Table of Contents
Cover
Title Page
Preface
List of Abbreviations
About the Companion Website
1 Introduction to Evidence Synthesis
1.1 Introduction
1.2 Why Indirect Comparisons and Network Meta-Analysis?
1.3 Some Simple Methods
1.4 An Example of a Network Meta-Analysis
1.5 Assumptions Made by Indirect Comparisons and Network Meta-Analysis
1.6 Which Trials to Include in a Network
1.7 The Definition of Treatments and Outcomes: Network Connectivity
1.8 Summary
1.9 Exercises
2 The Core Model
2.1 Bayesian Meta-Analysis
2.2 Development of the Core Models
2.3 Technical Issues in Network Meta-Analysis
2.4 Advantages of a Bayesian Approach
2.5 Summary of Key Points and Further Reading
2.6 Exercises
3 Model Fit, Model Comparison and Outlier Detection
3.1 Introduction
3.2 Assessing Model Fit
3.3 Model Comparison
3.4 Outlier Detection in Network Meta-Analysis
3.5 Summary and Further Reading
3.6 Exercises
4 Generalised Linear Models
4.1 A Unified Framework for Evidence Synthesis
4.2 The Generic Network Meta-Analysis Models
4.3 Univariate Arm-Based Likelihoods
4.4 Contrast-Based Likelihoods
4.5 *Multinomial Likelihoods
4.6 *Shared Parameter Models
4.7 Choice of Prior Distributions
4.8 Zero Cells
4.9 Summary of Key Points and Further Reading
4.10 Exercises
5 Network Meta-Analysis Within Cost-Effectiveness Analysis
5.1 Introduction
5.2 Sources of Evidence for Relative Treatment Effects and the Baseline Model
5.3 The Baseline Model
5.4 The Natural History Model
5.5 Model Validation and Calibration Through Multi-Parameter Synthesis
5.6 Generating the Outputs Required for Cost-Effectiveness Analysis
5.7 Strategies to Implement Cost-Effectiveness Analyses
5.8 Summary and Further Reading
5.9 Exercises
6 Adverse Events and Other Sparse Outcome Data
6.1 Introduction
6.2 Challenges Regarding the Analysis of Sparse Data in Pairwise and Network Meta-Analysis
6.3 Strategies to Improve the Robustness of Estimation of Effects from Sparse Data in Network Meta-Analysis
6.4 Summary and Further Reading
6.5 Exercises
7 Checking for Inconsistency
7.1 Introduction
7.2 Network Structure
7.3 Loop Specific Tests for Inconsistency
7.4 A Global Test for Loop Inconsistency
7.5 Response to Inconsistency
7.6 The Relationship between Heterogeneity and Inconsistency
7.7 Summary and Further Reading
7.8 Exercises
8 Meta-Regression for Relative Treatment Effects
8.1 Introduction
8.2 Basic Concepts
8.3 Heterogeneity, Meta-Regression and Predictive Distributions
8.4 Meta-Regression Models for Network Meta-Analysis
8.5 Individual Patient Data in Meta-Regression
8.6 Models with Treatment-Level Covariates
8.7 Implications of Meta-Regression for Decision Making
8.8 Summary and Further Reading
8.9 Exercises
9 Bias Adjustment Methods
9.1 Introduction
9.2 Adjustment for Bias Based on Meta-Epidemiological Data
9.3 Estimation and Adjustment for Bias in Networks of Trials
9.4 Elicitation of Internal and External Bias Distributions from Experts
9.5 Summary and Further Reading
9.6 Exercises
10 *Network Meta-Analysis of Survival Outcomes
10.1 Introduction
10.2 Time-to-Event Data
10.3 Parametric Survival Functions
10.4 The Relative Treatment Effect
10.5 Network Meta-Analysis of a Single Effect Measure per Study
10.6 Network Meta-Analysis with Multivariate Treatment Effects
10.7 Data and Likelihood
10.8 Model Choice
10.9 Presentation of Results
10.10 Illustrative Example
10.11 Network Meta-Analysis of Survival Outcomes for Cost-Effectiveness Evaluations
10.12 Summary and Further Reading
10.13 Exercises
11 *Multiple Outcomes
11.1 Introduction
11.2 Multivariate Random Effects Meta-Analysis
11.3 Multinomial Likelihoods and Extensions of Univariate Methods
11.4 Chains of Evidence
11.5 Follow-Up to Multiple Time Points: Gastro-Esophageal Reflux Disease
11.6 Multiple Outcomes Reported in Different Ways: Influenza
11.7 Simultaneous Mapping and Synthesis
11.8 Related Outcomes Reported in Different Ways: Advanced Breast Cancer
11.9 Repeat Observations for Continuous Outcomes: Fractional Polynomials
11.10 Synthesis for Markov Models
11.11 Summary and Further Reading
11.12 Exercises
12 Validity of Network Meta-Analysis
12.1 Introduction
12.2 What Are the Assumptions of Network Meta-Analysis?
12.3 Direct and Indirect Comparisons: Some Thought Experiments
12.4 Empirical Studies of the Consistency Assumption
12.5 Quality of Evidence Versus Reliability of Recommendation
12.6 Summary and Further Reading
12.7 Exercises
Solutions to Exercises
Appendices
References
Index
End User License Agreement
List of Tables
Chapter 01
Table 1.1 The thrombolytics dataset, 14 trials, six treatments (data from Boland et al., 2003): streptokinase (SK), tissue-plasminogen activator (t-PA), accelerated tissue-plasminogen activator (Acc t-PA), tenecteplase (TNK), and reteplase (r-PA) 14 trials.
Table 1.2 Findings from the HTA report on thrombolytics drugs (Boland et al., 2003).
Table 1.3 Thrombolytics example, fixed effect analysis: odds ratios (posterior medians and 95% CrI).
Table 1.4 Thrombolytics example, fixed effect analysis: posterior summaries.
Chapter 02
Table 2.1 Extended thrombolytics example.
Table 2.2 Extended thrombolytics example (pairwise meta-analysis): results from fixed and random effects meta-analyses of mortality on PTCA compared with Acc t-PA.
Table 2.3 Extended thrombolytics example: median and 95% CrI for the odds ratios and between-study standard deviation (heterogeneity) from fixed and random effects models.
Table 2.4 Extended thrombolytics example: results from the fixed effects network meta-analysis model.
Chapter 03
Table 3.1 Full thrombolytics example: p D σ and DIC for both the fixed and random effects models.
Table 3.2 Adverse events in chemotherapy example: number of adverse events rik , out of the total number of patients receiving chemotherapy nik , in arms 1 and 2 of 25 trials for the four treatments tik . Data from Madan et al. (2011).
Chapter 04
Table 4.1 Commonly used likelihood, link functions, inverse link functions and formulae for the residual deviance.
Table 4.2 Dietary fat example: study names and treatment codes for the 10 included studies and person-years and total mortality observed in each study. Data from Hooper et al. (2000).
Table 4.3 Dietary fat example: posterior median and 95% CrI for both fixed and random effects models for the treatment effect d 12 , absolute effects of the control diet (T 1 ) and the reduced fat diet (T 2 ) for a log rate of mortality on the control diet with mean −3 and precision 1.77; heterogeneity standard deviation, σ ; and model fit statistics.
Table 4.4 Diabetes example: study names, follow-up time in years, treatments compared, total number of new cases of diabetes and number of patients in each trial arm, where diuretic = treatment 1, placebo = treatment 2, β-blocker = treatment 3, CCB = treatment 4, ACE inhibitor = treatment 5 and ARB = treatment 6. Data from Elliott & Meyer (2007).
Table 4.5 Diabetes example: posterior median and 95% CrI for both fixed and random effects models for the treatment effects of placebo (d 12 ), β-blocker (d 13 ), CCB (d 14 ), ACE inhibitor (d 15 ) and ARB (d 16 ) relative to diuretic; absolute effects of diuretic (T 1 ) placebo (T 2 ), β-blocker (T 3 ), CCB (T 4 ), ACE inhibitor (T 5 ) and ARB (T 6 ); heterogeneity parameter σ and model fit statistics.
Table 4.6 Parkinson’s example: mean off-time reduction (y ) with its standard deviation (sd) and total number of patients in each trial arm (n ); treatment differences (diff) and standard error of the differences (se(diff)); where treatment 1 is a placebo and treatments 2–5 are active drugs. Data from Franchini et al. (2012).
Table 4.7 Parkinson’s example: posterior median and 95% CrI for both fixed and random effects models for the treatment effects of treatments 2–5 (d 12 –d 15 ) relative to placebo, absolute effects of placebo (T 1 ) and treatments 2–5 (T 2 –T 5 ), heterogeneity parameter σ and model fit statistics for the data presented as arm-level means and standard errors.
Table 4.8 Parkinson’s example (treatment differences): posterior median and 95% CrI for both fixed and random effects models for the treatment effects of treatments 2–5 (d 12 –d 15 ) relative to placebo, absolute effects of placebo (T 1 ) and treatments 2–5 (T 2 –T 5 ), heterogeneity parameter σ and model fit statistics for trial-level data.
Table 4.9 Psoriasis example: study names, treatments compared, total number of patients with different percentage improvement and total number of patients in each trial arm, where supportive care = treatment 1, etanercept 25 mg = 2, etanercept 50 mg = 3, efalizumab = 4, ciclosporin = 5, fumaderm = 6, infliximab = 7 and methotrexate = 8. Data from Woolacott et al. (2006).
Table 4.10 Psoriasis example: posterior median and 95% CrI from the random effects model on the probit scale for the relative effects of all treatments compared with supportive care and absolute probabilities of achieving at least 50, 70 or 90% relief in symptoms for each treatment (PASI-50, 75, 90).
Table 4.11 Schizophrenia example (data from Ades et al., 2010): study names, follow-up time in weeks, treatments compared, total number of events for each of the four states and total number of patients in each trial arm, where placebo = treatment 1, olanzapine = 2, amisulpride = 3, zotepine = 4, aripiprazole = 5, ziprasidone = 6, paliperidone = 7, haloperidol = 8 and risperidone = 9.
Table 4.12 Schizophrenia example: posterior median and 95% CrI for both fixed and random effects models for the treatment effects of olanzapine (d 12 ), amisulpride (d 13 ), zotepine (d 14 ), aripiprazole (d 15 ), ziprasidone (d 16 ), paliperidone (d 17 ), haloperidol (d 18 ) and risperidone (d 19 ) relative to placebo, absolute probabilities of reaching each of the outcomes for placebo (Pr 1 ), olanzapine (Pr 2 ), amisulpride (Pr 3 ), zotepine (Pr 4 ), aripiprazole (Pr 5 ), ziprasidone (Pr 6 ), paliperidone (Pr 7 ), haloperidol (Pr 8 ) and risperidone (Pr 9 ); heterogeneity parameter τ for each of the three outcomes; and model fit statistics for the fixed and random effects models.
Table 4.13 Parkinson’s example (shared parameter model): posterior median and 95% CrI for both fixed and random effects models for the treatment effects of treatments 2–5 (d 12 –d 15 ) relative to placebo, absolute effects of placebo (T 1 ) and treatments 2–5 (T 2 –T 5 ), heterogeneity parameter τ and model fit statistics for different data types.
Chapter 05
Table 5.1 Smoking Cessation Data (Lu and Ades 2006): events, r , are the number of individuals with successful smoking cessation at 6–12 months out of the total individuals randomised to each trial arm, n .
Table 5.2 Comparison of separate estimation of absolute and relative effects, the preferred approach, with joint estimation of absolute and relative effect.
Chapter 07
Table 7.1 Direct estimates for virologic suppression in patients with HIV (data from Chou et al., 2006).
Table 7.2 Enuresis example: all possible direct estimates presented as log relative risks, ln(RR), obtained from separate meta-analysis using a fixed effects model. Data from Caldwell et al., 2010.
Table 7.3 Enuresis example: indirect estimates of alarm versus no treatment effect presented as log relative risks, ln(RR).
Table 7.4 Thrombolytics example: posterior summaries (mean and 95% credible interval) on the log odds ratio scale for treatments Y compared with X for all contrasts that are informed by direct and indirect evidence; and posterior mean of the residual deviance (resdev), pD and DIC, from the fixed effects consistency and UME inconsistency models.
Table 7.5 Adjusted data for studies 1 and 6, given as treatment differences with adjusted standard errors.
Table 7.6 Parkinson’s example: assessment of inconsistency for a single loop using Bucher’s method in WinBUGS.
Chapter 08
Table 8.1 BCG vaccine example: number of patients diagnosed with TB, r , out of the total number of patients, n , in the vaccinated and unvaccinated groups and the absolute latitude at which the trial was conducted, x .
Table 8.2 BCG vaccine example: results from the random effects meta-analyses with and without the covariate absolute distance from the equator.
Table 8.3 Certolizumab example: number of patients achieving ACR-50 at 6 months, r , out of the total number of patients, n , in the arms 1 and 2 of the 12 trials and mean disease duration (in years) for patients in trial i , xi .
Table 8.4 Certolizumab example: results from the fixed and random effects models with and without the covariate ‘disease duration’.
Table 8.5 Certolizumab example: results from the fixed and random effects models with and without the covariate ‘baseline risk’.
Table 8.6 Statins example: data on statins and placebo for cholesterol lowering in patients with and without previous heart disease (Sutton, 2002) – number of deaths due to all-cause mortality in the control and statin arms of 19 RCTs.
Table 8.7 Statins example: results from the fixed and random effects models for primary and secondary prevention groups.
Chapter 09
Table 9.1 Fluoride example: posterior summaries for the bias model using allocation concealment rated as inadequate or unclear as an indicator of high risk of bias.
Chapter 10
Table 10.1 Common distributions used for the analysis of time-to-event data along with the corresponding survival and hazard functions.
Table 10.2 Model fit statistics for the different competing network meta-analysis models for the multiple myeloma example.
Table 10.3 Model parameter estimates representing multidimensional treatment effects of each intervention (MPT, CTDa, MPV) relative to the baseline treatment (MP) as obtained with fixed effects second-order fractional polynomial model with p 1 = 0 and p 2 = 1.
Chapter 11
Table 11.1 Coronary patency example (Ades 2003). Reproduced with permission of John Wiley & sons.
Table 11.2 Trials on intravenous antibiotic prophylaxis to prevent neonatal early onset group B streptococcal (EOGBS) infection.
Table 11.3 Gastro-esophageal reflux (Lu et al., 2007).
Table 11.4 Influenza treatment (Welton et al., 2008b).
Table 11.5 Ankylosing spondylitis (Lu et al., 2014).
Table 11.6 Social anxiety (Ades et al., 2015).
Table 11.7 Advanced breast cancer data structure: overall proportion in each category; median time to tumour progression, by category; median overall survival, by category.
Table 11.8 Data to inform the Markov transition probability or rate models of Figure 11.4 for a single arm.
Chapter 12
Table 12.1 Expected error and expected absolute error in a ‘direct comparison’ meta-analysis with N = 1 RCTs in the presence of an unrecognised effect modifier, present with probability π = 0.5.
Table 12.2 Expected error and expected absolute error in a ‘direct comparison’ meta-analysis with N = 2 RCTs in the presence of an unrecognised effect modifier, present with probability π = 0.5.
List of Illustrations
Chapter 01
Figure 1.1 Some examples of connected networks: (a) a pairwise comparison, (b) an indirect comparison via reference treatment A, (c) a ‘snake’ indirect comparison structure, (d) another indirect comparison structure, (e) a simple triangle network and (f) a network of evidence on thrombolytics drugs for acute myocardial infarction (Boland et al., 2003).
Figure 1.2 (a) An unconnected network; (b) use of an intermediate treatment to link a network (dashed lines); (c) other intermediate treatments that could also be used as links; and (d) incorporation of all trials comparing the enlarged set of treatments.
Chapter 02
Figure 2.1 Extended thrombolytics example: network plot. Seven treatments are compared (data from Caldwell et al., 2005): Streptokinase (SK), tissue-plasminogen activator (t-PA), accelerated tissue-plasminogen activator (Acc t-PA), reteplase (r-PA), tenecteplase (TNK), percutaneous transluminal coronary angioplasty (PTCA). The numbers on the lines and line thickness represent the number of studies making those comparisons, the widths of the circles are proportional to the number of patients randomised to each treatment, and the numbers in brackets are the treatment codes used in WinBUGS.
Figure 2.2 Extended thrombolitics example (pairwise meta-analysis): posterior distribution of d[2], the log odds ratio of PTCA compared with Acc t-PA, from the fixed effects model – from WinBUGS.
Figure 2.3 Extended thrombolytics example (pairwise meta-analysis): posterior distribution of the between-study standard deviation (sd) for the meta-analysis of PTCA and Acc t-PA – from WinBUGS.
Figure 2.4 Extended thrombolytics example: caterpillar plot – from WinBUGS. Dots are posterior medians and lines represent 95% CrI for the log odds ratios of all treatments compared with SK, the reference treatment, from the fixed effects model. Numbers represent the treatment being compared (see Figure 2.1) and negative log odds ratios favour that treatment.
Figure 2.5 Extended thrombolytics example: summary forest plot – medians (dots) and 95% CrI (solid lines) for the ORs of all treatments compared with each other from the fixed effects model, plotted on a log scale. ORs < 1 favour the second treatment. Treatment definitions are given in Figure 2.1.
Figure 2.6 Extended thrombolytics example: probability that each treatment is ranked 1–7 for fixed and random effects models. Treatment definitions are given in Figure 2.1.
Figure 2.7 Extended thrombolytics example: posterior distribution of the between-study standard deviation – from WinBUGS.
Chapter 03
Figure 3.1 Full thrombolytic treatments network: lines connecting two treatments indicate that a comparison between these treatments (in one or more RCTs) has been made: streptokinase (SK), tissue plasminogen activator (t-PA), accelerated t-PA (Acc t-PA), reteplase (r-PA), tenecteplase (TNK), percutaneous transluminal coronary angioplasty (PTCA), urokinase (UK) and anistreplase (ASPAC). The width of the lines reflects the number of studies providing evidence on that comparison, the size of the circles is proportional to the number of patients randomised to that treatment, and the numbers by the treatment names are the treatment codes used in the modelling. There are 2 three-arm trials: SK versus Acc t-PA versus SK + t-PA and SK versus t-PA versus ASPAC.
Figure 3.2 Full thrombolytic network example: output from the DIC tool for the network meta-analysis – from WinBUGS.
Figure 3.3 Full thrombolytics example: box plot of the contribution of each study to the residual deviance – from WinBUGS. The boxes represent the interquartile range, the line across the box represents the median, and the whiskers represent the 95% credible intervals. Numbers above the lines represent the study. The horizontal line indicates a contribution to residual deviance of 2, which is expected from a two-arm trial. For the 2 three-arm trials (studies 1 and 6), we would expect a contribution of 3.
Figure 3.4 Full thrombolytics example: posterior mean (asterisks) and 95% credible intervals displayed for log odds ratios of each treatment compared to treatment 1 (SK) for both fixed effects (solid) and random effects (dashed) models. The vertical line indicates the line of no effect (log odds ratio = 0).
Figure 3.5 Full thrombolytics example, fixed effects model: plot of leverage, leverageik , versus posterior mean deviance residual, wik , for each data point, with curves of the form x 2 + y = c representing a contribution to the DIC of c = 1, 2, 3 as indicated. Studies 44 and 45 are indicated with a star plotting symbol.
Figure 3.6 Full thrombolytics example, random effects model: plot of leverage, leverageik , versus posterior mean deviance residual, wik , for each data point, with curves of the form x 2 + y = c representing a contribution to the DIC of c = 1, 2, 3 as indicated. Studies 44 and 45 are indicated with a star plotting symbol.
Figure 3.7 Magnesium example: crude log odds ratios with 95% CI (filled squares, solid lines); posterior mean with 95% CrI of the trial-specific log odds ratios, ‘shrunken’ estimates (open squares, dashed lines); posterior mean with 95% CrI of the posterior (filled diamond, solid line) and predictive distribution (open diamond, dashed line) of the pooled treatment effect, obtained from a random effects model including all the trials.
Figure 3.8 Magnesium example: crude log odds ratios with 95% CI (filled squares, solid lines); posterior mean with 95% CrI of the trial-specific log odds ratios, ‘shrunken’ estimates (open squares, dashed lines); posterior mean with 95% CrI of the posterior (filled diamond, solid line) and predictive distribution (open diamond, dashed line) of the pooled treatment effect, obtained from a random effects model excluding the ISIS-4 trial.
Figure 3.9 Adverse events in chemotherapy example: treatment network. Lines connecting two treatments indicate that a comparison between these treatments has been made. The width of the lines is proportional to the number of studies providing evidence on that comparison (also marked on the lines), the size of the circles is proportional to the number of patients randomised to that treatment, and the numbers by the treatment names are the treatment codes used in the modelling.
Figure 3.10 Adverse events in chemotherapy example – comparison of treatment 1 and 3: crude log odds ratios with 95% CI (filled squares, solid lines); posterior mean with 95% CrI of the trial-specific log odds ratios, ‘shrunken’ estimates (open squares, dashed lines); posterior mean with 95% CrI of the posterior (filled diamond, solid line) and predictive distribution (open diamond, dashed line) of the pooled treatment effect for a random effects model (a) including all the trials and (b) excluding trial 25 (cross-validation model).
Figure 3.11 Adverse events in chemotherapy example: beta distribution representing the probability of an event in arm 1 predicted for a study like trial 25, equation (3.8). The solid line indicates the observed proportion of events in arm 1 of trial 25, 78/465 = 0.168.
Chapter 04
Figure 4.1 Dietary fat example: WinBUGS DIC tool output for the fixed and random effects models.
Figure 4.2 Dietary fat example: posterior distribution of the between-study standard deviation – from WinBUGS.
Figure 4.3 Diabetes network: each circle represents a treatment, and connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Figure 4.4 Diabetes example: caterpillar plot showing log hazard ratios of all treatments compared to the reference for the random effects model – from WinBUGS. The treatment being compared is indicated in square brackets; negative values favour this treatment.
Figure 4.5 Diabetes example: posterior distribution of the between-study standard deviation – from WinBUGS.
Figure 4.6 Parkinson’s network: each circle represents a treatment, and connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Figure 4.7 Parkinson’s example: posterior distribution of the between-study standard deviation – from WinBUGS.
Figure 4.8 Parkinson’s example: caterpillar plot showing posterior medians and 95% CrI of the mean differences of all treatments compared to the reference for the fixed effects model. The treatment being compared is indicated in square brackets; negative values favour this treatment – from WinBUGS.
Figure 4.9 Example of categorised measurement scale as reported in arm k of trial i (assumed normal) where five categories are defined by thresholds X 0 to X 4 (the upper bound of the last category is the scale’s natural upper bound).
Figure 4.10 Psoriasis network: each circle represents a treatment, and connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Figure 4.11 Schizophrenia example: outcomes and parameters of interest in the model.
Figure 4.12 Schizophrenia network: each circle represents a treatment, and connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Chapter 05
Figure 5.1 Smoking Cessation network: there are 22 two-arm and 2 three-arm trials. Each circle represents a treatment; connecting lines indicate pairs of treatments, which have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Figure 5.2 Smoking Cessation: decision tree for cost-effectiveness analysis of the four strategies (Welton et al. 2012).
Figure 5.3 Smoking Cessation: cost-effectiveness acceptability curves, (a) distribution of mean treatment effects and (b) distribution of predictive treatment effects.
Chapter 07
Figure 7.1 Hypothetical network with two independent loops.
Figure 7.2 Enuresis treatment network (Caldwell et al., 2010): lines connecting two treatments indicate that a comparison between these treatments has been made and the thickness of the lines is proportional to the number or RCTs making that comparison.
Figure 7.3 Full Thrombolytics example: plot of the individual data points’ posterior mean deviance contributions for the network meta-analysis model (NMA) (horizontal axis) and the UME inconsistency model with original arm-level data (vertical axis), along with the line of equality. Points that have a better fit in the inconsistency model or correspond to a zero cell have been marked with the trial and arm number.
Figure 7.4 Parkinson’s example: plot of each data points’ contribution to the residual deviance for the network meta-analysis (NMA) with consistency and UME inconsistency models.
Figure 7.5 Diabetes example: plot of the individual data points’ posterior mean deviance contributions for the network meta-analysis model with consistency (NMA) (horizontal axis) and the UME inconsistency model (vertical axis) along with the line of equality. Points that have a better fit in one of the models have been marked with the trial and arm number, respectively.
Chapter 08
Figure 8.1 BCG vaccine example: effect of covariate adjustment (absolute distance from the equator). Observed log ORs with 95% CI (black circles, solid lines); posterior median with 95% CrI of the trial-specific log ORs (the ‘shrunken’ estimates) for the random effects models with no covariate (black squares, black dashed lines) and with covariate (grey triangles, grey dashed lines); median with 95% CrI of the posterior (black diamond, solid line) and predictive distribution (open diamond, dashed line) of the pooled treatment effect for the random effects model with no covariates; and median with 95% CrI of the posterior (grey diamond, grey solid line) and predictive distribution (grey open diamond, grey dashed line) of the pooled treatment effect at the mean covariate value for the random effects model with covariate absolute distance from the equator.
Figure 8.2 BCG vaccine example: plot of the crude odds ratios (on a log scale) against absolute distance from the equator in degrees latitude. The size of the circles is proportional to the studies’ precisions, the horizontal line (dashed) represents no treatment effect, the vertical line (dashed) is at the mean covariate value (33.46° latitude), and the solid line is the regression line estimated by the random effects model including degrees latitude as a continuous covariate. Odds ratios below 1 favour the vaccine.
Figure 8.3 Certolizumab example: treatment network. Each circle represents a treatment, and connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling. Line thickness is proportional to the number of trials making that comparison, and the width of the circles is proportional to the number of patients randomised to that treatment.
Figure 8.4 Certolizumab example: plot of the crude odds ratios (on a log scale) of the six active treatments relative to placebo plus MTX against mean disease duration (in years). The plotted numbers refer to the treatment being compared with placebo plus MTX, the blobs around the numbers are proportional to the precision of the study, and the lines represent the relative effects of the following treatments (from top to bottom) compared with placebo plus MTX based on a random effects meta-regression model: etanercept plus MTX (treatment 4, dotted line), CZP plus MTX (treatment 2, solid line), tocilizumab plus MTX (treatment 7, short–long dash line), adalimumab plus MTX (treatment 3, dashed line), infliximab plus MTX (treatment 5, dot-dashed line) and rituximab plus MTX (treatment 6, long-dashed line). Odds ratios above 1 favour the plotted treatment, and the horizontal line (thin dashed) represents no treatment effect.
Figure 8.5 Certolizumab example: probability density function of (a) Half-Normal(0,0.322 ) prior distribution simulated in WinBUGS and (b) the posterior distribution for the between-study heterogeneity for the meta-regression model with informative Half-Normal(0,0.322 ) prior distribution – from WinBUGS.
Figure 8.6 Certolizumab example: plot of the crude odds ratios of the six active treatments relative to placebo plus MTX against odds of baseline response on a log scale. The plotted numbers refer to the treatment being compared with placebo plus MTX, and the lines represent the relative effects of the following treatments (from top to bottom) compared with placebo plus MTX based on a random effects meta-regression model: tocilizumab plus MTX (7, short–long dash line), adalimumab plus MTX (3, dashed line), etanercept plus MTX (4, dotted line), CZP plus MTX (2, solid line), infliximab plus MTX (5, dot-dashed line) and rituximab plus MTX (6, long-dashed line). Odds ratios above 1 favour the plotted treatment, and the horizontal line (dashed) represents no treatment effect.
Figure 8.7 Pain data example (data from Achana et al., 2013): treatment network. Connecting lines indicate pairs of treatments that have been directly compared in randomised trials. The numbers on the lines indicate the numbers of trials making that comparison, and the numbers by the treatment names are the treatment codes used in the modelling.
Figure 8.8 Mortality after cardiac surgery example (Zangrillo et al., 2015): treatment network. Connecting lines indicate pairs of treatments that have been directly compared in randomised trials. Solid lines represent two-arm studies, and the connected dotted lines represent a three-arm study. The numbers on the lines indicate the numbers of trials making each comparison, and the numbers by the treatment names are the treatment codes used in the modelling.
Chapter 09
Figure 9.1 Fluoride example: network of treatment comparisons (drawn using R code from Salanti (2011)). The thickness of the lines is proportional to the number of trials making that comparison and the width of the bubbles is proportional to the number of patients randomised to each treatment (Salanti et al., 2009).
Figure 9.2 Fluoride example: estimated posterior means and 95% credible intervals for log-hazard ratios compared with no treatment for the following: Pl, placebo; T, toothpaste; R, rinse; G, gel; V, varnish. Results from a network meta-analysis model with no bias adjustment shown with diamonds and solid lines. Circles and dotted lines represent results from bias adjustment model 1 with common mean bias term for the active versus placebo or no-treatment comparisons, zero mean bias for active versus active comparisons, a probability of being at risk of bias in studies rated as unclear. The vertical dotted line represents no effect.
Chapter 10
Figure 10.1 Hazard functions with intervention A and B according to Weibull distributions with different scale and shape parameters along with corresponding time-varying hazard ratio. The constant hazard ratio relying on the proportional hazard assumption is not supported by the data resulting in a biased estimate of the relative treatment effect.
Figure 10.2 Evidence network of randomised controlled trials comparing melphalan–prednisone–bortezomib (MPV), melphalan–prednisone–thalidomide (MPT) and cyclophosphamide–thalidomide–dexamethasone attenuated (CTDa) regimen for the first-line treatment of multiple myeloma in patients not eligible for HDT-SCT.
Figure 10.3 Relative treatment effect estimates of each intervention (MPT, CTDa, MPV) versus reference treatment (MP) expressed as hazard ratios as obtained with fixed effects second-order FP network meta-analysis model with p 1 = 0 and p 2 = 1. 95% credible intervals indicated by broken lines.
Figure 10.4 Relative treatment effect estimates of MPV versus MPT, CTDa and MP expressed as hazard ratios as obtained with second-order FP network meta-analysis model with p 1 = 0 and p 2 = 1. 95% credible intervals indicated by broken lines.
Figure 10.5 Overall survival by intervention based on relative treatment effect estimates of each intervention (MPT, CTDa, MPV) versus reference treatment (MP) as obtained with second-order FP network meta-analysis model with p 1 = 0 and p 2 = 1 and applied to OS curve with MP from study 8. 95% credible intervals indicated by broken lines.
Chapter 11
Figure 11.1 Decision tree for coronary patency example (Ades, 2003).
Figure 11.2 Decision tree for early onset group B streptococcus example (Colbourn et al., 2007a).
Figure 11.3 Evidence structure in the gastro-esophageal reflux disease example (Lu et al., 2007).
Figure 11.4 Influenza example (Welton et al., 2008b). (a) The underlying Markov model. (b) Structure of evidence and relation to the model.
Figure 11.5 Simultaneous mapping and synthesis: (a) connected network of six outcomes in trials of biologic therapy in ankylosing spondylitis (Lu et al., 2014). ASQOL, ankylosing spondylitis quality of life; BASDAI, Bath Ankylosing Spondylitis Disease Activity Index; BASFI, bath ankylosing spondylitis functional index; PAIN VAS, pain visual analog scale; SF36-PCS/MCS, short form 36 physical/mental summary. (b) A connected network of nine outcomes in treatments for social anxiety (Ades et al., 2015). BSPS, brief social phobia scale; CGI-S, clinical global impression – severity; FNE, fear of negative evaluation; FQ-SP, fear quotient – social phobia; LSAS, Liebowitz social anxiety scale; SADS, social avoidance and distress scale; SDS, Sheehan disability scale; SPAI-SP, social phobia and anxiety inventory – social phobia; SPIN, social phobia inventory.
Figure 11.6 Advanced breast cancer: network of evidence (Welton et al., 2010). CAP, capecitabine; DOC, docetaxel; GEM, gemcitabine; M + V, mitomycin and vinblastine; PAC, paclitaxel. The numbers in brackets reflect the treatment ordering used in modelling.
Figure 11.7 (a) Markov transition probability model, (b) Markov rate model. STW, successfully treated weeks; TF, treatment failure; UTW, unsuccessfully treated weeks; X, exacerbation (Price et al., 2011).
Chapter 12
Figure 12.1 Direct comparisons: expected absolute error in meta-analyses, in units of θ , as a function of the number of trials and the population proportion π of trials with a trial-level effect modifier that adds θ to the treatment effect.
Figure 12.2 Absolute expected error in direct comparisons, or indirect comparisons, where only one of the direct contrasts is subject to an effect modifier present with probability
Figure 12.3 Illustration of the difference between direct and indirect estimates formed from two direct comparisons that are both affected by an unrecognised effect modifier.
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Advisory Editor, Marian Scott, University of Glasgow, Scotland, UK
Founding Editor, Vic Barnett, Nottingham Trent University, UK
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Advisory Editor, Marian Scott, University of Glasgow, Scotland, UK
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Sofia Dias
University of Bristol
A. E. Ades
University of Bristol
Nicky J. Welton
University of Bristol
Jeroen P. Jansen
Precision Health Economics
Alexander J. Sutton
University of Leicester
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