# Statistics in Medicine

Statistics in Medicine, Fourth Edition, by Robert H. Riffenburgh and Daniel L. Gillen, is an excellent book, useful as a reference for researchers in the medical sciences and as a textbook. It focuses largely on understanding statistical concepts rather than on mathematical and theoretical underpinnings. The authors cover both introductory statistical techniques and advanced methods commonly appearing in medical journals.

The text begins with a discussion related to planning studies and writing articles to report results. Following this, it introduces statistics that would typically be covered in an introductory biostatistics course. These include summary statistics, distributions, two-way tables, confidence intervals, and hypothesis tests. In addition, the authors give an overview of a variety of more sophisticated statistical techniques such as regression models for binary and count outcomes, survival analysis, equivalence testing, Bayesian analysis, and meta-analysis.

PLANNING STUDIES: FROM DESIGN TO PUBLICATION
Organizing a Study
Stages of Scientific Investigation
Science Underlying Clinical Decision-Making
Why Do We Need Statistics?
Concepts in Study Design
Study Types
Convergence with Sample Size
Sampling Schemes in Observational Studies
Sampling Bias
Randomizing a Sample
How to Plan and Conduct a Study
Mechanisms to Improve Your Study Plan
Where Articles May Fall Short
Writing Medical Articles
Statistical Ethics in Medical Studies
Conclusion

PLANNING ANALYSIS: HOW TO REACH MY SCIENTIFIC OBJECTIVE
What Is in This Chapter
Notation (or Symbols)
Quantification and Accuracy
Data Types
Multivariable Concepts and Types of Adjustment Variables
How to Manage Data
Defining the Scientific Goal: Description, Association Testing, Prediction
Reporting Statistical Results
A First-Step Guide to Descriptive Statistics
An Overview of Association Testing
A Brief Discussion of Prediction Modeling

PROBABILITY AND RELATIVE FREQUENCY
Probability Concepts
Probability and Relative Frequency
Graphing Relative Frequency
Continuous Random Variables
Frequency Distributions for Continuous Variables
Probability Estimates From Continuous Distributions
Probability as Area Under the Curve

DISTRIBUTIONS
Characteristics of a Distribution
Greek Versus Roman Letters
What Is Typical
The Shape
Sampling Distribution of a Variable Versus a Statistic
Statistical Inference
Distributions Commonly Used in Statistics
Approximate Distribution of the Mean (Central Limit Theorem)
Approximate Distribution of a Sample Quantile

DESCRIPTIVE STATISTICS
Purpose of Descriptive Statistics
Numerical Descriptors, One Variable
Numerical Descriptors, Two Variables
Numerical Descriptors, Three Variables
Graphical Descriptors, One Variable
Graphical Descriptors, Two Variables
Graphical Descriptors, Three Variables
Principles of Informative Descriptive Tables and Figures

FINDING PROBABILITIES
Probability and Area Under the Curve
The Normal Distribution
The t Distribution
The Chi-Square Distribution
The F Distribution
The Binomial Distribution
The Poisson Distribution

HYPOTHESIS TESTING: CONCEPT AND PRACTICE
Hypotheses in Inference
Error Probabilities
Two Policies of Testing
Distinguishing Between Statistical and Clinical Significance
Controversies Regarding the Rigid Use and Abuse of p-Values
Avoiding Multiplicity Bias
Organizing Data for Inference

TOLERANCE, PREDICTION, AND CONFIDENCE INTERVALS
Overview
Tolerance Intervals for Patient Measurements
Concept of a Confidence Interval for a Parameter
Confidence Interval for a Population Mean, Known Standard Deviation
Confidence Interval for a Population Mean, Estimated Standard Deviation
Confidence Interval for a Population Proportion
Confidence Interval for a Population Median
Confidence Interval for a Population Variance or Standard Deviation
Confidence Interval for a Population Correlation Coefficient

TESTS ON CATEGORICAL DATA
Categorical Data Basics
Tests on Categorical Data: 2 × 2 Tables
The Chi-Square Test of Contingency
Fisher’s Exact Test of Contingency
Tests on r × c Contingency Tables
Tests on Proportion
Tests of Rare Events (Proportions Close to Zero)
McNemar’s Test: Matched Pair Test of a 2 × 2 Table
Cochran’s Q: Matched Pair Test of a 2 × r Table
Three or More Ranked Samples With Two Outcome Categories: Royston’s Ptrend Test

RISKS,ODDS, AND RECEIVER OPERATING CHARACTERISTIC CURVES
Association Measures for Categorical Data: Risks and Odds
Inference for the Risk Ratio: The Log Risk Ratio Test
Inference for the Odds Ratio: The Log Odds Ratio Test
Comparing Two Receiver Operating Characteristic Curves

TESTS OF LOCATION WITH CONTINUOU OUTCOMES
Basics of Location Testing
Single or Paired Means: One-Sample Normal (z) and t Tests
Two Means Two-Sample Normal (z) and t Tests
Three or More Means: One-Factor Analysis of Variance
Three or More Means in Rank Order: Analysis of Variance Trend Test
The Basics of Nonparametric Tests
Single or Paired Sample Distribution(s): The Signed-Rank Test
Two Independent Sample Distributions: The Rank-Sum Test
Large Sample-Ranked Outcomes
Three or More Independent Sample Distributions: The Kruskal—Wallis Test
Three or More Matched Sample Distributions: The Friedman Test
Three or More Ranked Independent Samples With Ranked Outcomes: Cusick’s Nptrend Test
Three or More Ranked Matched Samples With Ranked Outcomes: Page’s L Test
Potential Drawbacks to Using Nonparametric Tests

EQUIVALENCE TESTING
Concepts and Terms
Basics Underlying Equivalence Testing
Choosing a Noninferiority or Equivalence Margin
Methods for Noninferiority Testing
Methods for Equivalence Testing
Joint Difference and Equivalence Testing

TESTS ON VARIABILITY AND DISTRIBUTIONS
Basics of Tests on Variability
Testing Variability on a Single Sample
Testing Variability Between Two Samples
Testing Variability Among Three or More Samples
Basics on Tests of Distributions
Test of Normality of a Distribution
Test of Equality of Two Distributions

MEASURING ASSOCIATION AND AGREEMENT
What Are Association and Agreement?
Contingency as Association
Correlation as Association
Contingency as Agreement
Correlation as Agreement
Agreement Among Ratings: Kappa
Agreement Among Multiple Rankers
Reliability
Intraclass Correlation

LINEAR REGRESSION AND CORRELATION
Introduction
Regression Concepts and Assumptions
Simple Regression
Assessing Regression: Tests and Confidence Intervals
Deming Regression
Types of Regression
Correlation Concepts and Assumptions
Correlation Coefficients
Correlation as Related to Regression
Assessing Correlation: Tests and Confidence Intervals
Interpretation of Small-But-Significant Correlations
References

MULTIPLE LINEAR AND CURVILINEAR REGRESSION AND MULTIFACTOR ANALYSIS OF VARIANCE
Introduction
Multiple Linear Regression
Model Diagnosis and Goodness of Fit
Accounting for Heteroscedasticity
Curvilinear Regression
Two-Factor Analysis of Variance
Analysis of Covariance
Three-Way and Higher Way Analysis of Variance
Concepts of Experimental Design

LOGISTIC REGRESSION FOR BINARY OUTCOMES
Introduction
Extensions of Contingency Table Analyses Simple Logistic Regression
Multiple Logistic Regression Model Specification and Interpretation
Inference for Association Parameters
Model Diagnostics and Goodness-of-Fit

POISSON REGRESSION FOR COUNT OUTCOMES
Introduction
The Poisson Distribtution
Means Versus Rates
Inference for the Rate of a Poisson Random Variable
Comparing Poisson Rates From Two Independent Samples
The Simple Poisson Regression Model
Multiple Poisson Regression: Model Specification and Interpretation
Obtaining Predicted Rates
Inference for Association Parameters

ANALYSIS OF CENSORED TIME-TO-EVENT DATA
Survival Concepts
Censoring
Survival Estimation: Life Table Estimates and Kaplan—Meier Curves
Survival Testing: The Log-Rank Test
Adjusted Comparison of Survival Times: Cox Regression

ANALYSIS OF REPEATED CONTINUOUS MEASUREMENTS OVER TIME
Introduction
Distinguishing Longitudinal Data From Time-Series Data
Analysis of Longitudinal Data
Time-Series:
References

SAMPLE SIZE ESTIMATION
Issues in Sample Size Considerations
Is the Sample Size Estimate Adequate
The Concept of Power Analysis
Sample Size Methods
Test on One Mean (Normal Distribution)
Test on Two Means (Normal Distribution)
Tests When Distributions Are Nonnormal or Unknown
Test With No Objective Prior Data
Confidence Intervals on Means
Test of One Proportion (One Rate)
Test of Two Proportions (Two Rates)
Confidence Intervals on Proportions (On Rates)
Test on a Correlation Coefficient
Tests on Ranked Data
Variance Tests, Analysis of Variance, and Regression
Equivalence Tests
Number Needed to Treat or Benefit

CLINICAL TRIALS AND GROUP SEQUENTIAL TESTING
Introduction
Fundamentals of Clinical Trial Design
Reducing Bias in Clinical Trials Blinding and Randomization
Interim Analyses in Clinical Trials: Group Sequential Testing
References
Chpater 23 Epidemiology
The Nature of Epidemiology
Some Key Stages in the History of Epidemiology
Concept of Disease Transmission
Descriptive Measures
Types of Epidemiologic Studes
Retrospective Study Designs: The Case—Control Study Design
The Nested Case—Control Study Design
The Case—Cohort Study Design
Methods to Analyze Survival and Causal Factors
A historical note

META-ANALYSES
Introduction
Publication Bias in Meta-analyses
Fixed- and Random-Effects Estimates of the Pooled Effect
Tests for Heterogeneity of Estimated Effects Across Studies
Reporting the Results of a Meta-analysis
Further References

BAYESIAN STATISTICS
What Is Bayesian Statistics
Bayesian Concepts
Describing and Testing Means
On Parameters Other Than Means
Describing and Testing a Rate (Proportion)
Conclusion

QUESTIONNAIRES AND SURVEYS
Introduction
Surveys
Questionnaires
Chapter 27 Techniques to Aid Analysis
Interpreting Results
Significance in Interpretation
Post Hoc Confidence and Power
Multiple Tests and Significance
Bootstrapping, Resampling, and Simulation
Bland-Altman Plot: A Diagnostic Tool
Cost Effectiveness

METHODS YOU MIGHT MEET, BUT NOT EVERY DAY
Overview
Analysis of Variance Issues
Regression Issues
Rates and Proportions Issues
Multivariate Methods
Markov Chains: Following Multiple States through Time
Markov Chain Monte Carlo: Evolving Models
Markov Chain Monte Carlo: Stationary Models
Further Nonparametric Tests
Imputation of Missing Data
Frailty Models in Survival Analysis
Bonferroni “Correction”
Logit and Probit
Curve Fitting to Data
Sequential Analysis
Another Test of Normality
Data Mining
Data Science and The Relationship Among Statistics, Machine Learning, and Artificial Intelligence

Appendix 1: Answers to exercises: Final
Appendix 2: Databases
Appendix 3: Tables of probability distributions
Appendix 4: Symbol index
Statistical Subject Index
Medical Suject Index
Author: Robert H. Riffenburgh and Daniel L. Gillen
Edition: Fourth Edition
ISBN13: 978-0-12-815328-4