Statistical Thinking for Non-Statisticians in Drug Regulation

Cover
Title Page
Copyright Page
Contents
Preface to the third edition
Preface to the second edition
Preface to the first edition
Abbreviations
CHAPTER 1 Basic ideas in clinical trial design
1.1 Historical perspective
1.2 Control groups
1.3 Placebos and blinding
1.4 Randomisation
1.4.1 Unrestricted randomisation
1.4.2 Block randomisation
1.4.3 Unequal randomisation
1.4.4 Stratified randomisation
1.4.5 Central randomisation
1.4.6 Dynamic allocation and minimisation
1.4.7 Cluster randomisation
1.5 Bias and precision
1.6 Between- and within-patient designs
1.7 Crossover trials
1.8 Signal, noise and evidence
1.8.1 Signal
1.8.2 Noise
1.8.3 Signal-to-noise ratio
1.9 Confirmatory and exploratory trials
1.10 Superiority, equivalence and non-inferiority trials
1.11 Endpoint types
1.12 Choice of endpoint
1.12.1 Primary endpoints
1.12.2 Secondary endpoints
1.12.3 Surrogate endpoints
1.12.4 Global assessment endpoints
1.12.5 Composite endpoints
1.12.6 Categorisation
CHAPTER 2 Sampling and inferential statistics
2.1 Sample and population
2.2 Sample statistics and population parameters
2.2.1 Sample and population distribution
2.2.2 Median and mean
2.2.3 Standard deviation
2.2.4 Notation
2.2.5 Box plots
2.3 The normal distribution
2.4 Sampling and the standard error of the mean
2.5 Standard errors more generally
2.5.1 The standard error for the difference between two means
2.5.2 Standard errors for proportions
2.5.3 The general setting
CHAPTER 3 Confidence intervals and p-values
3.1 Confidence intervals for a single mean
3.1.1 The 95% confidence interval
3.1.2 Changing the confidence coefficient
3.1.3 Changing the multiplying constant
3.1.4 The role of the standard error
3.2 Confidence intervals for other parameters
3.2.1 Difference between two means
3.2.2 Confidence interval for proportions
3.2.3 General case
3.2.4 Bootstrap confidence interval
3.3 Hypothesis testing
3.3.1 Interpreting the p-value
3.3.2 Calculating the p-value
3.3.3 A common process
3.3.4 The language of statistical significance
3.3.5 One-sided and two-sided tests
CHAPTER 4 Tests for simple treatment comparisons
4.1 The unpaired t-test
4.2 The paired t-test
4.3 Interpreting the t-tests
4.4 The chi-square test for binary endpoints
4.4.1 Pearson chi-square
4.4.2 The link to a ratio of the signal to the standard error
4.5 Measures of treatment benefit
4.5.1 Odds ratio
4.5.2 Relative risk
4.5.3 Relative and absolute risk reduction
4.5.4 Number needed to treat
4.5.5 Confidence intervals
4.5.6 Interpretation
4.6 Fisher’s exact test
4.7 Tests for categorical and ordered categorical endpoints
4.7.1 Categorical endpoints
4.7.2 Ordered categorical (ordinal) endpoints
4.7.3 Measures of treatment benefit
4.8 Count endpoints
4.9 Extensions for multiple treatment groups
4.9.1 Continuous endpoints
4.9.2 Binary, categorical and ordered categorical endpoints
4.9.3 Dose-ranging studies
4.9.4 Further discussion
CHAPTER 5 Adjusting the analysis
5.1 Objectives for adjusted analysis
5.2 Comparing treatments for continuous endpoints
5.3 Least squares means
5.4 Evaluating the homogeneity of the treatment effect
5.4.1 Treatment-by-factor interactions
5.4.2 Quantitative and qualitative interactions
5.5 Methods for binary and ordered categorical endpoints
5.6 Multi-centre trials
5.6.1 Adjusting for centre
5.6.2 Significant treatment-by-centre interactions
5.6.3 Combining centres
CHAPTER 6 Regression and analysis of covariance
6.1 Adjusting for baseline factors
6.2 Simple linear regression
6.3 Multiple regression
6.4 Logistic regression for binary endpoints
6.4.1 Negative binomial regression for count endpoints
6.5 Analysis of covariance for continuous outcomes
6.5.1 Main effect of treatment
6.5.2 Treatment-by-covariate interactions
6.5.3 A single model
6.5.4 Connection with adjusted analyses
6.5.5 Advantages of ANCOVA
6.5.6 Least squares means
6.5.7 Random element
6.6 Other endpoint types
6.6.1 Binary endpoints and extensions
6.6.2 Count endpoints
6.7 Mixed models
6.8 Regulatory aspects of the use of covariates
6.9 Baseline testing
6.10 Correlation and regression
CHAPTER 7 Intention-to-treat, analysis sets and missing data
7.1 The principle of intention-to-treat
7.2 The practice of intention-to-treat
7.2.1 Full analysis set
7.2.2 Per-protocol set
7.2.3 Further aspects of ITT
7.3 Missing data
7.3.1 Introduction
7.3.2 Complete cases analysis
7.3.3 Last observation carried forward (LOCF)
7.3.4 Baseline observation carried forward (BOCF)
7.3.5 Success/failure classification
7.3.6 Worst-case/best-case classification
7.3.7 Sensitivity
7.3.8 Avoidance of missing data
7.3.9 Classification of missing data
7.3.10 Multiple imputation
7.4 Intention-to-treat and time-to-event data
7.5 General questions and considerations
CHAPTER 8 Estimands
8.1 ICH E9 (R1)
8.2 Attributes of an estimand
8.2.1 Population
8.2.2 Variable
8.2.3 Intercurrent event (ICE)
8.2.4 Statistic for treatment effect
8.3 Estimand strategies
8.3.1 Five strategies
8.3.2 Treatment policy, composite and hypothetical strategies
8.3.3 While on treatment
8.3.4 Principal stratification
8.4 Sensitivity and supplementary analyses
8.4.1 Main estimator
8.4.2 Sensitivity analyses
8.4.3 Supplementary analyses
CHAPTER 9 Power, sample size and clinical relevance
9.1 Type I and type II errors
9.2 Power
9.3 Calculating sample size
9.4 Impact of changing the parameters
9.4.1 Standard deviation
9.4.2 Event rate in the control group
9.4.3 Clinically relevant difference
9.5 Regulatory aspects
9.5.1 Power 80%
9.5.2 Sample size adjustment
9.6 Reporting the sample size calculation
9.7 Post hoc power
9.8 Link between p-values and confidence intervals
9.9 Confidence intervals for clinical importance
9.10 Misinterpretation of the p-value
9.10.1 Conclusions of similarity
9.10.2 The problem with 0.05
9.11 Single pivotal trial and 0.05
CHAPTER 10 Multiple testing
10.1 Inflation of the type I error
10.1.1 False positives
10.1.2 A simulated trial
10.2 How does multiplicity arise?
10.3 Regulatory and scientific view
10.4 Methods for adjustment
10.4.1 Bonferroni correction
10.4.2 Holm correction
10.4.3 Hochberg correction
10.4.4 Interim analyses
10.5 Avoiding adjustment
10.5.1 Co-primary endpoints
10.5.2 Composite endpoints
10.5.3 Hierarchical testing
10.6 Fallback procedure
10.7 Multiple comparisons of treatments
10.8 Subgroup testing
10.9 Other aspects of multiplicity
10.9.1 Using different statistical tests
10.9.2 Different analysis sets and methods for missing data
10.9.3 Pre-planning
10.9.4 Nominal significance
CHAPTER 11 Non-parametric and related methods
11.1 Assumptions underlying the t-tests and their extensions
11.2 Homogeneity of variance
11.3 The assumption of normality
11.4 Non-normality and transformations
11.5 Non-parametric tests
11.5.1 The Mann–Whitney U-test
11.5.2 The Wilcoxon signed rank test
11.5.3 General comments
11.6 Advantages and disadvantages of non-parametric methods
11.7 Outliers
CHAPTER 12 Equivalence and non-inferiority
12.1 Demonstrating similarity
12.2 Confidence intervals for equivalence
12.3 Confidence intervals for non-inferiority
12.4 A p-value approach
12.5 Assay sensitivity
12.6 Analysis sets
12.7 The choice of 
12.7.1 Bioequivalence
12.7.2 Therapeutic equivalence, biosimilars
12.7.3 Non-inferiority
12.7.4 The 10% rule for cure rates
12.7.5 The synthesis method
12.8 Biocreep and constancy
12.9 Sample size calculations
12.10 Switching between non-inferiority and superiority
12.11 Biosimilars
CHAPTER 13 The analysis of survival data
13.1 Time-to-event data and censoring
13.2 Kaplan-Meier curves
13.2.1 Plotting Kaplan-Meier curves
13.2.2 Event rates and relative risk
13.2.3 Median event times
13.3 Treatment comparisons
13.4 The hazard ratio
13.4.1 The hazard rate
13.4.2 Constant hazard ratio
13.4.3 Non-constant hazard ratio
13.4.4 Link to survival curves
13.4.5 Calculating Kaplan-Meier curves
13.5 Restricted mean survival time
13.6 Adjusted analyses
13.6.1 Stratified methods
13.6.2 Proportional hazards regression
13.6.3 Accelerated failure time model
13.7 Independent censoring
13.8 Crossover
13.8.1 Rank Preserving Structural Failure Time Model
13.8.2 Regulatory position
13.9 Composite time-to-event endpoints
13.9.1 Cumulative incidence functions
13.9.2 Regulatory position
13.10 Sample size calculations
CHAPTER 14 Interim analysis and data monitoring committees
14.1 Stopping rules for interim analysis
14.2 Stopping for efficacy and futility
14.2.1 Efficacy
14.2.2 Futility and conditional power
14.2.3 Some practical issues
14.2.4 Point estimates and confidence intervals
14.3 Monitoring safety
14.4 Data monitoring committees
14.4.1 Introduction and responsibilities
14.4.2 Structure and process
14.4.3 Meetings and recommendations
CHAPTER 15 Bayesian statistics
15.1 Introduction
15.2 Prior and posterior distributions
15.2.1 Prior beliefs
15.2.2 Prior to posterior
15.2.3 Bayes theorem
15.3 Bayesian inference
15.3.1 Frequentist methods
15.3.2 Posterior probabilities
15.3.3 Credible intervals
15.4 Case study
15.5 History and regulatory acceptance
15.6 Discussion
CHAPTER 16 Adaptive designs
16.1 What are adaptive designs?
16.1.1 Advantages and drawbacks
16.1.2 Restricted adaptations
16.1.3 Flexible adaptations
16.2 Minimising bias
16.2.1 Control of type I error
16.2.2 Estimation
16.2.3 Operational bias
16.3 Unblinded sample size re-estimation
16.3.1 Product of p-values
16.3.2 Weighting the two parts of the trial
16.3.3 Rationale
16.4 Seamless phase II/III studies
16.4.1 Standard framework
16.4.2 Multiplicity
16.4.3 Incorporating the phase II data
16.4.4 Logistical challenges
16.5 Other types of adaptation
16.5.1 Changing the primary endpoint
16.5.2 Enrichment
16.5.3 Dropping the placebo arm in a non-inferiority trial
16.6 Further regulatory considerations
CHAPTER 17 Observational studies
17.1 Introduction
17.1.1 Non-randomised comparisons
17.1.2 Study types
17.1.3 Sources of bias
17.1.4 An empirical investigation
17.1.5 Selection bias in concurrently controlled studies
17.1.6 Selection bias in historically controlled studies
17.1.7 Some conclusions
17.2 Guidance on design, conduct and analysis
17.2.1 Regulatory guidance
17.2.2 Strengthening the Reporting of Observational Studies in Epidemiology
17.3 Assessing the presence of baseline balance
17.4 Adjusting for selection bias: stratification and regression
17.5 Adjusting for selection bias: propensity scoring
17.5.1 Defining propensity scores
17.5.2 Propensity score stratification, regression and matching
17.6 Comparing methods that correct for selection bias
17.7 Inverse propensity score weighting
17.8 Case–control studies
17.8.1 Background
17.8.2 Odds ratio and relative risk
CHAPTER 18 Meta-analysis and network meta-analysis
18.1 Definition
18.2 Objectives
18.3 Statistical methodology
18.3.1 Methods for combination
18.3.2 CIs
18.3.3 Fixed and random effects
18.3.4 Graphical methods
18.3.5 Detecting heterogeneity
18.3.6 Robustness
18.3.7 Rare events
18.3.8 Individual patient data
18.4 Case study
18.5 Ensuring scientific validity
18.5.1 Planning
18.5.2 Assessing the risk of bias
18.5.3 Publication bias and funnel plots
18.5.4 Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)
18.6 Regulatory aspects of meta-analysis
18.7 Introduction to network meta-analysis
18.8 Case Study
18.9 Indirect treatment comparisons
18.9.1 Cross-trial calculations
18.9.2 Effect modifiers
18.9.3 Critique
18.10 Bayesian rank analysis
CHAPTER 19 Methods for safety analysis, safety monitoring and assessment of benefit-risk
19.1 Introduction
19.1.1 Methods for safety data
19.1.2 The rule of three
19.2 Routine evaluation in clinical studies
19.2.1 Types of data
19.2.2 Adverse events
19.2.3 Laboratory data
19.2.4 ECG data
19.2.5 Vital signs
19.2.6 Safety summary across trials
19.2.7 Specific safety studies
19.3 Data monitoring committees
19.4 Assessing benefit–risk
19.4.1 Current approaches
19.4.2 Multi-criteria decision analysis
19.4.3 Quality-adjusted time without symptoms or toxicity
19.5 Pharmacovigilance
19.5.1 Post-approval safety monitoring
19.5.2 Proportional reporting ratios
19.5.3 Bayesian neural networks
CHAPTER 20 Diagnosis
20.1 Introduction
20.2 Measures of diagnostic performance
20.2.1 Sensitivity and specificity
20.2.2 Positive and negative predictive value
20.2.3 False positive and false negative rates
20.2.4 Prevalence
20.2.5 Likelihood ratio
20.2.6 Predictive accuracy
20.2.7 Choosing the correct cutpoint
20.3 Receiver operating characteristic curves
20.3.1 Receiver operating characteristic
20.3.2 Comparing ROC curves
20.4 Diagnostic performance using regression models
20.5 Aspects of trial design for diagnostic agents
20.6 Assessing agreement
20.6.1 The kappa statistic
20.6.2 Other applications for kappa
20.7 Companion diagnostics
CHAPTER 21 The role of statistics and statisticians
21.1 The importance of statistical thinking at the design stage
21.2 Regulatory guidelines
21.3 The statistics process
21.3.1 The statistical methods section of the protocol
21.3.2 The statistical analysis plan
21.3.3 The data validation plan
21.3.4 The blind review
21.3.5 Statistical analysis
21.3.6 Reporting the analysis
21.3.7 Pre-planning
21.3.8 Sensitivity and robustness
21.4 The regulatory submission
21.5 Publications and presentations
References
Index
EULA