Supplementary material table of contents
Appendix I: PMA/NMA-based evidence synthesis
Appendix II: Model parameters
Appendix III: The expected value of partial perfect information (EVPPIs) for costs and utilities
Appendix I:PMA/NMA-based evidence synthesis
We used a random-effects Poisson regression, as described in Mills et al (1). In this model,the total number of exacerbations per person-year, n, under treatment T, in the ith studyfollows the following equation
where is the expected number of exacerbations per person-yearfor the ith study and under treatment Tthat follows the following equations
where represents the log rate of exacerbations in the placebo arm, whereas represents the log rate ratio of exacerbation with treatment T versus placebo in the corresponding study. follows the random effects distribution in which
.
Prior distributions for and were assumed to follow a Normal distribution
, and prior distribution for the between study heterogeneity was assumed to be a uniform distribution between 0 and 2, . More details is provided in Mills et al (1).
Table A Presents all the direct and indirect rate ratio estimates and associated 95% credible intervals from each comparison in the treatment network were both were available. For the indirect comparisons, the ‘indirect control’ column indicates which treatment is used as the ‘common control’ in obtaining an estimate for the comparison outlines in the first column (to the left). Consistency between direct and indirect evidence is evaluated based on the agreement in direction and magnitude of effect, and the degree of certainty surrounding those estimates. Generally, all direct and indirect estimates lined up very closely. For LAMA vs placebo the direction of effect was similar, but not the magnitude. However, considerable uncertainty around the indirect estimate likely explains this finding.
Table A Consistency table
Comparison / Direct estimate(IRR, 95% CI) / Indirect control / Indirect estimate
(IRR, 95% CI)
LABA vs Placebo / 0.87 (0.75-1.01) / ICS
ICS+LABA / 0.84 (0.69-1.04)
0.91 (0.77-1.06)
ICS vs Placebo / 0.81 (0.68-0.95) / LABA
ICS+LABA / 0.84 (0.66-1.06)
0.83 (0.74-0.93)
LAMA vs Placebo / 0.74 (0.59-0.91) / LABA / 0.95 (0.71-1.28)
ICS+LABA vs Placebo / 0.71 (0.60-0.88) / LABA
ICS / 0.70 (0.57-0.87)
0.70 (0.55-0.89)
ICS vs LABA / 0.96 (0.92-1.00) / Placebo
ICS+LABA / 0.93 (0.81-1.06)
0.95 (0.82-1.09)
ICS+LABA vs LABA / 0.81 (0.75-0.86) / Placebo
ICS / 0.82 (0.58-1.15)
0.83 (0.69-0.99)
LAMA vs LABA / 0.91 (0.80-1.06) / Placebo / 0.86 (0.59-1.21)
ICS+LABA vs ICS / 0.86 (0.80-0.93) / Placebo
LABA / 0.88 (0.60-1.29)
0.84 (0.74-0.96)
Abbreviations: IRR (Incidence Rate Ratio); CI (Credible Interval); ICS (Inhaled Corticosteroids); LABA (Long-acting Beta Agonists); LAMA (Long-acting Muscarinic Agents). Second column shows direct estimates for rate ratios using DerSimonian-Laird random-effects, and column dour shows the indirect estimates using Bucher approach. Column 3 indicates which treatment has been used as the 'common control' to obtain indirect evidence.
Appendix II:Model Parameters
We developed a discrete time Markov model of COPD with a yearly cycle length and 10 health states similar to the model used in the Burden of Obstructive Lung Disease (BOLD) studies(2). In this model, COPD is categorized intothree levels of disease severity (mild=stage I, moderate=stageII, and severe=stage III) and three levels of smoking status (current smoker, ex-smoker, and never-smoker). At any cycle, individuals can remain in the same COPD stage, transition to a more severe stage, or die. Transition to milder state was not possible. Transition rates between different health stages were derived from a study by Hoogendoorn et al (3).
Similar to other studies the effects of different treatment options on clinical outcomes were mediated through their impacts on the rate of exacerbations (4). The rate ratios (RRs) for treatment effect on exacerbation rate represents the core model parameters for which different evidence synthesis paradigms were evaluated.
Baseline utilities for different disease severity levels and exacerbations were derived from Spencer et al (5), and beta distribution was used to represent uncertainty around utilities in the probabilistic analyses. Direct costs of exacerbations were derived from Spencer et al (5), and was assumed to be independent of the COPD stage. Indirect costs of COPD were derived from Najafzadeh et al (6), which itself was estimated from studies by Spencer et al (5), and Chapman et al (7). All costs were adjusted to Canadian 2011 dollars. Gamma distributions with the coefficientof variation 25% were assigned to the costs in the model.
Appendix III:The expected value of partial perfect information (EVPPIs) for costs and utilities
Figure 1 Ranking changes based on PMA and NMA evidence synthesis. (A): Group EVPPIs for costs, (B): group EVPPIs for utilities.
(A)
(B)
EVPPI: expected value of partial perfect information, PMA: Pairwise meta-analysis, NMA: network meta-analysis. Bars are grouped based on the number of comparisons (2,3,4, and 5), and are ranked based on the EVPPIs from the PMA-based analysis (dark bars on the left).
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