Basic Biostatistics For Medical And Biomedical Practitioners

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BASIC BIOSTATISTICS
FOR MEDICAL AND
BIOMEDICAL
PRACTITIONERS
Copyright
About the Author
Preface
	References
Acknowledgments
Section I: Basic Aspects of Statistics
1
Basic Concepts
	Introduction
		Populations and samples
		The effects of variability
		Variables and parameters
	Basic Uses of Statistics
		Description
		Statistical inference
	Data
		Models
	General Approach to Study Design
		Replication and pseudoreplication
	A Brief History of Statistics
	References
2
Statistical Use and Misuse in Scientific Publications
	Early Use of Statistics
	Current-Tests in Common Use
	Statistical Misuse
	Basic Guides to Statistics
	References
3
Hypothesis Testing: Sample Size, Effect Size, Power, and Type II Errors
	Basic Concepts
		Statistical Power
		Effect Size
		Posthoc Power Analysis
	Appendix
		Calculation of Power
	References
4
Exploratory Descriptive Analysis
	Basic Concepts
		Counting
		Distribution
			A Sorting Experiment
			Histograms and Frequency Polygons
		Shapes of Distributions
			Transformations
		Stem and Leaf Diagrams
		Measures of Central Tendency (Location)
			Arithmetic Mean
			Median and Quantiles
			Mode
			The Geometric Mean
			Harmonic Mean
		Measures of Variability
			Range
			Standard Deviation
			Interquartile Distance
			Coefficient of Variation
		Tables and Graphs
			Tables
			Figures and Graphs
		Box Plots
	Advanced and Alternative Concepts
		Classical versus Robust Methods
			General Aspects
			Trimean
			Trimming and Winsorization
			Order Statistics
				Median Absolute Deviation
		Propagation of Errors
			Combining Experiments (Addition)
			Simple Multiplication (Scale Factor)
			Multiplying Means (Taylor, 1982)
			Dividing Means (Taylor, 1982)
		Three Useful Applications of the Variance
	Appendix
		Least Squares Principle
	References
5
Basic Probability
	Introduction
	Types of Probability
	Basic Principles and Definitions
		Additional definitions
		Other definitions
	Conditional Probability
	Bayes Theorem
	Worked Problems
	References
Section II: Continuous Distributions
6
Normal Distribution
	Introduction
	Normal or Gaussian Curve
		The Quincunx
		Properties of the Normal Curve
	Populations and Samples
	Description of the Distribution Shape
		Skewness
		Kurtosis
	Determining Normality
	Ungrouped Data
	How Important Is Normality?
	References
7
Statistical Inference: Confidence Limits and the Central Limit Theorem
	Central Limit Theorem
	Generalizations Based on a Single Sample
		Setting confidence limits
	Tolerance and Prediction Limits
	Reporting Results
	Graphic Representation
	References
8
Other Continuous Distributions
	Continuous Uniform Distribution
	Exponential Distribution
	Logarithmic Distribution
	Chi-square Distribution
	Variance Ratio (F) Distribution
	References
9
Outliers and Extreme Values
	Outliers
		Grubb\'s test
		Slippage and contamination
		Robust tests
		Dealing with outliers
	Extreme Values
	References
Section III: Hypothesis Testing
10
Hypothesis Testing: The Null Hypothesis, Significance and Type I Error
	Hypotheses
	Criticism of NHST
	Hypothesis Testing and Maximum Likelihood; the Bayes Factor
	Appendix
		Bayes Factor
		Terminology
		Type I Error and α
	References
11
Hypothesis Testing: Sample Size, Effect Size, Power, and Type II Errors
	Basic Concepts
		Statistical Power
		Effect Size
		Posthoc Power Analysis
	Appendix
		Calculation of Power
	References
Section IV: Discrete Distributions
12
Permutations and Combinations; Logarithms
	Permutations
	Combinations
	Logarithms
		Exponents
		Logarithms
		Antilogarithms
	Worked Problems
	References
13
Hypergeometric Distribution
	Introduction
	General Formula
	Fisher\'s Exact Test (Fisher-Irwin Test)
	Multiple Groups
	Reference
14
Categorical and Cross-Classified Data: Goodness of Fit and Association
	Basic Concepts
		Introduction
		Goodness of Fit
			Continuity Correction
		Degrees of Freedom
		2x2 Contingency Tables
			Practical Matters
		Odds Ratio
		Cautionary Tales
		Larger Contingency Tables
		Fisher\'s Exact Test
		Determining Power and Sample Size
	Advanced Concepts
		Cochran-Mantel-Haenszel (C-M-H) Test and Confounders
		Pooling Data
			Testing for Trends in Proportions (Cochran-Armitage Test)
		Problems With R x C Tables
		Multidimensional Tables
	References
15
Categorical and Cross-Classified Data: McNemar\'s and Bowker\'s Tests, Kolmogorov-Smirnov Tests, Concord
	Paired Samples: McNemars Test
	Bowker\'s Test
	Testing Ordered Categorical Data: Kolmogorov-Smirnov (K-S) Tests
		Kolmogoro-Smirnov One-Sample Test
		Kolmogorov-Smirnov Two-Sample Test
	Concordance (Agreement) Between Observers
		Two Categories
		More Than Two Categories
		Weighted Kappa
	References
16
Binomial and Multinomial Distributions
	Basic Concepts
		Introduction
			Bernoulli formula
		Binomial basics
		The normal approximation
		Fitting a binomial distribution to a set of trial results
		Cumulative binomial probabilities
		Confidence limits
			Continuity correction
		Comparing two binomial distributions
		Estimating sample size
		Comparing probabilities
	Advanced or Alternative Concepts
		Exact confidence limits
	Multinomial Distribution
	Appendix
	References
17
Proportions
	Introduction
	Proportions and Binomial Theorem
	Confidence Limits
	Sample and Population Proportions
	Sample Size
	Comparing Proportions
		Pooling samples
	References
18
The Poisson Distribution
	Introduction
	Relationship to the Binomial Distribution
	Goodness of Fit to a Poisson Distribution
	The Ratio of the Variance to the Mean of a Poisson Distribution
	Setting Confidence Limits
		Normal Approximation
		Exact Method
	The Square Root Transformation
	Cumulative Poisson Probabilities
	Differences Between Means of Poisson Distributions
		Comparison of Counts Based on Same Units
		Comparison of Counts Not Based on Same Units
		Comparing the Ratio of Two Poisson Variates
	Determining the Required Sample Size
	Appendix
	References
19
Negative Binomial Distribution
	Introduction
	Probability of r Successes
	Overdispersed Distribution
	Uses of the Negative Binomial
	References
Section V: Probability in Epidemiology and Medical Diagnosis
20
Odds Ratio, Relative Risk, Attributable Risk, and Number Needed to Treat
	Basic Concepts
		Introduction
			Cohort study
			Noncohort study
		Sample size and power
		Attributable risk
			Population attributable risk
		Relative risks below 1; number needed to treat
	Advanced Concepts
		Confidence limits for attributable risk
			Differences between proportions
			Difference between proportional ratios (Proportional AR and Proportional PAR)
		Confidence limits for NNT
	References
	Further Reading
21
Probability, Bayes Theorem, Medical Diagnostic Evaluation, and Screening
	Bayes Theorem Applied
	Sensitivity and Specificity
		Cautionary Tales
			Practical Issues of Screening Tests
			Spectrum Bias or Effect
			Verification Bias
		Likelihood Ratios
		Cutting Points
		ROC Curves
		Some Comments on Screening Tests
	References
Section VI: Comparing Means
22
Comparison of Two Groups: t-Tests and Nonparametric Tests
	Basic Concepts
		Introduction
		Paired t-Test
		Sample Size for Paired Test
		Unpaired t-Test
		Unequal Variances
		Sample Size for Unpaired Test
		Conclusion
		Nonparametric or Distribution-Free Tests
			The Wilcoxon Signed Rank Test
			The Sign Test
			The Mann-Whitney U-Test
				Requirements
	Advanced Concepts
		Comparing Two Coefficients of Variation
		The Paired t-Test Implies an Additive Model
		Confidence Limits for Medians
		Ranking Transforms
		The Meaning of the Mann-Whitney Test
		Problems
	References
23
t-Test Variants: Cross-Over Tests, Equivalence Tests
	Cross-Over Trials
		N of 1 Trials
	Equivalence and Noninferiority Testing
	References
24
Multiple Comparisons
	Introduction
	Bonferroni Correction and Equivalent Tests
		Error Rates
		Extreme Multiplicity and False Discovery Rates
	Group Sequential Boundaries
	Sequential Analysis
	Adaptive Methods
	References
25
Analysis of Variance. I. One-Way
	Basic Concepts
		Basic Test
			Requirements for Test
		Homogeneity of Variance
		Kruskal-Wallis Test
		Independence of Observations
		Effect Size
		Sample Size
	Advanced Concepts
		Multiple Comparisons
			Studentized Range Test
				Single Step Tests
				Multiple Step Tests
				Recommendations
			Linear Combinations
		Planned Experiments
	References
26
Analysis of Variance. II. More Complex Forms
	Basic Concepts
		Introduction
		Two-Way ANOVA
		Additivity
		Multiple Factors
		Friedman Test
		Cochrane\'s Q-Test
		Interaction
	Advanced and Alternative Concepts
		Missing Data or Unequal Cell Sizes
		Nested Designs
		Transformations
		Model II ANOVA
		More About Repeated Measures Designs
	Bibliography
Section VII: Regression and Correlation
27
Linear Regression
	Basic Concepts
		Introduction
		Exploratory Data Analysis
		Transforming Curves
		Model I Linear Regression Basics
		Additional Calculations
		Residuals
		Confidence Limits
		Comparison Methods (Basic)
	Advanced or Alternative Concepts
		Heteroscedasticity
		The Comparison Problem (Advanced)
		Comparing Two or More Lines
		Outliers
			Leverage
			Influence
		Ratio Measurements and Scaling Factors
	References
28
Variations Based on Linear Regression
	Transforming the Y Variate
	Inverse Prediction
	Line of Best Fit Passes Through Zero
	Errors in the X Variate
	Break Points
	Resistant Lines
	Appendix
		Derivation of Formulas for a Straight Line Passing Through Zero
	References
29
Correlation
	Basic Concepts
		Introduction
		P Values and Confidence Limits
		Sample Size and Power
		Ordinal Numbers
			Spearman\'s Test
			Kendall\'s Tau Test
	Advanced and Alternative Concepts
		Partial Correlation
		Spurious Correlation
		Ratios and Scaling Factors
		Intraclass Correlation
			Reliability
			Rater Agreement
	Appendix
		Related Expressions
	References
30
Multiple Regression
	Basic Concepts
		Introduction
		Multiple Linear Regression With Two X Variables
		Multiple Collinearity
		Prerequisites for Multiple Regression
		Determining the ``Best´´ Regression
			Which Is the Best Regression?
		Nonlinear Regression: Polynomial Regression
		Conclusions About Regression Methods in General
	Advanced Concepts and Examples
		Multiple Regression With Many Independent X Variates
			Analysis of Cystic Fibrosis Example
		Detecting Multicollinearity
		Determining the Correct Model
			All Subsets Regression
			Forward Selection
			Backward Elimination
		Nonlinear Regression: Polynomial Regression
			Splines
		Correcting for Multicollinearity
		Principles of Nonlinear Regression
		Dummy or Indicator Variables
		Multivariate Analysis
		Longitudinal Regression
	References
31
Serial Measurements: Time Series, Control Charts, Cusums
	Introduction
	Serial Correlation
		Wald-Wolfowitz Runs Test
		Up-and-Down Runs Test
		Rank von Neumann Ratio
		Ratio Measurements
	Control Charts
	Cumulative Sum Techniques
	Serial Measurements
	References
32
Dose-Response Analysis
	General Principles
	Quantal Dose-Response Curves
	References
33
Logistic Regression
	Introduction
	Single Explanatory Variable
	Multiple Explanatory Variables
	Appropriateness of Model
	References
34
Poisson Regression
	Introduction
	Suitability of Poisson Regression
	Detecting Overdispersion
	Correcting for Overdispersion
	References
Section VIII: Miscellaneous Topics
35
Survival Analysis
	Basic Concepts
		Introduction
		Basic Method
		Confidence Limits
		Comparison of Different Survival Curves
		Sample Size
	Advanced Concepts
		Calculating the Log-Rank Test
		The Hazard Function
		Hazard Ratio
		Cox Proportional Hazards Regression
		Competing Risks Analysis
	References
36
Meta-analysis
	Introduction
	Forest Graphs
	Funnel plots
	Radial Plots
	LAbbé Plots
	Appendix
	References
37
Resampling Statistics
	Introduction
	Bootstrap
	Permutations (or Randomization) Test
	Jackknife
	Monte Carlo Methods
	References
38
Design: Sampling, Clinical Trials
	Sampling Problems
	Historical Controls
	Randomization
	Clinical Trials
	Placebo Effect
	Alternatives to Randomized Clinical Trials
		Propensity Analysis
	References
Answers to Problems
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 11
	Chapter 12
	Chapter 13
	Chapter 14
	Chapter 15
	Chapter 16
	Chapter 17
	Chapter 18
	Chapter 19
	Chapter 20
	Chapter 22
	Chapter 25
	Chapter 26
	Chapter 27
	Chapter 29
	Chapter 31
	Chapter 35
Glossary
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z
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