CIHC 2010 Computational methods for evidence-based decision support in pharmaceutical decision making Tommi Tervonen Econometric Institute, Erasmus University Rotterdam Eindhoven, 20/10/2010
Outline 1 Introduction to regulatory drug benefit-risk analysis Evidence-based medicine Benefit-risk analysis 2 Evidence synthesis methods for clinical trials Meta-analysis Network meta-analysis 3 Decision aiding for pharmaceutical decisions Utility theory Value functions MAVT SMAA 4 Aggregate Data Drug Information System (ADDIS) Case study
A simple example of evidence-based medicine Q: Should we advise parents to administer over the counter cough medicines for acute cough? Aims: To determine the effectiveness of over the counter (OTC) cough medicines for acute cough in children (...) Methods: Systematic review of randomised controlled trials (RCTs) (...) Results: Six trials involving 438 children met all inclusion criteria. Antitussives, antihistamine–decongestant combinations, other fixed drug combinations, and antihistamines were no more effective than placebo in relieving symptoms of acute cough (...) Most drugs appeared to be well tolerated with a low incidence of mostly minor adverse effects. Conclusion: OTC cough medicines do not appear more effective than placebo in relieving symptoms of acute cough (...) Schroeder & Fahey, BMJ, 2002
Randomized Controlled Trial (RCT) Properly designed RCT’s provide the highest quality evidence on the treatments’ effects
Evidence-Based Medicine (EBM) Evidence-based medicine aims to apply the best available evidence gained from scientific research to medical decision making A large share of decisions made by health care professionals are informed by evidence-based medicine, e.g. prescription, regulatory- and reimbursement policy decisions Although the scientific evidence is transparent and achieved with methodological rigour, the actual decisions are often unstructured, ad hoc and lack transparency as the treatment benefit-risk valuation is not explicit
Application of EBM in regulatory drug benefit-risk analysis For a drug to be granted marketing authorization, it must be proven efficant, safe, and have a sufficient benefit-risk (BR) profile compared to other drugs already in the market Knowledge s urfa ce a c b e Knowledg S ev erity of condition/unm et m edica l need Tim e Eichler & al., Nature Drug Disc, 2008
Drug benefit-risk analysis BR analysis should include all relevant evidence, and therefore apply (network) meta-analysis
Drug benefit-risk analysis Problems 1 Inclusion of all relevant evidence in the meta-analysis is not guaranteed 2 The BR analysis is unstructured and non-transparent
Approach taken in ADDIS Separate clinical data (measurements) from the value judgements (MCDA) Include all data present in the original analysis (imprecise measurements) Provide metrics for decision uncertainty Enable model generation for re-applicability
Outline 1 Introduction to regulatory drug benefit-risk analysis Evidence-based medicine Benefit-risk analysis 2 Evidence synthesis methods for clinical trials Meta-analysis Network meta-analysis 3 Decision aiding for pharmaceutical decisions Utility theory Value functions MAVT SMAA 4 Aggregate Data Drug Information System (ADDIS) Case study
Meta-analyses Often clinical trials are under-powered to reach statistical significance Sometimes different trials give different results (e.g. due to heterogenous population) → need to synthesize, that is, to meta-analyze the existing evidence base
Example meta-analysis Hansen et al. Ann Intern Med 2005;143:415-426
Fixed effect meta-analysis A fixed effect model is based on assumption that every study is evaluating a common treatment effect . That means the effect of treatment, allowing for the play of chance, was the same in all studies. Another way of explaining this is to imagine that if all the studies were infinitely large they’d give identical results. The resulting summary treatment effect estimate is this one ’true’ or ’fixed’ treatment effect, and the confidence interval describes how uncertain we are about the estimate.
From fixed to random effects Sometimes this underlying assumption of a fixed effect meta-analysis (i.e. that diverse studies can be estimating a single effect) is too simplistic The alternative approaches to meta-analysis are (i) to try to explain the variation or (ii) to use a random effects model A “group” effect is random if we can think of the levels we observe in that group to be samples from a large population (e.g. when collecting data from different medical centers, the “center” can be thought of as random)
Random effects meta-analysis Assumes that the true treatment effects in the individual studies may be different from each other. That means there is no single number to estimate in the meta-analysis, but a distribution of numbers. The most common random effects model assumes that these different true effects are normally distributed. The meta-analysis therefore estimates the mean and standard deviation of the different effects. In inverse variance random effects model, the weight of each study is proportional to the inverse of its variance
Fixed- and random effects models
Meta-analysis limits Hansen et al. (2005) systematic review: 46 studies comparing n = 10 second-generation AD In total, 20 comparisons are available Out of n ( n − 1) = 45 possible comparisons 2 3 meta-analyses are performed
Meta-analysis limits Fluoxetine (8) (5) (6) Paroxetine Sertraline Venlafaxine Hansen et al. Ann Intern Med 2005;143:415-426
Meta-analysis limits Fluoxetine (8) Paroxetine (1) (7) (1) (6) (1) (2) (2) (3) Duloxetine Venlafaxine Citalopram (1) (2) (1) (2) (1) (2) (1) (2) Sertraline Escitalopram (3) (1) (2) Bupropion Mirtazapine Fluvoxamine
Meta-analysis with more than 2 treatments? Fluoxetine (baseline) 1.00 (1.00 - 1.00) Paroxetine 1.09 (0.97 - 1.21) Sertraline 1.10 (1.01 - 1.20) Venlafaxine 1.12 (1.02 - 1.23) ... ... ... How likely is it that Venlafaxine has the greatest efficacy? Fluoxetine What happens if we choose (8) Paroxetine (1) (7) (1) another baseline? (6) (1) (2) Other studies included → (2) (3) Duloxetine Venlafaxine Citalopram (1) (2) (1) (2) (1) (2) (1) (2) possibly different results Sertraline Escitalopram (3) (1) (2) Not all drugs can be Bupropion Mirtazapine Fluvoxamine included (escitalopram) We’re “double counting” multi-arm trials
Network meta-analysis Fluoxetine (8) Paroxetine (1) (7) (1) (6) (1) (2) (2) (3) Duloxetine Venlafaxine Citalopram (1) (2) (1) (2) (1) (2) (1) (2) Sertraline Escitalopram (3) (1) (2) Bupropion Mirtazapine Fluvoxamine Include all evidence in one analysis
Network meta-analysis Is an extension of normal meta-analysis Allows comparison of ≥ 2 alternatives Integrating direct and indirect evidence While checking for (in-)consistencies A.K.A.: Mixed/Multiple Treatment Comparison (MTC)
Network meta-analysis models Is a Bayesian hierarchical model That can be estimated with a Markov Chain Monte Carlo software (BUGS, JAGS) ADDIS ( http://drugis.org/ ) can do it for you
Network meta-analysis: model Main components are: 1 Individual effect estimates 2 Linkage of the effect estimates (relative effects) 3 Random effects for the relative effects 4 Priors 5 Linkage of the relative effects
Level 1 (likelyhood) Modeling the effect r ik / n ik , for treatment k of study i , as a binomial proccess with success probability p ik : r ik ∼ Bin ( p ik , n ik ) Using MCMC simulation, the model converges to maximum joint likelyhood estimate of these p ik given the data on r ik and n ik .
Linkage to relative effects Apply a transformation to obtain normally distributed variable: p ik ; p ik = logit − 1 ( θ ik ) θ ik = logit ( p ik ) = log 1 − p ik And choose a baseline b ( i ) and define θ ik (the log odds) in terms of a baseline µ i and relative effect δ ib ( i ) k (the log odds-ratio): θ ik = µ i + δ ib ( i ) k
Level 2 (random effects) We assume the relative effects (LORs) to be normally distributed: δ ixy = N ( d xy , σ 2 xy ) And, for a three-arm trial i with treatments x , y , z , b ( i ) = x : � δ ixy �� d xy σ 2 � � � ρ xy , xz σ xy σ xz �� xy ∼ N , σ 2 δ ixz d xz ρ xy , xz σ xy σ xz xz
Level 2 (random effects) We assume the relative effects (LORs) to be normally distributed: δ ixy = N ( d xy , σ 2 ) And, for a three-arm trial i with treatments x , y , z , b ( i ) = x : � δ ixy �� d xy σ 2 σ 2 / 2 � � � �� ∼ N , σ 2 / 2 σ 2 δ ixz d xz Under the assumption of equal variances
Level 3 (Priors) For each of the parameters of interest, µ i , d jk and σ , specify priors: µ i ∼ N (0 , 1000) d jk ∼ N (0 , 1000) σ ∼ U (0 , 2)
Overview So far, this is just a random effects meta-analysis!
Consistency assumption d yz = d xy − d xz ‘Borrow strength’ from indirect evidence. The left-hand term ( d yz ) is a functional parameter The right-hand terms ( d xy , d xz ) are basic parameters Only basic parameters are stochastic
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