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Biostatistics
A Guide to Design, Analysis and Discovery
2nd Edition - December 14, 2006
Authors: Ronald N. Forthofer, Eun Sul Lee, Mike Hernandez
Hardback ISBN:
9 7 8 - 0 - 1 2 - 3 6 9 4 9 2 - 8
eBook ISBN:
9 7 8 - 0 - 0 8 - 0 4 6 7 7 2 - 6
Biostatistics, Second Edition, is a user-friendly guide on biostatistics, which focuses on the proper use and interpretation of statistical methods. This textbook does not require… Read more
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Biostatistics, Second Edition, is a user-friendly guide on biostatistics, which focuses on the proper use and interpretation of statistical methods.
This textbook does not require extensive background in mathematics, making it user-friendly for all students in the public health sciences field. Instead of highlighting derivations of formulas, the authors provide rationales for the formulas, allowing students to grasp a better understanding of the link between biology and statistics.
The material on life tables and survival analysis allows students to better understand the recent literature in the health field, particularly in the study of chronic disease treatment. This updated edition contains over 40% new material with modern real-life examples, exercises, and references, including new chapters on Logistic Regression, Analysis of Survey Data, and Study Designs.
The book is recommended for students in the health sciences, public health professionals, and practitioners.
- Over 40% new material with modern real-life examples, exercises and references
- New chapters on Logistic Regression; Analysis of Survey Data; and Study Designs
- Introduces strategies for analyzing complex sample survey data
- Written in a conversational style more accessible to students with real data
Students in the health sciences, public health professionals, practitioners
1. INTRODUCTION
1.1 What is Biostatistics?
1.2 Data – The Key Component of a Study
1.3 Design – The Road to Relevant Data
1.4 Replication – Part of the Scientific Method
1.5 Applying Statistical Methods
Concluding Remarks
Exercises
References
2. DATA AND NUMBERS
2.1 Data: Numerical Representation
2.2 Observations and Variables
2.3 Scales Used with Variables
2.4 Reliability and Validity
2.5 Randomized Response Technique
2.6 Common Data Problems
Concluding Remarks
Exercises
References
3. DESCRIPTIVE METHODS
3.1 Introduction to Descriptive Methods
3.2 Tabular and Graphic Presentation of Data
3.2.1 Frequency Tables
3.2.2 Line Graphs
3.2.3 Bar Charts
3.2.4 Histograms
3.2.5 Stem-and-Leaf Plots
3.2.6 Dot Plots
3.2.7 Scatter Plots
3.3 Measures of Central Tendency
3.3.1 Mean, Median, and Mode
3.3.2 Use of the Measures of Central Tendency
3.3.3 The Geometric Mean
3.4 Measures of Variability
3.4.1 Ranges and Percentiles
3.4.2 Box Plots
3.4.3 Variance and Standard Deviation
3.5 Rates and Ratios
3.5.1 Crude and Specific Rates
3.5.2 Adjusted Rates
3.6 Measures of Change Over Time
3.6.1 Linear Growth
3.6.2 Geometric Growth
3.6.3 Exponential Growth
3.7 Correlation Coefficients
3.7.1 Pearson Correlation Coefficient
3.7.2 Spearman Rank Correlation Coefficient
Concluding Remarks
Exercises
References
4. PROBABILITY AND LIFE TABLES
4.1 A Definition of Probability
4.2 Rules for Calculating Probabilities
4.2.1 Addition Rule for Probabilities
4.2.2 Conditional Probabilities
4.2.3 Independent Events
4.3 Definitions from Epidemiology
4.3.1 Rates and Probabilities
4.3.2 Sensitivity, Specificity, and Predicted Value Positive and Negative
4.3.3 Receiver Operating Characteristic Plot
4.4 Bayes’ Theorem
4.5 Probability in Sampling
4.5.1 Sampling With Replacement
4.5.2 Sampling Without Replacement
4.6 Estimating Probabilities by Simulation
4.7 Probability and the Life Table
4.7.1 The First Four Columns of the Life Table
4.7.2 Some Uses of the Life Table
4.7.3 Expected Values in the Life Table
4.7.4 Other Expected Values in the Life Table
Concluding Remarks
Exercises
References
5. PROBABILITY DISTRIBUTIONS
5.1 The Binomial Distribution
5.1.1 Binomial Probabilities
5.1.2 Mean and Variance of the Binomial Distribution
5.1.3. Shapes of the Binomial Distribution
5.2 The Poisson Distribution
5.2.1 Poisson Probabilities
5.2.2 Mean and Variance of the Poisson Distribution
5.2.3 Finding Poisson Probabilities
5.3 The Normal Distribution
5.3.1 Normal Probabilities
5.3.2 Transforming to the Standard Normal Distribution
5.3.3 Calculation of Normal Probabilities
5.3.4 Normal Probability Plot
5.4 The Central Limit Theorem
5.5 Approximations to the Binomial and Poisson Distributions
5.5.1 Normal Approximation to the Binomial Distribution
5.5.2 Normal Approximation to the Poisson Distribution
Concluding Remarks
Exercises
References
6. STUDY DESIGNS
6.1 Design: Putting Chance to Work
6.2 Sample Surveys and Experiments
6.3 Sampling and Sample Designs
6.3.1 Sampling Frame
6.3.2 Importance of Probability Sampling
6.3.3 Simple Random Sampling
6.3.4 Systematic Sampling
6.3.5 Stratified Random Sampling
6.3.6 Cluster Sampling
6.3.7 Problems Due to Unintended Sampling
6.4 Designed Experiments
6.4.1 Comparison Groups and Randomization
6.4.2 Random Assignment
6.4.3 Sample Size
6.4.4 Single and Double Blind Experiments
6.4.5 Blocking and Extraneous Variables
6.4.6 Limitations of Experiments
6.5 Variations in Study Designs
6.5.1 The Cross-Over Design
6.5.2 The Case Control Design
6.5.3 The Cohort Study Design
Concluding Remarks
Exercises
References
7. INTERVAL ESTIMATION
7.1 Prediction, Confidence, and Tolerance Intervals
7.2 Distribution-Free Intervals
7.2.1 Prediction Interval
7.2.2 Confidence Interval
7.2.3 Tolerance Interval
7.3 Confidence Intervals Based on the Normal Distribution
7.3.1 Confidence Interval for the Mean
7.3.2 Confidence Interval for a Proportion
7.3.3 Confidence Interval for Crude and Adjusted Rates
7.4 Confidence Interval for the Difference of Two Means and Proportions
Difference of Two Independent Means
7.4.1 Difference of Two Dependent Means
7.4.2 Difference of Two Independent Proportions
7.4.3 Difference of Two Dependent Proportions
7.5 Confidence Interval and Sample Size
7.6 Confidence Interval for Other Measures
7.6.1 Confidence Interval for the Variance
7.6.2 Confidence Interval for Pearson Correlation Coefficient
7.7 Prediction and Tolerance Intervals Based on the Normal Distribution
7.7.1 Prediction Interval
7.7.2 Tolerance Interval
Concluding Remarks
Exercises
References
8. TESTS OF HYPOTHESES
8.1 Preliminaries in Tests of Hyppotheses
8.1.1 Definitions of Terms Used in Hypothesis Testing
8.1.2 Determination of Decision Rule
8.1.3 Relationship of the Decision Rule, á and â
8.1.4 Conducting the Test
8.2 Testing Hypotheses about the Mean
8.2.1 Known Variance
8.2.2 Unknown Varinace
8.3 Testing Hypotheses about the Proportion and Rates
8.4 Testing Hypotheses about the Variance
8.5 Testing Hypotheses about the Pearson Correlation Coefficient
8.6 Testing Hypotheses about the Difference of Two Means
8.6.1 Difference of Two Independent Means
8.6.2 Difference of Two Dependent Means
8.7 Testing Hypotheses about the Difference of Two Proportions
8.7.1 Difference of Two Independent Proportions
8.7.2 Difference of Two Dependent Means
8.8 Tests of Hypotheses and Sample Size
8.9 Statistical and Practical Significance
Concluding Remarks
Exercises
References
9. NONPARAMETRIC TESTS
9.1 Why Nonparametric Tests?
9.2 The Sign Test
9.3 The Wilcoxon Signed Rank Test
9.4 The Wilcoxon Rank Sum Test
9.5 The Kruskal-Wallis Test
9.6 The Friedman Test
Concluding Remarks
Exercises
References
10. ANALYSIS OF CATEGORICAL DATA
10.1 Goodness-of-Fit Test
10.2 The 2 by 2 Contingency Table
10.2.1 Comparing Two Independent Binomial Proportions
10.2.2 Expected Cell Counts Assuming No Association
10.2.3 The Odds Ratio – a Measure of Association
10.2.4 The Fisher’s Exact Test
10.2.5 Analysis of Paired Data: The McNemar Test
10.3 The r by c Contingency Table
10.3.1 Testing Hypothesis of Non Association: The Chi-Square Test
10.3.2 Testing Hypothesis of No Trend
10.4 Multiple 2 by 2 Tables
10.4.1 Analyzing the Tables Separately
10.4.2 The Cochran-Mantel-Haenszel Test
104.3 The Mantel-Haenszel Common Odds Ratio
Concluding Remarks
Exercises
References
11. ANALYSIS OF SURVIVAL DATA
11.1 Data Collection in Follow-Up Studies
11.2 The Life Table Method
11.3 The Product-Limit Method
11.4 Comparison of Two Survival Distributions
11.4.1 The Cochran-Mantel-Haenszel Test
11.4.2 The Log-Rank Test
Concluding Remarks
Exercises
References
12. ANALYSIS OF VARIANCE
12.1 Assumptions for the Use of the ANOVA
12.2 One-Way ANOVA
12.2.1 Sums of Squares and Mean Squares
12.2.2 The F Statistics
12.2.3 The ANOVA Table
12.3 Multiple Comparisons
12.3.1 Error Rates: Individual and Family
12.3.2 Tukey-Kramer Method
12.3.3 Fisher’s Least Significant Difference Method
12.3.4 Dunnett’s Method
12.4 Two-Way ANOVA for the Randomized Block Design with m Replicates
12.5 Two-Way ANOVA with Interaction
12.6 Linear Model Representation of the ANOVA
12.6.1 The Completely Randomized Design
12.6.2 The Randomized Block Design with m Replicates
12.6.3 Two-Way ANOVA with Interaction
12.7 ANOVA with Unequal Numbers of Observations in Subgroups
Concluding Remarks
Exercises
References
13. LINEAR REGRESSION
13.1 Simple Linear Regression
13.1.1 Estimation of Coefficients
13.1.2 The Variance of Y
1.1 What is Biostatistics?
1.2 Data – The Key Component of a Study
1.3 Design – The Road to Relevant Data
1.4 Replication – Part of the Scientific Method
1.5 Applying Statistical Methods
Concluding Remarks
Exercises
References
2. DATA AND NUMBERS
2.1 Data: Numerical Representation
2.2 Observations and Variables
2.3 Scales Used with Variables
2.4 Reliability and Validity
2.5 Randomized Response Technique
2.6 Common Data Problems
Concluding Remarks
Exercises
References
3. DESCRIPTIVE METHODS
3.1 Introduction to Descriptive Methods
3.2 Tabular and Graphic Presentation of Data
3.2.1 Frequency Tables
3.2.2 Line Graphs
3.2.3 Bar Charts
3.2.4 Histograms
3.2.5 Stem-and-Leaf Plots
3.2.6 Dot Plots
3.2.7 Scatter Plots
3.3 Measures of Central Tendency
3.3.1 Mean, Median, and Mode
3.3.2 Use of the Measures of Central Tendency
3.3.3 The Geometric Mean
3.4 Measures of Variability
3.4.1 Ranges and Percentiles
3.4.2 Box Plots
3.4.3 Variance and Standard Deviation
3.5 Rates and Ratios
3.5.1 Crude and Specific Rates
3.5.2 Adjusted Rates
3.6 Measures of Change Over Time
3.6.1 Linear Growth
3.6.2 Geometric Growth
3.6.3 Exponential Growth
3.7 Correlation Coefficients
3.7.1 Pearson Correlation Coefficient
3.7.2 Spearman Rank Correlation Coefficient
Concluding Remarks
Exercises
References
4. PROBABILITY AND LIFE TABLES
4.1 A Definition of Probability
4.2 Rules for Calculating Probabilities
4.2.1 Addition Rule for Probabilities
4.2.2 Conditional Probabilities
4.2.3 Independent Events
4.3 Definitions from Epidemiology
4.3.1 Rates and Probabilities
4.3.2 Sensitivity, Specificity, and Predicted Value Positive and Negative
4.3.3 Receiver Operating Characteristic Plot
4.4 Bayes’ Theorem
4.5 Probability in Sampling
4.5.1 Sampling With Replacement
4.5.2 Sampling Without Replacement
4.6 Estimating Probabilities by Simulation
4.7 Probability and the Life Table
4.7.1 The First Four Columns of the Life Table
4.7.2 Some Uses of the Life Table
4.7.3 Expected Values in the Life Table
4.7.4 Other Expected Values in the Life Table
Concluding Remarks
Exercises
References
5. PROBABILITY DISTRIBUTIONS
5.1 The Binomial Distribution
5.1.1 Binomial Probabilities
5.1.2 Mean and Variance of the Binomial Distribution
5.1.3. Shapes of the Binomial Distribution
5.2 The Poisson Distribution
5.2.1 Poisson Probabilities
5.2.2 Mean and Variance of the Poisson Distribution
5.2.3 Finding Poisson Probabilities
5.3 The Normal Distribution
5.3.1 Normal Probabilities
5.3.2 Transforming to the Standard Normal Distribution
5.3.3 Calculation of Normal Probabilities
5.3.4 Normal Probability Plot
5.4 The Central Limit Theorem
5.5 Approximations to the Binomial and Poisson Distributions
5.5.1 Normal Approximation to the Binomial Distribution
5.5.2 Normal Approximation to the Poisson Distribution
Concluding Remarks
Exercises
References
6. STUDY DESIGNS
6.1 Design: Putting Chance to Work
6.2 Sample Surveys and Experiments
6.3 Sampling and Sample Designs
6.3.1 Sampling Frame
6.3.2 Importance of Probability Sampling
6.3.3 Simple Random Sampling
6.3.4 Systematic Sampling
6.3.5 Stratified Random Sampling
6.3.6 Cluster Sampling
6.3.7 Problems Due to Unintended Sampling
6.4 Designed Experiments
6.4.1 Comparison Groups and Randomization
6.4.2 Random Assignment
6.4.3 Sample Size
6.4.4 Single and Double Blind Experiments
6.4.5 Blocking and Extraneous Variables
6.4.6 Limitations of Experiments
6.5 Variations in Study Designs
6.5.1 The Cross-Over Design
6.5.2 The Case Control Design
6.5.3 The Cohort Study Design
Concluding Remarks
Exercises
References
7. INTERVAL ESTIMATION
7.1 Prediction, Confidence, and Tolerance Intervals
7.2 Distribution-Free Intervals
7.2.1 Prediction Interval
7.2.2 Confidence Interval
7.2.3 Tolerance Interval
7.3 Confidence Intervals Based on the Normal Distribution
7.3.1 Confidence Interval for the Mean
7.3.2 Confidence Interval for a Proportion
7.3.3 Confidence Interval for Crude and Adjusted Rates
7.4 Confidence Interval for the Difference of Two Means and Proportions
Difference of Two Independent Means
7.4.1 Difference of Two Dependent Means
7.4.2 Difference of Two Independent Proportions
7.4.3 Difference of Two Dependent Proportions
7.5 Confidence Interval and Sample Size
7.6 Confidence Interval for Other Measures
7.6.1 Confidence Interval for the Variance
7.6.2 Confidence Interval for Pearson Correlation Coefficient
7.7 Prediction and Tolerance Intervals Based on the Normal Distribution
7.7.1 Prediction Interval
7.7.2 Tolerance Interval
Concluding Remarks
Exercises
References
8. TESTS OF HYPOTHESES
8.1 Preliminaries in Tests of Hyppotheses
8.1.1 Definitions of Terms Used in Hypothesis Testing
8.1.2 Determination of Decision Rule
8.1.3 Relationship of the Decision Rule, á and â
8.1.4 Conducting the Test
8.2 Testing Hypotheses about the Mean
8.2.1 Known Variance
8.2.2 Unknown Varinace
8.3 Testing Hypotheses about the Proportion and Rates
8.4 Testing Hypotheses about the Variance
8.5 Testing Hypotheses about the Pearson Correlation Coefficient
8.6 Testing Hypotheses about the Difference of Two Means
8.6.1 Difference of Two Independent Means
8.6.2 Difference of Two Dependent Means
8.7 Testing Hypotheses about the Difference of Two Proportions
8.7.1 Difference of Two Independent Proportions
8.7.2 Difference of Two Dependent Means
8.8 Tests of Hypotheses and Sample Size
8.9 Statistical and Practical Significance
Concluding Remarks
Exercises
References
9. NONPARAMETRIC TESTS
9.1 Why Nonparametric Tests?
9.2 The Sign Test
9.3 The Wilcoxon Signed Rank Test
9.4 The Wilcoxon Rank Sum Test
9.5 The Kruskal-Wallis Test
9.6 The Friedman Test
Concluding Remarks
Exercises
References
10. ANALYSIS OF CATEGORICAL DATA
10.1 Goodness-of-Fit Test
10.2 The 2 by 2 Contingency Table
10.2.1 Comparing Two Independent Binomial Proportions
10.2.2 Expected Cell Counts Assuming No Association
10.2.3 The Odds Ratio – a Measure of Association
10.2.4 The Fisher’s Exact Test
10.2.5 Analysis of Paired Data: The McNemar Test
10.3 The r by c Contingency Table
10.3.1 Testing Hypothesis of Non Association: The Chi-Square Test
10.3.2 Testing Hypothesis of No Trend
10.4 Multiple 2 by 2 Tables
10.4.1 Analyzing the Tables Separately
10.4.2 The Cochran-Mantel-Haenszel Test
104.3 The Mantel-Haenszel Common Odds Ratio
Concluding Remarks
Exercises
References
11. ANALYSIS OF SURVIVAL DATA
11.1 Data Collection in Follow-Up Studies
11.2 The Life Table Method
11.3 The Product-Limit Method
11.4 Comparison of Two Survival Distributions
11.4.1 The Cochran-Mantel-Haenszel Test
11.4.2 The Log-Rank Test
Concluding Remarks
Exercises
References
12. ANALYSIS OF VARIANCE
12.1 Assumptions for the Use of the ANOVA
12.2 One-Way ANOVA
12.2.1 Sums of Squares and Mean Squares
12.2.2 The F Statistics
12.2.3 The ANOVA Table
12.3 Multiple Comparisons
12.3.1 Error Rates: Individual and Family
12.3.2 Tukey-Kramer Method
12.3.3 Fisher’s Least Significant Difference Method
12.3.4 Dunnett’s Method
12.4 Two-Way ANOVA for the Randomized Block Design with m Replicates
12.5 Two-Way ANOVA with Interaction
12.6 Linear Model Representation of the ANOVA
12.6.1 The Completely Randomized Design
12.6.2 The Randomized Block Design with m Replicates
12.6.3 Two-Way ANOVA with Interaction
12.7 ANOVA with Unequal Numbers of Observations in Subgroups
Concluding Remarks
Exercises
References
13. LINEAR REGRESSION
13.1 Simple Linear Regression
13.1.1 Estimation of Coefficients
13.1.2 The Variance of Y
- No. of pages: 528
- Language: English
- Published: December 14, 2006
- Imprint: Academic Press
- Hardback ISBN: 9780123694928
- eBook ISBN: 9780080467726
RF
Ronald N. Forthofer
Affiliations and expertise
Boulder County, Colorado, U.S.A.EL
Eun Sul Lee
Affiliations and expertise
Oregon Health Science University, Portland, U.S.A.MH
Mike Hernandez
Mike Hernandez has been working as a statistical analyst in the Department of Biostatistics at the MD Anderson Cancer Center for over 10 years. Working in a large medical center, he has developed an expertise in doing collaborative research spanning several disciplines from health disparities to clinical trials. He has coauthored over 40 peer-reviewed manuscripts, and is a co-author of: Biostatistics: A Guide to Design, Analysis, and Discovery 2nd ed.
Affiliations and expertise
Anderson Cancer Center, Houston, TX, USA