A Guide to Sample Size for Animal-based Studies

Cover
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgements
Part I What is Sample Size?
	Chapter 1 The Sample Size Problem in Animal-Based Research
		1.1 Organisation of the Book
		References
	Chapter 2 Sample Size Basics
		2.1 Introduction
		2.2 Experimental Unit
		2.3 Biological Unit
		2.4 Technical Replicates
		2.5 Repeats, Replicates, and Pseudo-Replication
			2.5.1 Repeats of Entire Experiments
			2.5.2 Pseudo-Replication
		References
	Chapter 3 Ten Strategies to Increase Information (and Reduce Sample Size)
		3.1 Introduction
		3.2 The \'Well-Built\' Research Question
		3.3 Structured Inputs (Experimental Design)
		3.4 Reduce Variation I: Process Control
		3.5 Reduce Variation II: Research Animals
		3.6 Reduce Variation III: Statistical Control
		3.7 Appropriate Comparators and Controls
			3.7.1 Types of Controls
			3.7.2 When Are Controls Unnecessary?
		3.8 Informative Outcome Variables
		3.9 Minimise Bias
		3.10 Think Sequentially
		3.11 Think \'Right-Sizing\', Not \'Significance\'
		References
Part II Sample Size for Feasibility and Pilot Studies
	Chapter 4 Why Pilot Studies?
		4.1 Introduction
		4.2 Pilot Study Applications
			4.2.1 The Role of Pilot Studies in Laboratory Animal-Based Research
			4.2.2 The Role of Pilot Studies in Veterinary Research
			4.2.3 Pilot Study Results Should Be Reported
		4.3 Pilot Studies: What They Are Not
			4.3.1 Pilot Studies Differ from Exploratory and Screening Studies
		4.4 Pilot Study Planning
			4.4.1 Principles
			4.4.2 Justification
				4.4.2.1 Literature Reviews
				4.4.2.2 Stakeholder Requirements
		4.5 What Kind of Pilot Trial?
		4.6 How Large a Pilot?
			4.6.1 Zero-Animal Sample Size
			4.6.2 Pragmatic Sample Size
			4.6.3 Precision-Based Sample Size
		References
	Chapter 5 Operational Pilot Studies: \'Can It Work?\'
		5.1 Introduction
		5.2 Operational Tools
			5.2.1 Process, or Workflow, Maps
			5.2.2 Checklists
			5.2.3 Run Charts, Process Behaviour Charts
		5.3 Performance Metrics
			5.3.1 Measurement Times
			5.3.2 Subjective Measurements
		5.4 Pilots for Retrospective Chart Review Studies
			5.4.1 Standardising Performance
		5.5 Sample Size Considerations
		References
	Chapter 6 Empirical and Translational Pilots
		6.1 Introduction
		6.2 Building in Evidentiary Strength
			6.2.1 Internal Validity
			6.2.2 External Validity
				6.2.2.1 Representativeness
				6.2.2.2 Sex as a Biological Variable
				6.2.2.3 Body Size and Allometric Scaling
		6.3 Sample Size Determination
			6.3.1 Information Density
			6.3.2 Information Power
			6.3.3 Veterinary Clinical Trials
			6.3.4 A Note on Safety and Tolerability
		6.4 Assessing Evidentiary Strength
			6.4.1 Exploratory Data Analysis
			6.4.2 Coverage Plots
			6.4.3 Sample Size From Confidence Intervals and Standard Deviation
			6.4.4 Profile Plots
			6.4.5 Half-Normal. Plots
			6.4.6 Interaction Plots
			6.4.7 Replication
			6.4.8 Design and Sample Size for Replication
		References
	Chapter 7 Feasibility Calculations: Arithmetic
		7.1 Introduction
		7.2 The Process
			7.2.1 Problem Structuring
			7.2.2 Calculations
			7.2.3 Reality Checks
			7.2.4 Refinement
		7.3 Determining Operational Feasibility
			7.3.1 Basic Science/Laboratory Studies
			7.3.2 Veterinary Clinical Trials
			7.3.3 High Dimensionality Studies
			7.3.4 Training, Teaching, Skill Acquisition
			7.3.5 Rodent Breeding Production
		References
	Chapter 8 Feasibility: Counting Subjects
		8.1 Introduction
		8.2 Normal Distribution
		8.3 Binomial (Exact) Distribution
			8.3.1 Rare or Non-Existent Events
		8.4 Batch Testing for Disease Detection
		8.5 Negative Binomial Distribution
		8.6 Hypergeometric Distribution
			8.6.1 Estimating the Proportion of Subjects with the Target Effect
		8.A Determining Cumulative Probabilities for Binomial, Negative Binomial, and Hypergeometric Distributions with SAS
			8.A.1 Binomial Distribution
			8.A.2 Negative Binomial Distribution
			8.A.3 Hypergeometric Distribution
		References
Part III Sample Size for Description
	Chapter 9 Descriptions and Summaries
		9.1 Introduction
		9.2 Describing Sample Data
		9.3 Describing Results
		9.4 Confidence and Other Intervals
		9.5 Relationship Between Interval Width, Power, and Significance
		References
	Chapter 10 Confidence Intervals and Precision
		10.1 Introduction
		10.2 Definitions
		10.3 Sample Size Calculations
			10.3.1 Absolute Versus Relative Precision
		10.4 Continuous (Normal) Outcome Data
			10.4.1 Simultaneous Confidence Intervals
		10.5 Proportions
		10.6 Multinomial samples
		10.7 Skewed Count Data
			10.7.1 Poisson Distribution
			10.7.2 Negative Binomial Distribution
		10.A SAS Code for Computing Simultaneous Confidence Intervals (Data from German et al. 2015)
		10.B Sample SAS Code for Computing Confidence Intervals for a Single Sample Proportion where x is the Number of Events, N is the Sample Size, and Proportion p = x/N (Adapted from Newcombe 1998; Hu 2015)
		10.C SAS Code for Calculating the Critical Values for z(α/2)/k and χ2α/k,1
		10.D SAS Code for Calculating Confidence Limits for Poisson Data
		10.E Evaluating Poisson and negative binomial distributions for fitting counts of red mites on apple leaves (Data from Bliss and Fisher 1953)
		References
	Chapter 11 Prediction Intervals
		11.1 Introduction
		11.2 Prediction Intervals: Continuous Data
			11.2.1 Continuous Data, Single Observation
			11.2.2 Continuous Data, Comparing Two Means
			11.2.3 Continuous Data, Linear Regression
		11.3 Prediction Intervals: Binary Data
		11.4 Prediction Intervals: Meta-Analyses
		References
	Chapter 12 Tolerance Intervals
		12.1 Introduction
		12.2 Tolerance Interval Width and Bounds
		12.3 Parametric Formulations
			12.3.1 Two-Sided Limits
			12.3.2 One-Sided Limits
		12.4 Non-parametric Tolerance Limits
		12.5 Determining Sample Size for Tolerance Intervals
		12.6 Sample Size for Tolerance Based on Permissible Number of Failures
		12.A SAS and R Code for Calculating Tolerance
			12.A.1 Solving for k
			12.A.2 SAS Code Racehorse Medication Threshold Limits for N = 20, Mean = 0.43 and Standard Deviation STD = 1.50
			12.A.3 R Code for Package Tolerance (Young 2010) for Racehorse Medication Threshold Limits
		References
	Chapter 13 Reference Intervals
		13.1 Introduction
		13.2 Constructing the Reference Interval
			13.2.1 Regression-Based Reference Ranges
		13.3 Sample Size Determination
			13.3.1 Rules of Thumb
			13.3.2 Sample-Based Coverage Methods
			13.3.3 Parametric Sample Size Estimates
			13.3.4 Non-parametric Sample Size Estimates
			13.3.5 Covariate-Dependent Sample Size Estimates
		References
Part IV Sample Size for Comparison
	Chapter 14 Sample Size and Hypothesis Testing
		14.1 Introduction
		14.2 Power and Significance
		14.3 Non-centrality
		14.4 Estimating Sample Size
			14.4.1 Non-central t-Distribution
			14.4.2 Non-central F-Distribution
		14.5 Sample Size Balance and Allocation Ratio
		References
	Chapter 15 A Bestiary of Effect Sizes
		15.1 Introduction
		15.2 Effect Size Basics
		15.3 d Family Effect Sizes
			15.3.1 The Basic Equation for Continuous Outcome Data
			15.3.2 Two-Group Comparisons, Continuous Outcomes, Independent Samples
		15.4 r Family (Strength of Association) Effect Sizes
			15.4.1 Correlation
			15.4.2 Regression
			15.4.3 Analysis of Variance (ANOVA) Methods
		15.5 Risk Family Effect Sizes
			15.5.1 Risk Difference, Relative Risk, and Odds Ratio
			15.5.2 Interpretation
			15.5.3 Nominal Variables: Cramer\'s V
		15.6 Time to Event Effect Size
		15.7 Interpreting Effect Sizes
			15.7.1 Interpreting Effect Sizes as Ratios
			15.7.2 What Is a Meaningful Effect Size?
		References
	Chapter 16 Comparing Two Groups: Continuous Outcomes
		16.1 Introduction
		16.2 Sample Size Calculation Methods
			16.2.1 Asymptotic Large-Scale. Approximation
			16.2.2 Sample Size Based on the t-Distribution
			16.2.3 Sample Size Derived From Percentage Change in Means
			16.2.4 Sample Size Rule of Thumb
		16.3 Which Standard Deviation?
			16.3.1 One-Sample Comparison
			16.3.2 Two Independent Samples
			16.3.3 Paired Samples or A/B Crossover Designs
		16.4 Sample Size for Two-Arm Veterinary Clinical Trials
		16.A Sample SAS Code for Calculating Sample Size for Two-Group Comparisons
			16.A.1 Sample Size Based on z-Distribution
			16.A.2 Total Sample Size Based on the Non-Centrality. Parameter for t
			16.A.3 Sample Size for a Fixed Power: Crossover Design (Cattle Example)
		16.B Sample SAS Code for Calculating Sample Size for a Veterinary Clinical Trial. The standard deviation obtained from pilot data is corrected by computation of its upper confidence interval (UCL) or by the inverse function of power and pilot degrees of freedom
			16.B.1 Conventional (Uncorrected Standard Deviation)
			16.B.2 Upper Confidence Interval Correction
			16.B.3 Simplified Non-Central t Correction
		References
	Chapter 17 Comparing Two Groups: Proportions
		17.1 Introduction
		17.2 Difference Between Two Proportions
			17.2.1 One Proportion Known
			17.2.2 Sex Ratios
			17.2.3 Two Independent Samples
			17.2.4 Confidence Intervals
		17.3 Relative Risk and Odds Ratio
			17.3.1 Relative Risk
			17.3.2 Odds Ratios
		17.4 Skewed Count Data
			17.4.1 Poisson Distribution
			17.4.2 Negative Binomial Distribution
		References
	Chapter 18 Time-to-Event (Survival) Data
		18.1 Introduction
		18.2 Methodological Considerations
			18.2.1 Define the Research Question
			18.2.2 Define All Survival-Related Items
			18.2.3 Randomisation Schedule
			18.2.4 Data Structure
			18.2.5 \'Responders\' Versus \'Non-Responders\' and Post Hoc Dichotomisation
		18.3 Outcome Data
			18.3.1 Count Data
			18.3.2 Survival Times
			18.3.3 Hazard Rate and Hazard Ratio
		18.4 Time-to-Event Sample Size Calculations
		18.5 Veterinary Clinical Trials
		18.6 Other Study Design Considerations
			18.6.1 More Than Two Groups
		References
	Chapter 19 Comparing Multiple Factors
		19.1 Introduction
		19.2 Design Components
			19.2.1 Constructing the F-Distribution
		19.3 Sample Size Determination Methods
			19.3.1 Effect Sizes
			19.3.2 Non-Centrality Parameter
			19.3.3 Mead\'s Resource Equation
			19.3.4 Skeleton ANOVA
		19.4 Completely Randomised Design, Single Factor
			19.4.1 Sample Size Approximations Based on Mean Differences
			19.4.2 Sample Size Approximations Based on Number of Levels for a Single Factor
			19.4.3 Sample Size Approximations Based on Expected Range of Variation
		19.5 Randomised Complete Block Design
		19.6 Factorial Designs
		19.7 Split-Plot Design
		19.8 Repeated-Measures (Within-Subject) Designs
			19.8.1 Before-After and Crossover Designs
			19.8.2 Repeated Measures on Time: Continuous Outcome
			19.8.3 Repeated Measures on Time: Proportions Outcome
			19.8.4 Repeated Measures in Space: Spatial Autocorrelation
		19.A Guinea-Pig Data: Sample SAS Code for Calculating Sample Size for a Single-Factor Four-Level (a) Completely Randomised Design; (b) Randomised Complete Block Design
			19.A.1 Completely Randomised Design
			19.A.2 Randomised Complete Block Design
		19.B Sample SAS Code for Calculating Sample Size per Group for a Simple Repeated-Measures Design
		References
	Chapter 20 Hierarchical or Nested Data
		20.1 Introduction
		20.2 Steps in Multilevel Sample Size Determinations
			20.2.1 Identify the Unit of Randomisation
			20.2.2 No Predictors
			20.2.3 Multilevel Models with Predictors
			20.2.4 Constructing the Model
		20.3 Estimating Effect Size
			20.3.1 Cohen\'s d
			20.3.2 Fixed Effects Regression Coefficients
			20.3.3 Intraclass Correlation Coefficient (ICC)
		20.4 Other Considerations: Balance, Sparse Data, Costs
			20.4.1 Balanced Versus Unbalanced Designs
			20.4.2 Sparse Data
			20.4.3 Costs
		20.5 Sample Size Determinations
			20.5.1 Rules of Thumb
			20.5.2 Sample Size Based on Design Effect
			20.5.3 Initial Approximations
			20.5.4 Asymptotic Normal Approximation: Balanced Cluster Sizes
			20.5.5 Asymptotic Normal Approximation: Unbalanced Cluster Sizes
			20.5.6 Sample Size Based on the Non-centrality Parameter
			20.5.7 Two-Level Model, Subjects Within Cluster as Unit of Randomisation
			20.5.8 Two-Level Model, Cluster as Unit of Randomisation
		21.A Sample SAS Code For Calculating Cohen’s k from Raw Data
		References
	Chapter 21 Ordinal Data
		21.1 Introduction
		21.2 Sample Size Considerations
		21.3 Sample Size Approximations
		21.4 Paired or Matched Ordinal Data
		21.5 Sample Size for Observer Agreement Studies
		References
	Chapter 22 Dose-Response Studies
		22.1 Introduction
		22.2 Sample Size Requirements
			22.2.1 Translational Considerations
		22.3 Dose-Response Regression Models
		22.4 Sample Size: Binary Response
		22.5 Sample Size: Continuous Response
			22.5.1 Linear Dose-Response
			22.5.2 Nonlinear Dose-Response
		22.A SAS Code for Dose-Response Calculations
		References
Index
EULA