Cover
Preface
1 Basic Design Considerations
1. 1.1 Why Sample Size Calculations?
2. 1.2 Statistical Significance
3. 1.3 Planning Issues
4. 1.4 The Normal Distribution
5. 1.5 Distributions
6. 1.6 Confidence Intervals
7. 1.7 Use of Sample Size Tables
8. 1.8 Numerical Accuracy
9. 1.9 Software for Sample Size Calculations
10. References
2 Further Design Considerations
1. 2.1 Group Allocation
2. 2.2 More than Two Groups
3. 2.3 The Role of Covariates
4. 2.4 Multiple Endpoints
5. 2.5 Repeated Significance Tests
6. 2.6 Epidemiological Studies
7. 2.7 The Protocol and Publication
8. 2.8 Ethical Issues and Sample Size
9. References
3 Binary Outcomes
1. 3.1 Introduction
2. 3.2 Comparing Proportions
3. 3.3 One Proportion Known
4. 3.4 Bibliography
5. 3.5 Examples and Use of the Tables
6. References
4 Ordered Categorical Outcomes
1. 4.1 Introduction
2. 4.2 Ordered Categorical Data
3. 4.3 Bibliography
4. 4.4 Examples
5. References
5 Continuous Outcomes
1. 5.1 Introduction
2. 5.2 Comparing Means
3. 5.3 One Mean Known
4. 5.4 Bibliography
5. 5.5 Examples
6. References
6 Rate Outcomes
1. 6.1 Introduction
2. 6.2 Comparing Rates
3. 6.3 Post‐Marketing Surveillance
4. 6.4 Bibliography
5. 6.5 Examples and Use of the Tables
6. References
7 Survival Time Outcomes
1. 7.1 Introduction
2. 7.2 Events of a Single Type
3. 7.3 Competing Risks
4. 7.4 Subject Withdrawals
5. 7.5 Bibliography
6. 7.6 Examples
7. References
8 Paired Binary, Ordered Categorical and Continuous Outcomes
1. 8.1 Introduction
2. 8.2 Within and Between Subject Variation
3. 8.3 Designs
4. 8.4 Binary Data
5. 8.5 Ordered Categorical Data
6. 8.6 Continuous Data
7. 8.7 Bibliography
8. 8.8 Examples and Use of the Tables
9. References
9 Confidence Intervals
1. 9.1 Introduction
2. 9.2 Single Proportion
3. 9.3 Proportions from Two Groups
4. 9.4 Single Mean
5. 9.5 Difference Between Means
6. 9.6 Bibliography
7. 9.7 Examples and Use of the Tables
8. References
10 Repeated Outcome Measures
1. 10.1 Design Features
2. 10.2 Design Effects and Sample Size
3. 10.3 Practicalities
4. 10.4 Bibliography
5. 10.5 Examples
6. References
11 Non‐Inferiority and Equivalence
1. 11.1 Introduction
2. 11.2 Hypotheses
3. 11.3 Non‐Inferiority
4. 11.4 Equivalence
5. 11.5 Bioequivalence
6. 11.6 Practical Issues
7. 11.7 Bibliography
8. 11.8 Examples
9. References
12 Cluster Designs
1. 12.1 Introduction
2. 12.2 Design Features
3. 12.3 Sample Size for Cluster Trials
4. 12.4 Baseline Observations
5. 12.5 Number of Clusters Fixed
6. 12.6 Practicalities
7. 12.7 Bibliography
8. 12.8 Examples
9. References
13 Stepped Wedge Designs
1. 13.1 Introduction
2. 13.2 Basic Structure
3. 13.3 Cross‐Sectional Design
4. 13.4 Closed‐Cohort Design
5. 13.5 Link with a Repeated Measures Design
6. 13.6 Bibliography
7. 13.7 Examples
8. References
14 More than Two Groups Designs
1. 14.1 More than Two Groups
2. 14.2 Bibliography
3. 14.3 Examples
4. References
15 Genomic Targets and Dose‐Finding
1. 15.1 Introduction
2. 15.2 Genomic Targets
3. 15.3 Dose‐Finding
4. 15.4 Examples
5. References
16 Feasibility and Pilot Studies
1. 16.1 Introduction
2. 16.2 Feasibility or Pilot?
3. 16.3 Design Criteria
4. 16.4 External‐Pilot
5. 16.5 Considerations Across External‐Pilot and Main Trials
6. 16.6 Internal‐Pilot Studies
7. 16.7 Bibliography
8. 16.8 Examples
9. References
17 Therapeutic Exploratory Trials
1. 17.1 Introduction
2. 17.2 Theory and Formulae
3. 17.3 Bibliography
4. 17.4 Examples
5. References
18 Therapeutic Exploratory Trials
1. 18.1 Time‐to‐Event (Survival) Endpoint
2. 18.2 Response and Toxicity Endpoints
3. 18.3 Randomised Designs
4. 18.4 Genomic Targets
5. 18.5 Bibliography
6. 18.6 Examples
7. References
19 The Correlation Coefficient
1. 19.1 Introduction
2. 19.2 Theory and Formulae
3. 19.3 Practical Considerations
4. 19.4 Bibliography
5. 19.5 Examples and Use of the Tables
6. References
20 Observer Agreement Studies
1. 20.1 Introduction
2. 20.2 Binary Outcomes
3. 20.3 Continuous Outcomes
4. 20.4 Bibliography
5. 20.5 Examples and Use of the Tables
6. References
21 Reference Intervals and Receiver Operating Curves
1. 21.1 Introduction
2. 21.2 Reference Intervals
3. 21.3 Sensitivity and Specificity
4. 21.4 Receiver Operating Curvess
5. 21.5 Bibliography
6. 21.6 Examples and Use of the Tables
7. References
22 Sample Size Software
1. 22.1 Introduction
2. 22.2 System Requirements
3. 22.3 Installation Instructions
4. 22.4 Help Guide
Cumulative References
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 The cumulative Normal distribution function, Φ(z): The probability that a Normally distributed variable is less than z [Equation (1.2)].
2. Table 1.2 Percentage points of the Normal distribution for differing α and 1 − β.
3. Table 1.3 Student’s t‐distribution, t_df,1‐α/2.
Chapter 03
1. Table 3.1 Sample size for the comparison of two proportions – two sided α = 0.05 and power, 1 – β = 0.8 [Equation (3.2) with ϕ = 1].
2. Table 3.2 Sample size for the comparison of two proportions using the odds ratio (OR) – two sided α = 0.05 and power, 1 – β = 0.8 [Equation (3.4) with ϕ = 1].
Chapter 05
1. Table 5.1 Sample sizes for the two sample t‐test with 2‐sided α = 0.05 [Equation (5.4) with ϕ = 1].
2. Table 5.2 Sample sizes for the two sample t‐test with unequal variances for 2‐sided α = 0.05, power 1 ‐ β = 0.8 [Equation (5.6) with ϕ = 1].
3. Table 5.3 Prob (Y > X) when X and Y are Normally distributed for standardised difference Δ [Equation (5.10)].
4. Table 5.4 Sample sizes for the one sample t‐test with 1‐ and 2‐sided α = 0.05 [Equation (5.11)].
Chapter 06
1. Table 6.1 Sample size, N, required to observe a total of a or more adverse events with a given probability 1 − γ and anticipated incidence λ_Plan [Equation 6.6].
2. Table 6.2 Sample size, N, required for detection of a specific increase in adverse reactions, ε_Plan, with background incidence, λ_Back, known [Equation 6.8].
3. Table 6.3 Sample size, n_T, required for the Test group to detect a specific additional adverse reaction rate, ε_Plan, over an unknown background incidence, λ_PlanC, for the Control group [Equation 6.9].
4. Table 6.4 Number of units, U, comprising 1 case to m controls, to be observed in a matched‐case‐control study [Equation 6.11].
Chapter 07
1. Table 7.1 Number of critical events for comparison of two survival distributions compared when the hazards remain proportional (PH) over time [Equations 7.6 and 7.7].
2. Table 7.2 Total number of critical events, E, required with subjects allocated equally to the two intervention groups [Equation 7.7].
3. Table 7.3 Total number of subjects, N, required with subjects allocated equally to the two intervention groups [Equations 7.7, 7.8 and combined].
Chapter 08
1. Table 8.1 Sample sizes for paired binary data [Equation 8.1].
2. Table 8.2 Sample Sizes for paired continuous data with 2‐sided α = 0.05 [Equation 8.12].
Chapter 09
1. Table 9.1 Sample size, N, required to observe a pre‐specified confidence interval width for an anticipated proportion [from equation (9.5)].
2. Table 9.2 Sample sizes required to observe a given confidence interval width for the difference between proportions from two independent groups of equal size [derived iteratively from equation (9.11)].
3. Table 9.3 Total sample size required to observe a proportionate confidence interval width when comparing two independent groups of equal size expressed via their Odds Ratio (OR) [from equation (9.15)].
4. Table 9.4 Sample sizes required to observe a given confidence interval width for the difference between two paired or matched proportions [from equation (9.16)].
5. Table 9.5 Sample sizes for a planned confidence interval width for (a) single mean, N, or a matched pair of means, N_Pair. [derived from equations (9.18) and (9.24)] and (b) the difference between two means from independent groups of equal size (N = 2n) [from equation (9.22)].
Chapter 10
1. Table 10.1 Multiplying factor for repeated measures designs summarised by comparing post‐intervention means from each of two groups [Equation 10.8]. v: number of pre‐intervention assessments including baseline; w: number of post‐intervention assessments.
Chapter 11
1. Table 11.1 Sample Sizes for testing the non‐inferiority of two means from two groups of equal size [Equation 11.3]. For pair matched designs each entry is divided by 2 [Equation 11.4]. Standardised Difference: Δ = λε%. Each cell gives the total number of subjects required, N.
2. Table 11.2 Total sample sizes for testing the non‐inferiority of two proportions from two groups of equal size – reference group π_S, anticipated difference π_S − π_T, non‐inferiority limit η: 1‐sided α = 0.05, 1‐sided β = 0.2 [Equation 11.5].
3. Table 11.3 Number of pairs, N_Pair_s, required for testing the non‐inferiority of two proportions in a matched pair design [Equation 11.7].
4. Table 11.4 Sample sizes for cross‐over bioequivalence studies – ratio of two paired means, Λ: 1‐sided α = 0.05, β = 0.1. When the ratio μ_T/μ_R = 1, it is assumed the power is 2‐sided, otherwise it is 1‐sided [Equation 11.13].
Chapter 12
1. Table 12.1 The Design Effect [Equation 12.5].
2. Table 12.2 The Design Effect for Cluster Crossover Trials [Equation 12.23].
Chapter 13
1. Table 13.1 The Design Effect (), with the cluster‐correlation ω =1, for a full cross‐sectional SWD and the corresponding multiplier required for sample size inflation when compared to an independent two‐group parallel trial [Equations 13.2 to 13.6 and part of 13.7].
2. Table 13.2 Design Effect(DE^CC_Full) required for sample size adjustment for a full Closed‐Cohort SWD for differing intra‐class correlation (ρ) cluster and individual auto‐correlations (w and π), S and m, as compared to the case of an independent two‐group comparative trial. [Equations 13.14 to 13.15].
Chapter 16
1. Table 16.1 The multiplier κ of the estimated standard deviation, s, to obtain the estimated γ% upper confidence limit (UCL) for the actual standard deviation σ [Equation 16.2].
2. Table 16.2 Flat rule‐of‐thumb for the total sample size of a two equal‐group comparative External‐Pilot trial (partly based on Whitehead, Julious, Cooper and Campbell, 2015, Table 4).
3. Table 16.3 Stepped rule‐of‐thumb total sample size for an External‐Pilot trial for varying standardised differences, Δ, and power of the potential two equal‐group comparative Main trial using the UCL and NCT approaches (partly based on Whitehead, Julious, Cooper and Campbell, 2015, Table 8).
4. Table 16.4 Optimal values of Pilot, Main and hence Overall two equal‐group comparative trial size for UCL80%, UCL90% and NCT inflation methods for a given standardised difference, Δ [From a combined iterative solution of Equations 16.4 and 16.5 to minimise 16.7] (based on Whitehead, Julious, Cooper and Campbell, 2015, Table 6).
Chapter 17
1. Table 17.1 Fleming‐A’Hern Single‐Stage Design.
2. Table 17.2 Simon Optimal and Minimax Designs.
3. Table 17.3 Bayesian Single Threshold Design (STD).
4. Table 17.4 Bayesian Dual Threshold Design (DTD): Sample sizes, and cut‐off values, for Stage 1 and Overall trial size for π_Prior, π₀ and π_New. [Based on exact calculations].
Chapter 18
1. Table 18.1 Stage 1, n_C_‐M₁, and Final, N, Sample Sizes and Thresholds C₁ and C₂ for the Case‐Morgan Expected Duration of Accrual (EDA) design with 1‐sided α = 0.05.
2. Table 18.2 Stage 1, n_C_‐M₁, and Final, N, Sample Sizes and Thresholds C₁ and C₂ for the Case‐Morgan Expected Total Study Length (ETSL) design with 1‐sided α = 0.05.
3. Table 18.3 Bryant and Day Response and Toxicity design.
4. Table 18.4 Simon‐Wittes‐Ellenberg Design.
Chapter 19
1. Table 19.1 Sample sizes for detecting a statistically significant Pearson or Spearman correlation coefficient [Equations 19.1, 19.2 and 19.3].
2. Table 19.2 Sample sizes for a pre‐specified width of the 2‐sided confidence interval for a Pearson correlation coefficient [Equations 19.5, 19.6, 19.7 and 19.8].
3. Table 19.3 Sample sizes for a pre‐specified width of the 2‐sided confidence interval for a Spearman correlation coefficient [Equations 19.7, 19.8, 19.10 and 19.11].
Chapter 20
1. Table 20.1 Sample size, m_Repea_t, required to observe a pre‐specified confidence interval width, W_DisA_g, for an anticipated proportion of disagreements, π_DisA_g, between two readers [Equation 20.5].
2. Table 20.2 Required number of specimens each assessed twice, m_Specimens, by two readers to yield a confidence interval of a given width, w_ξ, for the probability of making a chance error in diagnosis, ξ. [Equation 20.9].
3. Table 20.3 Total number of specimens, N, required, each assessed twice by each reader, to yield a given confidence interval width of the probability of their disagreement, Θ_DisAg. [Equation 20.14].
4. Table 20.4 Number of specimens required, m_κ, to observe a given confidence interval width for inter‐observer agreement using Cohen’s Kappa, κ [Equation 20.18].
5. Table 20.5 Sample sizes required to estimate an intra‐class correlation for a pre‐specified confidence interval width [Equations 20.20 and 20.21].
6. Table 20.6 Sample sizes required to observe a given intra‐class correlation using the hypothesis testing approach with 1‐sided α = 0.05 for different numbers of readers, k [Equations 20.22 and 20.23].
Chapter 21
1. Table 21.1 Sample Sizes in order to obtain a pre‐specified width of the confidence interval for the Cut‐off value defining a limit of a Reference Interval for a continuous outcome measure having an assumed Normal distribution [Equation 21.6].
2. Table 21.2 Sample sizes in order to obtain a pre‐specified width of the confidence interval for the Cut‐off value defining a limit of a Reference Interval for a continuous outcome measure having an Non‐Normal distribution [Equations 21.11 and 21.14].
3. Table 21.3 Single group sample sizes required to observe a given sensitivity and specificity in diagnostic accuracy studies [Approximated by Equation 21.15].
4. Table 21.4 Sample sizes required for a two group unpaired design for given sensitivity and specificity in diagnostic accuracy studies [Equation 21.16].
5. Table 21.5 Sample sizes required for a two group matched pair design for given sensitivity and specificity in diagnostic accuracy studies. [Equation 21.17].
6. Table 21.6 Sample sizes required to observe a given 2‐sided confidence interval width for the AUC of a ROC [Equations 21.18 and 21.19].

List of Illustrations

Chapter 01
1. Figure 1.1 The probability density function of a standardised Normal distribution.
2. Figure 1.2 Distribution of d under the null (δ = 0) and alternative hypotheses (δ > 0).
3. Figure 1.3 Central t‐distributions with different degrees of freedom (df) and the corresponding Normal distribution.
4. Figure 1.4 Non‐central t‐distributions with μ = σ = 1, hence non‐centrality parameters ψ = √n, with increasing df = n − 1 with n equal to 2, 4, 9 and 31. For n = 31 the corresponding Normal distribution with mean √31 = 5.57 is added.
5. Figure 1.5 Binomial distribution for π = 0.25 and various values of n.
6. Figure 1.6 Poisson distribution for various values of λ.
7. Figure 1.7 The Exponential survival function with constant hazards of θ = 0.125, 0.25 and 0.5.
Chapter 02
1. Figure 2.1 Sample size multiplication factors to compensate for k multiple comparisons when applying a Bonferroni correction with two‐sided α = 0.05.
2. Figure 2.2 Sample size for a randomised trial assessing the benefit of adjuvant levamisole added to busulphan for good‐risk patients with chronic myelogenous leukaemia.
3. Figure 2.3 Sample size for a cluster randomised trial to evaluate cardiovascular guideline implementation in primary care.
Chapter 03
1. Figure 3.1 Notation for a clinical study comparing the proportion of successes in two (independent) groups.
Chapter 04
1. Figure 4.1 Playfulness in feverish children following treatment with paracetamol (P) and without (Control, C).
2. Figure 4.2 Weight change in patients with impaired glucose tolerance following treatment with placebo or combination of rosiglitazone and metformin.
3. Figure 4.3 Deriving the anticipated proportions within each category for the Test intervention calculated from that anticipated for women who have experienced intimate partner violence in the Standard group with an assumed planning odds ratio, OR_Plan = 1.5.
4. Figure 4.4 Modified Rankin scale at month 3 following treatment with Placebo or MLC601.
5. Figure 4.5 Distribution of modified Rankin scores according to intervention received.
6. Figure 4.6 Retinopathy status by smoking status in patients with diabetes mellitus.
Chapter 05
1. Figure 5.1 Sample size estimates for randomised controlled trials (RCT) using LOS and TRD as outcome measures of short‐term recovery post colorectal surgery.
2. Figure 5.2 Variation in sample size with changing 1: ϕ allocation and accounting for block size assuming 2‐sided α = 0.05.
Chapter 06
1. Figure 6.1 Changing number of person‐years per group with varying allocation ratio 1: ϕ for planning values λ_C‐E = 0.23 and λ_S‐E = 0.1725, for a 2‐sided α = 0.05 and 1 – β = 0.90 [Equation 6.2].
2. Figure 6.2 Variation in the required total number of patients with asthma required for a comparative trial according to the assumptions for the mean patient exposure, τ, and the Negative‐Binomial distribution parameter, κ. [Equations 6.4 and 6.5].
Chapter 07
1. Figure 7.1 Infants receiving chemotherapy for their brain tumour: Number experiencing differing events, with the corresponding 5‐year CMI rates, and competing risk hazard ratios, csHR and subHR, comparing those with Ependymoma histology with those of Other malignant brain tumours.
2. Figure 7.2 Cause‐specific and subdistribution HRs for the competing risks of distant metastases and local recurrence in patients with advanced non‐metastatic nasopharyngeal cancer from a randomised trial comparing radiotherapy alone (RT) and RT with adjuvant chemotherapy (ChemoRT).
Chapter 08
1. Figure 8.1 Notation for a 2 × 2 cross‐over trial comparing treatments S and T for a binary endpoint with associated parameters.
2. Figure 8.2 Notation for a 1 to 1 matched Case‐Control study with a binary endpoint.
3. Figure 8.3 Results from the split‐mouth trial of two glass‐ionomer cements used in children with bilateral matched pairs of carious posterior primary teeth.
4. Figure 8.4 Case‐Control status by whether a child’s mother was single/divorced or married/cohabiting.
5. Figure 8.5 Reported levels of hypertension present in 166 Case‐Control pairs.
6. Figure 8.6 Distribution of score differences between cases and controls.
7. Figure 8.7 Influence of changing ρ on the planning values for (a) σ_Diff and hence (b) N_Pairs assuming σ_Within = 20.
Chapter 09
1. Figure 9.1 Partial results from a survey of patients attending a hospital clinic.
Chapter 10
1. Figure 10.1 Mean blood phenylalanine concentration over time in patients with phenylketonuria pre‐and post‐randomisation to Placebo (P) or Salpropterin (S) (after Levy, Milanowski, Chakrapani, et al, 2007).
2. Figure 10.2 Structure of the anticipated variance, Var(C), for a contrast with 3 weights: −1, 0.5 and 0.5 and assuming compound symmetry for ρ.
3. Figure 10.3 Structure of the anticipated variance, Var(C), for a contrast with 3 weights: −1, 0.5 and 0.5 at 0, 2 and 5 years assuming AR(1) with ρ being the per year intraclass correlation.
4. Figure 10.4 Planning values assumed for a repeated measures design and consequential changes in the proposed sample size with compound symmetry for differing autocorrelation values.
Chapter 11
1. Figure 11.1 Hypotheses tested in parallel group trials for (a) superiority, (b) non‐inferiority and (c) equivalence when comparing a test (T) with a standard (S), where δ = μ_S – μ_T.
2. Figure 11.2 Schematic diagram to illustrate the concept of non‐inferiority by using possible comparative trial outcomes as summarised by their 1‐sided confidence intervals: Non‐inferiority status: Trial A – Confirmed; Trial B – Confirmed; Trial C – Not accepted.
3. Figure 11.3 Maximum likelihood estimates of and of equation (11.5) (from Farrington and Manning, 1990).
4. Figure 11.4 The potential format of the results from a matched‐pair or cross‐over design.
5. Figure 11.5 Schematic diagram to illustrate the concept of equivalence by using a series of possible comparative trial outcomes of a Test against a Standard intervention as summarised by their reported (2‐sided) confidence intervals (after Jones, Jarvis, Lewis and Ebbutt, 1996).
6. Figure 11.6 Hypotheses tested in trials for bioequivalence when comparing a test ( T ) with a reference ( R ) in situations where μ_T and μ_R are assumed equal.
Chapter 13
1. Figure 13.1 Schema of a full SWD trial with λ = 2 interventions, I‐No and I‐Yes, K = 6 clusters with P = 4 periods, A = 3 arms with g = 2 clusters randomised at each of S = 3 steps.
2. Figure 13.2 Notation used for describing an SWD with examples from the literature.
3. Figure 13.3 Full stepped wedge design to assess the impact of the HEART risk score in patients with acute chest pain (from Poldervaart, Reitsma, Hoffijberg, et al, 2013, Figure 1).
4. Figure 13.4 Extension of the definition of ICC, ρ, together with the cluster autocorrelation, ω, for a cross‐sectional design.
5. Figure 13.5 Design matrices, D, corresponding to the full SWD of (a) Figure 13.1 and (b) Figure 13.3.
6. Figure 13.6 Design matrix, D, for a full A by P SWD with g = 1 allocated to I‐Yes in each post run‐in period.
7. Figure 13.7 Stepped wedge cluster design for evaluating a free school breakfast programme involving 14 schools. Each sequence (denoted Term) was allocated to either 3 or 4 schools (from Mhurchu, Gorton, Turley, et al, 2013, Figure 1).
8. Figure 13.8 Extension of the definitions of ICC, ρ, the cluster auto‐correlation, ω, and individual auto‐correlation, π, for a closed‐cohort SWD.
9. Figure 13.9 Design matrix, D, for a 2 by (v + w) repeated measures design of Chapter 10 in which it is assumed that all subjects in the prior intervention period receive I‐No.
Chapter 14
1. Figure 14.1 Randomised 2 × 2 factorial trial of diclofenac and manipulation as adjunct to advice and paracetamol in patients with low back pain (after Hancock, Maher, Latimer et al, 2007).
Chapter 15
1. Figure 15.1 Approach for drug development involving molecular targets.
2. Figure 15.2 An Enrichment Design in which subjects are selected for randomisation provided they are diagnosis positive (D+) for a specific molecular target.
3. Figure 15.3 Biomarker stratified design.
4. Figure 15.4 Establishing the MTD in a C33D for a Phase I trial.
5. Figure 15.5 Establishing the MTD in a ‘Best‐of‐5’ design for a Phase I trial.
6. Figure 15.6 Empirical dose‐response curve based on prior probabilities of DLT against a dose.
7. Figure 15.7 Hypothetical dose‐response curve of the probability of DLT against a received dose.
Chapter 16
1. Figure 16.1 Conceptual framework for feasibility and pilot studies.
2. Figure 16.2 Vital features of an Internal‐Pilot study.
Chapter 17
1. Figure 17.1 Considerations for the choice of Phase II/Therapeutic Exploratory Clinical Trial.
Chapter 18
1. Figure 18.1 Enrichment Design for a TE Trial.
2. Figure 18.2 Biomarker stratified design for TE trials.
3. Figure 18.3 Decision algorithm for recommendation of, or not, a subsequent Phase III trial (from Freidlin, McShane, Polley and Korn, 2012).
Chapter 19
1. Figure 19.1 Scatter plot of waist versus hip circumference in 166 individuals.
2. Figure 19.2 Spearman rank correlation coefficients between clinical signs and cone beam computed tomography findings with minimal sample sizes suggested by equation (19.2) (part data from Cömert Kiliç, Kiliç and Sümbüllü, 2015, Table 5).
Chapter 20
1. Figure 20.1 Possible outcomes for (i) two readers each reviewing the same specimens only once to determine the level of between‐reader disagreement or (ii) a single reader reviewing the same material on two occasions to determine their own lack of reproducibility.
2. Figure 20.2 Steps for sample size determination for reader‐agreement studies based on binary endpoints.
3. Figure 20.3 Diverging sample sizes between the Large sample, m_Tw_o, and Recommended, m_Re_c, methods for varying proportions of disagreement, π_DisA_g, for a given width of the 95% CI W_DisA_g = 0.1.
4. Figure 20.4 Intraclass correlations (ICC) established when evaluating a second generation pillcam colon capsule endoscope (from D’Haens, Löwenberg, Samaan, et al, 2015).

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Names: Machin, David, 1939– author. | Campbell, Michael J., 1950– author. | Tan, Say Beng, author. | Tan, Sze Huey, author.
Title: Sample Sizes for Clinical, Laboratory and Epidemiology Studies / David Machin, Michael J. Campbell, Say Beng Tan, Sze Huey Tan.
Description: Fourth edition. | Hoboken, NJ : Wiley, [2018]. | Preceded by Sample size tables for clinical studies / David Machin ... [et al.]. 3rd ed. 2009. | Includes bibliographical references and index. |
Identifiers: LCCN 2018001008 (print) | LCCN 2018002299 (ebook) | ISBN 9781118874929 (pdf) | ISBN 9781118874936 (epub) | ISBN 9781118874943 (hardback)
Subjects: | MESH: Research Design | Clinical Studies as Topic | Statistics as Topic | Sample Size | Tables
Classification: LCC R853.C55 (ebook) | LCC R853.C55 (print) | NLM W 20.55.C5 | DDC 615.5072/4–dc23
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Preface

It has been more than thirty years since the original edition of ‘Statistical Tables for the Design of Clinical trials’ was published. During this time, there have been considerable advances in the field of medical research, including the completion of the Human Genome Project, the growth of personalised (or precision) medicine using targeted therapies, and increasingly complex clinical trial designs.

However, the principles of good research planning and practice remain as relevant today as they did thirty years ago. Indeed, all these advances in research would not have been possible without investigators holding firm to these principles, including the need for a rigorous study design and the appropriate choice of sample size for the study.

This fourth edition of the book features a third change in title. The original title had suggested (although not intentionally) a focus on ‘clinical trials’, the second saw an extension to ‘clinical studies’ and now ‘clinical, laboratory and epidemiology studies’. Currently, sample size considerations are deeply imbedded in planning clinical trials and epidemiological studies but less so in other aspects of medical research. The change to the title is intended to draw more attention to areas where sample size issues are often overlooked.

This text cannot claim to be totally comprehensive and so choices had to be made as to what to include. In general terms, there has been a major reorganisation and extension of many of the chapters of the third edition, as well as new chapters, and many illustrative examples refreshed and others added. In particular, basic design considerations have been extended to two chapters; repeated measures, more than two groups and cluster designs each have their own chapter with the latter extended to include stepped wedge designs. Also there is a chapter concerning genomic targets and one concerned with pilot and feasibility studies.

In parallel to the increase in the extent of medical research, there has also been a rapid and extensive improvement in capability and access to information technology. Thus while the first edition of this book simply provided extensive tabulations on paper, the second edition provided some basic software on a floppy disc to allow readers to extend the applicability to situations outside the scope of the printed tables. This ability was further enhanced in the third edition with more user‐friendly and powerful software on a CD‐ROM provided with the book. The book is supported by user‐friendly software through the associated Wiley website. In addition, R statistical software code is provided.

Despite these improved software developments, we have still included some printed tables within the text itself as we wish to emphasise that determining the appropriate sample size for a study is not simply a task of plugging some numerical values into a formula with the parameters concerned, but an extensive investigation of what is suitable for the study intended. This would include face‐to‐face discussions between the investigators and statistical team members, for which having printed tables available can be helpful. The tabulations give a very quick ‘feel’ as to how sensitive sample sizes can often be to even small perturbations in the assumed planning values of some of the parameters concerned. This brings an immediate sense of realism to the processes involved.

For the general reader Chapters 1 and 2 give an overview of design considerations appropriate to sample size calculations. Thereafter the subsequent chapters are designed to be as self‐contained as possible. However, some later chapters, such as those describing cluster and stepped wedge designs, will require sample size formulae from the earlier chapters to complete the sample size calculations.

We continue to be grateful to many colleagues and collaborators who have contributed directly or indirectly to this book over the years. We specifically thank Tai Bee Choo for help with the section on competing risks, Gao Fei on cluster trials and Karla Hemming and Gianluca Baio on aspects of stepped wedge designs.

David Machin, Michael J. Campbell, Say Beng Tan and Sze Huey Tan
July 2017

Dedication

The authors would like to dedicate this book to Oliver, Joshua, Sophie and Caitlin; Matthew, Annabel, Robyn, Flora and Chloe; Lisa, Sophie, Samantha and Emma; Kim San, Geok Yan and Janet.