit of a Logistic Regression
Model
10.3.1 Checking the Assumptions of a
Logistic Regression Model
10.3.2 Testing for the Goodness of Fit of
a Logistic Regression Model
10.3.3 Model Diagnostics
10.4 Statistical Inferences Based on a
Logistic Regression Model
10.4.1 Inferences about the Logistic
Regression Coefficients
10.4.2 Comparing Models
10.5 Variable Selection
10.6 Classification with Logistic
Regression
10.6.1 The Logistic Classifier
10.6.2 Misclassification Errors
10.7 Some Final Comments on Logistic
Regression
Glossary
Exercises
CHAPTER 11 DESIGN OF EXPERIMENTS
11.1 Experiments Versus Observational
Studies
11.2 The Basic Principles of Experimental
Design
11.2.1 Terminology
11.2.2 Designing an Experiment
11.3 Experimental Designs
11.3.1 The Completely Randomized
Design
11.3.2 The Randomized Block
Design
11.4 Factorial Experiments
11.4.1 Two-Factor Experiments
11.4.2 Three-Factor Experiments
11.5 Models for Designed Experiments
11.5.1 The Model for a Completely
Randomized Design
11.5.2 The Model for a Randomized
Block Design
11.5.3 Models for Experimental Designs
with a Factorial Treatment
Structure
11.6 Some Final Comments of Designed
Experiments
Glossary
Exercises
CHAPTER 12 ANALYSIS OF VARIANCE
12.1 Single-Factor Analysis of Variance
12.1.1 Partitioning the Total Experimental
Variation
12.1.2 The Model Assumptions
12.1.3 The 𝐹-test
12.1.4 Comparing Treatment Means
12.2 Randomized Block Analysis of
Variance
12.2.1 The ANOV Table for the
Randomized Block Design
12.2.2 The Model Assumptions
12.2.3 The 𝐹-test
12.2.4 Separating the Treatment Means
12.3 Multi factor Analysis of Variance
12.3.1 Two-Factor Analysis of
Variance
12.3.2 Three-Factor Analysis of
Variance
12.4 Selecting the Number of Replicates in
Analysis of Variance
12.4.1 Determining the Number of
Replicates from the Power
12.4.2 Determining the Number of
Replicates from 𝐷
12.5 Some Final Comments on Analysis of
Variance
Glossary
Exercises
CHAPTER 13 SURVIVAL ANALYSIS
13.1 The Kaplan–Meier Estimate of the
Survival Function
13.2 The Proportional Hazards
Model
13.3 Logistic Regression and Survival
Analysis
13.4 Some Final Comments on Survival
Analysis
Glossary
Exercises
REFERENCES
APPENDIX A
PROBLEM SOLUTIONS
INDEX
EULA