Network Meta-Analysis for Decision-Making E-Book

Sofia Dias

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Statistics in Practice
• Sprache: Englisch

Seitenzahl: 876

Veröffentlichungsjahr: 2018

Beschreibung

A practical guide to network meta-analysis with examples and code

In the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish which interventions are effective and cost-effective. Often a single study will not provide the answers and it is desirable to synthesise evidence from multiple sources, usually randomised controlled trials. This book takes an approach to evidence synthesis that is specifically intended for decision making when there are two or more treatment alternatives being evaluated, and assumes that the purpose of every synthesis is to answer the question "for this pre-identified population of patients, which treatment is 'best'?"

A comprehensive, coherent framework for network meta-analysis (mixed treatment comparisons) is adopted and estimated using Bayesian Markov Chain Monte Carlo methods implemented in the freely available software WinBUGS. Each chapter contains worked examples, exercises, solutions and code that may be adapted by readers to apply to their own analyses.

This book can be used as an introduction to evidence synthesis and network meta-analysis, its key properties and policy implications. Examples and advanced methods are also presented for the more experienced reader.

• Methods used throughout this book can be applied consistently: model critique and checking for evidence consistency are emphasised.
• Methods are based on technical support documents produced for NICE Decision Support Unit, which support the NICE Methods of Technology Appraisal.
• Code presented is also the basis for the code used by the ISPOR Task Force on Indirect Comparisons.
• Includes extensive carefully worked examples, with thorough explanations of how to set out data for use in WinBUGS and how to interpret the output.

Network Meta-Analysis for Decision Making will be of interest to decision makers, medical statisticians, health economists, and anyone involved in Health Technology Assessment including the pharmaceutical industry.

Leseprobe

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

r

ik

, out of the total number of patients receiving chemotherapy

n

ik

, in arms 1 and 2 of 25 trials for the four treatments

t

ik

. 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),

p

D

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

,

x

i

.

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,

leverage

ik

, versus posterior mean deviance residual,

w

ik

, 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,

leverage

ik

, versus posterior mean deviance residual,

w

ik

, 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(0,0.32

2

) prior distribution simulated in WinBUGS and (b) the posterior distribution for the between-study heterogeneity for the meta-regression model with informative Half-Normal(0,0.32

2

) 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

(lower curve) and indirect comparisons where both direct contrasts are subject to the same effect modifier (upper curve). In units of the interaction term.

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.

Guide

Cover

Table of Contents

Begin Reading

Pages

ii

iii

iv

xiii

xiv

xv

xvi

xvii

xviii

xix

xx

xxi

xxii

xxiii

xxv

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

401

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

447

448

449

450

451

452

453

454

455

456

Wiley Series in Statistics in Practice

Advisory Editor, Marian Scott, University of Glasgow, Scotland, UK

Founding Editor, Vic Barnett, Nottingham Trent University, UK

Statistics in Practice is an important international series of texts that provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.

With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title’s special topic area.

The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences; and so on.

The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges.

It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim.

A complete list of titles in this series appears at the end of the volume.

Wiley Series in Statistics in Practice

Advisory Editor, Marian Scott, University of Glasgow, Scotland, UK

Founding Editor, Vic Barnett, Nottingham Trent University, UK

Human and Biological Sciences

Brown and Prescott · Applied Mixed Models in Medicine

Ellenberg, Fleming and DeMets · Data Monitoring Committees in Clinical Trials:

A Practical Perspective

Lawson, Browne and Vidal Rodeiro · Disease Mapping With WinBUGS and MLwiN

Lui · Statistical Estimation of Epidemiological Risk

*Marubini and Valsecchi · Analysing Survival Data from Clinical Trials and Observation Studies

Parmigiani · Modeling in Medical Decision Making: A Bayesian Approach

Senn · Cross-over Trials in Clinical Research, Second Edition

Senn · Statistical Issues in Drug Development

Spiegelhalter, Abrams and Myles · Bayesian Approaches to Clinical Trials and Health-Care Evaluation

Turner · New Drug Development: Design, Methodology, and Analysis

Whitehead · Design and Analysis of Sequential Clinical Trials, Revised Second Edition

Whitehead · Meta-Analysis of Controlled Clinical Trials

Zhou, Zhou, Liu and Ding · Applied Missing Data Analysis in the Health Sciences

Earth and Environmental Sciences

Buck, Cavanagh and Litton · Bayesian Approach to Interpreting Archaeological Data

Cooke · Uncertainty Modeling in Dose Response: Bench Testing Environmental Toxicity

Gibbons, Bhaumik, and Aryal · Statistical Methods for Groundwater Monitoring, Second Edition

Glasbey and Horgan · Image Analysis in the Biological Sciences

Helsel · Nondetects and Data Analysis: Statistics for Censored Environmental Data

Helsel · Statistics for Censored Environmental Data Using Minitab® and R, Second Edition

McBride · Using Statistical Methods for Water Quality Management: Issues, Problems and Solutions

Ofungwu · Statistical Applications for Environmental Analysis and Risk Assessment

Webster and Oliver · Geostatistics for Environmental Scientists

Industry, Commerce and Finance

Aitken and Taroni · Statistics and the Evaluation of Evidence for Forensic Scientists, Second Edition

Brandimarte · Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, Second Edition

Brandimarte and Zotteri · Introduction to Distribution Logistics

Chan and Wong · Simulation Techniques in Financial Risk Management, Second Edition

Jank · Statistical Methods in eCommerce Research

Jank and Shmueli · Modeling Online Auctions

Lehtonen and Pahkinen · Practical Methods for Design and Analysis of Complex Surveys, Second Edition

Lloyd · Data Driven Business Decisions

Ohser and Mücklich · Statistical Analysis of Microstructures in Materials Science

Rausand · Risk Assessment: Theory, Methods, and Applications

Network Meta-Analysis for Decision-Making

Sofia Dias

University of BristolBristol, UK

A. E. Ades

University of BristolBristol, UK

Nicky J. Welton

University of BristolBristol, UK

Jeroen P. Jansen

Precision Health EconomicsOakland, CA

Alexander J. Sutton

University of LeicesterLeicester, UK

This edition first published 2018© 2018 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Sofia Dias, A. E. Ades, Nicky J. Welton, Jeroen P. Jansen and Alexander J. Sutton to be identified as the authors of this work has been asserted in accordance with law.

Registered OfficesJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USAJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

Editorial Office9600 Garsington Road, Oxford, OX4 2DQ, UK

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data

Names: Dias, Sofia, 1977- author.Title: Network meta-analysis for decision-making / by Sofia Dias, University of Bristol, Bristol, UK [and four others].Description: Hoboken, NJ : Wiley, 2018. | Includes bibliographical references and index. |Identifiers: LCCN 2017036441 (print) | LCCN 2017048849 (ebook) | ISBN 9781118951712 (pdf) | ISBN 9781118951729 (epub) | ISBN 9781118647509 (cloth)Subjects: LCSH: Meta-analysis. | Mathematical analysis.Classification: LCC R853.M48 (ebook) | LCC R853.M48 N484 2018 (print) | DDC 610.72/7–dc23LC record available at https://lccn.loc.gov/2017036441

Cover Design: WileyCover Image: © SergeyNivens/Gettyimages

Preface

1. Who Is This Book for?

This book is intended for anyone who has an interest in the synthesis, or ‘pooling’, of evidence from randomised controlled trials (RCTs) and particularly in the statistical methods for network meta-analysis. A standard meta-analysis is used to pool information from trials that compare two interventions, while network meta-analysis extends this to the comparison of any number of interventions.

Network meta-analysis is one of the core methodologies of what has been called comparative effectiveness research (Iglehart, 2009), and, in view of the prime role accorded to trial evidence over other forms of evidence on comparative efficacy, it might be considered to be the most important.

The core material in this book is largely based on a 3-day course that we have been running for several years. Based on the spectrum of participants we see on our course, we believe the book will engage a broad range of professionals and academics. Firstly, it should appeal to all statisticians who have an interest in evidence synthesis, whether from a methodological viewpoint or because they are involved in applied work arising from systematic reviews, including the work of the Cochrane Collaboration.

Secondly, the methods are an essential component of health technology assessment (HTA) and are routinely used in submissions not only to re-imbursement agencies such as the National Institute for Health and Care Excellence (NICE) in England but also, increasingly, to similar organisations worldwide, including the Canadian Agency for Drugs and Technologies in Health, the US Agency for Healthcare Research and Quality and the Institute for Quality and Efficiency in Health Care in Germany. Health economists involved in HTA in academia and those working in pharmaceutical companies, or for the consultancy firms who assist them in making submissions to these bodies, comprise the largest single professional group for whom this book is intended.

Clinical guidelines are also making increasing use of network meta-analysis, and statisticians and health economists working with medical colleges on guideline development represent a third group who will find this book highly relevant.

Finally, the book will also be of interest, we believe, to those whose role is to manage systematic reviews, clinical guideline development or HTA exercises and those responsible at a strategic level for determining the methodological approaches that should underpin these activities. For these readers, who may not be interested in the technical details, the book sets out the assumptions of network meta-analysis, its properties, when it is appropriate and when it is not.

The book can be used in a variety of ways to suit different backgrounds and interests, and we suggest some different routes through the book at the end of the preface.

2. The Decision-Making Context

The contents of this book have their origins in the methodology guidance that was produced for submissions to NICE. This is the body in England and Wales responsible for deciding which new pharmaceuticals are to be used in the National Health Service. This context has shaped the methods from the beginning.

First and foremost, the book is about an approach to evidence synthesis that is specifically intended for decision-making. It assumes that the purpose of every synthesis is to answer the question ‘for this pre-identified population of patients, which treatment is “best”?’ Such decisions can be made on any one of a range of grounds: efficacy alone, some balance of efficacy and side effects, perhaps through multi-criteria decision analysis (MCDA) or cost-effectiveness. At NICE, decisions are based on efficacy and cost-effectiveness, but whatever criteria are used, the decision-making context impacts evidence synthesis methodology in several ways.

Firstly, the decision maker must have in mind a quite specific target population, not simply patients with a particular medical condition but also patients who have reached a certain point in their natural history or in their referral pathway. These factors influence a clinician’s choice of treatment for an individual patient, and we should therefore expect them to impact how the evidence base and the decision options are identified. Similarly, the candidate interventions must also be characterised specifically, bearing in mind the dose, mode of delivery and concomitant treatments. Each variant has a different effect and also a different cost, both of which might be taken into account in any formal decision-making process. It has long been recognised that trial inclusion criteria for the decision-making context will tend to be more narrowly drawn than those for the broader kinds of synthesis that aim for what may be best described as a ‘summary’ of the literature (Eccles et al., 2001). In a similar vein Rubin (1990) has distinguished between evidence synthesis as ‘science’ and evidence synthesis as ‘summary’. The common use of random effects models to average over important heterogeneity has attracted particular criticism (Greenland, 1994a, 1994b).

Recognising the centrality of this issue, the Cochrane Handbook (Higgins and Green, 2008) states: ‘meta-analysis should only be considered when a group of studies is sufficiently homogeneous in terms of participants, interventions and outcomes to provide a meaningful summary’. However, perhaps because of the overriding focus on scouring the literature to secure ‘complete’ ascertainment of trial evidence, this advice is not always followed in practice. For example, an overview of treatments for enuresis (Russell and Kiddoo, 2006) put together studies on treatments for younger, treatment-naïve children, with studies on older children who had failed on standard interventions. Not surprisingly, extreme levels of statistical heterogeneity were observed, reflecting the clinical heterogeneity of the populations included (Caldwell et al., 2010). This throws doubt on any attempt to achieve a clinically meaningful answer to the question ‘which treatment is best?’ based on such a heterogeneous body of evidence. Similarly, one cannot meaningfully assess the efficacy of biologics in rheumatoid arthritis by combining trials on first-time use of biologics with trials on patients who have failed on biologic therapy (Singh et al., 2009). These two groups of patients require different decisions based on analyses of different sets of trials. A virtually endless list of examples could be cited. The key point is that the immediate effect of the decision-making perspective, in contrast to the systematic review perspective, is to greatly reduce the clinical heterogeneity of the trial populations under consideration.

The decision-making context has also made the adoption of Bayesian Markov chain Monte Carlo (MCMC) methods almost inevitable. The preferred form of cost-effectiveness analysis at NICE is based on probabilistic decision analysis (Doubilet et al., 1985; Critchfield and Willard, 1986; Claxton et al., 2005b). Uncertainty in parameters arising from statistical sampling error and other sources of uncertainty can be propagated through the decision model to be reflected in uncertainty in the decision. The decision itself is made on a ‘balance of evidence’ basis: it is an ‘optimal’ decision, given the available evidence, but not necessarily the ‘correct’ decision, because it is made under uncertainty.

Simulation from Bayesian posterior distributions therefore gives a ‘one-step’ solution, allowing proper statistical estimation and inference to be embedded within a probabilistic decision analysis, an approach sometimes called ‘comprehensive decision analysis’ (Parmigiani and Kamlet, 1993; Samsa et al., 1999; Parmigiani, 2002; Cooper et al., 2003; Spiegelhalter, 2003). This fits perfectly not only with cost-effectiveness analyses where the decision maker seeks to maximise the expected net benefit, seen as monetarised health gain minus costs (Claxton and Posnett, 1996; Stinnett and Mullahy, 1998), but also with decision analyses based on maximising any objective function. Throughout the book we have used the flexible and freely available WinBUGS software (Lunn et al., 2009) to carry out the MCMC computations required.

3. Transparency and Consistency of Method

Decisions on which intervention is ‘best’ are increasingly decisions that are made in public. They are scrutinised by manufacturers, bodies representing the health professions, ministries of health and patient organisations, often under the full view of the media. As a result, these decisions, and by extension the technical methods on which they are based, must be transparent, open to debate and capable of being applied in a consistent and fair way across a very wide range of circumstances. In the specific context of NICE, there is not only a scrupulous attention to process (National Institute for Health and Clinical Excellence, 2009b, 2009c) and method (National Institute for Health and Care Excellence, 2013a) but also an explicit rationale for the many societal judgements that are implicit in any health guidance (National Institute for Health and Clinical Excellence, 2008c).

This places quite profound constraints on the properties that methods for evidence synthesis need to have. It encourages us to adopt the same underlying models, the same way of evaluating model fit and the same model diagnostics, regardless of the form of the outcome. It also encourages us to develop methods that will give the same answers, whether trials report the outcomes on each arm, or just the difference between arms, or whether they report the number of events and person-years exposure or the number of patients reaching the endpoint in a given period of time. Similarly, we should aim to cope with situations where results from different trials are reported in more than one format. Meeting these objectives is greatly facilitated by the generalised linear modelling framework introduced in Chapter 4 and by the use of shared parameter models. The extraordinary flexibility of MCMC software pays ample dividends here, as shared parameter models cannot be readily estimated by frequentist methods.

An even stronger requirement is that the same methods of analysis are used whether there are just two interventions to be compared or whether there are three, four or more. Similarly, the same methods should be used for two-arm trials or for multi-arm trials, that is, trials with three or more arms. For example, manufacturers of treatments B and C, which have both been compared with placebo A in RCTs, would accept that recommendations might have to change, following the addition of new evidence from B versus C trials, but not if this was because a different kind of model had been used to synthesise the data. The methods used throughout this book can be applied consistently: a single software code is capable of analysing any connected network of trials, with two or more treatments, consisting of any combination of indirect comparisons, pairwise comparisons and multi-arm trials, without distinction. This is not a property shared by several other approaches (Lumley, 2002; Jackson et al., 2014), in which fundamentally different models are proposed for networks with different structures. This is not to deny, of course, that these models could be useful in other circumstances, such as when checking assumptions.

4. Some Historical Background

The term ‘network meta-analysis’, from Lumley (2002), is relatively recent. Other terms used include mixed treatment comparisons (MTCs) or multiple-treatments meta-analysis (MTM). The idea of network meta-analysis as an extension of simple pairwise meta-analysis goes back at least to David Eddy’s Confidence Profile Method (CPM) (Eddy et al., 1992), particularly to a study of tissue plasminogen activator (t-Pa) and streptokinase involving both indirect comparisons and what was termed a ‘chain of evidence’ (Eddy, 1989) (see Chapter 11). Another early example, from 1998, was a four-treatment network on smoking cessation from Vic Hasselblad (1998), another originator of the CPM. This much studied dataset has been used by many investigators and lecturers to illustrate their models, and it continues to do service in this book.

A second strand of work can be found in the influential Handbook of Research Synthesis edited by Cooper and Hedges (1994), which came from an educational and social psychology tradition, rather than medicine. A chapter by Gleser and Olkin (1994) describes a method for combining data from trials of several interventions, including some multi-arm studies.