Biostatistics

Biostatistics

A Guide to Design, Analysis and Discovery

2nd Edition - December 14, 2006

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  • Authors: Ronald Forthofer, Eun Lee, Mike Hernandez
  • eBook ISBN: 9780080467726
  • Hardcover ISBN: 9780123694928

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Description

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.

Key Features

  • 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

Readership

Students in the health sciences, public health professionals, practitioners

Table of Contents

  • 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|X
    13.1.3 The Coefficient of Determination (R2)
    13.2 Inference about the Coefficients
    13.2.1 Assumptions for Inference in Linear Regression
    13.2.2 Regression Diagnostics
    13.2.3 The Slope Coefficient
    13.2.4 The Y-Intercept Coefficient
    13.2.5 The ANOVA Summary Table
    13.3 Interval Estimation for and
    13.3.1 Confidence Interval for
    13.3.2 Prediction Interval for
    13.4 Multiple Linear Regression
    13.4.1 The Multiple Linear Regression Model
    13.4.2 Specification of a Multiple Linear Regression Model
    13.4.3 The Parameter Estimates, ANOVA, and Diagnostics
    13.4.4 Multicollinearity Problems
    13.4.5 Extending the Regression Model: Dummy Variables
    Concluding Remarks
    Exercises
    References


    14. LOGISTIC AND PROPORTIONAL HAZARD REGRESSION

    14.1 Introduction to Logistic Regression
    14.2 Simple Logistic Regression
    14.3 Multiple Logistic Regression
    14.4 Ordered Logistic Regression
    14.5 Introduction to Proportional Hazard Regression
    Concluding Remarks
    Exercises
    References


    15. ANALYSIS OF SURVEY DATA

    15.1 Introduction to Design-Based Inference
    15.2 Complex Design and Unequal Selection Probability
    15.2.1 Sample Weight
    15.2.2 Poststratification
    15.2.3 The Design Effect
    15.3 Strategies for Variance Estimation
    15.3.1 Replicated Sampling: A General Approach
    15.3.2 Balanced Repeated Replication
    15.3.3 Jackknife Repeated Replication
    15.3.4 Linearization Method
    15.4 Strategies for Analysis
    15.4.1 Preliminary Analysis
    15.4.2 Subpopulation Analysis
    15.4.3 Descriptive Analysis
    15.4.4 Contingency Table Analysis
    15.4.5 Linear and Logistic Regression Analysis
    Concluding Remarks
    Exercises
    References



    Appendices

    A. BASIC MATHEMATIC CONCEPTS

    B. STATISTICAL TABLES

    B1. Random Digits
    B2. Binomial Probabilities
    B3. Poisson Probabilities
    B4. Critical Values for the t Distribution
    B6. Charts for Confidence Intervals for the Proportion
    B7. Critical Values for the Chi-Square Distribution
    B8. Factors, k, for Two-Sided Tolerance Limits for Normal Distribution
    B9. Critical Values for the Wilcoxon Signed Rank Test
    B10. Critical Values for the Wilcoxon Rank Sum Test
    B11. Critical Values for the F Distribution
    B12. The Studentized Range for the Kramer-Tukey Procedure
    B13. The Studentized Range for the Dunnett Procedure


    C. SELECTED GOVERNMENTAL BIOSTATISTICAL DATA

    C1. Population Census Data
    C2. Vital Statistics
    C3. Sample Surveys
    C4. Life Tables


    D. SOLUTIONS TO SELECTED EXERCISES

Product details

  • No. of pages: 520
  • Language: English
  • Copyright: © Academic Press 2006
  • Published: December 14, 2006
  • Imprint: Academic Press
  • eBook ISBN: 9780080467726
  • Hardcover ISBN: 9780123694928

About the Authors

Ronald Forthofer

Affiliations and Expertise

Boulder County, Colorado, U.S.A.

Eun Lee

Affiliations and Expertise

Oregon Health Science University, Portland, U.S.A.

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

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