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A Markov Chain approach for ranking treatments in network meta-analysis

A Markov Chain approach for ranking treatments in network meta-analysis. Anna Chaimani Dimitris Mavridis , Emilie Sbidian , Raphaël Porcher , Philippe Ravaud. Inserm Research Center of Epidemiology and Statistics Sorbonne Paris Cité (CRESS-UMR1153), University of Paris, France.

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A Markov Chain approach for ranking treatments in network meta-analysis

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  1. A Markov Chain approach for ranking treatments in network meta-analysis Anna Chaimani Dimitris Mavridis, Emilie Sbidian, RaphaëlPorcher, Philippe Ravaud • Inserm Research Center of Epidemiology and Statistics Sorbonne Paris Cité • (CRESS-UMR1153), University of Paris, France • SRSM Annual Meeting 2019 • Chicago, US

  2. Background • Network meta-analysis provides the highest possible level of evidence for the development of clinical guidelines • It can provide for a specific outcome a ranking of all alternative treatments as long as they form a connected network • Treatment ranking has attracted much attention as well as a lot of criticism over the last years • methods widely used in the literature do not always take into account the whole ranking distribution • ranking is a very influential output and when interpreted in isolation from relative effects can be misleading • ranking of treatments most often is not interpreted in light of the limitations of the evidence base

  3. Current ranking methods Treatment ranking may represent: • the mean of relative effects e.g. ranked forest plots -1 0 1 Drug A better Drug B better Cipriani et al. Lancet 2018

  4. Current ranking methods Treatment ranking may represent: • the mean of relative effects e.g. ranked forest plots • the mean and a part of the distribution of relative effects e.g. probability of being best -1 0 1 Drug A better Drug B better • Baldwin et al. • BMJ 2011

  5. Current ranking methods Treatment ranking may represent: • the mean of relative effects e.g. ranked forest plots • the mean and a part of the distribution of relative effects e.g. probability of being best • the mean and the full distribution of relative effects e.g. SUCRAs/P-scores/mean ranks -1 0 1 Drug A better Drug B better • Brunoni et al. • JAMA Psychiatry 2017

  6. Current ranking methods Treatment ranking may represent: • the mean of relative effects e.g. ranked forest plots • the mean and a part of the distribution of relative effects e.g. probability of being best • the mean and the full distribution of relative effects e.g. SUCRAs/P-scores/mean ranks -1 0 1 Drug A better Drug B better These methods produce rankings as reliable as the estimation of the distribution of relative effects

  7. Additional considerations in ranking

  8. PASI 90 100 CICLO MTX ALEFACEPT IFX ADA ACI 80 CICLO ETA MTX CERTO IFX ALEFACEPT 60 USK FUM FUM APRE SUCRA for SAE USK ACI SECU GUSEL ADA TOFA ETA PBO PBO 40 BRODA TILDRA IXE SECU IXE ITO 20 PONE PONE BRODA CERTO TILDRA 0 APRE GUSEL 0 20 40 60 80 100 TOFA SUCRA for PASI 90 Motivating example • Systemic pharmacological treatments for chronic plaque psoriasis

  9. Treatment ranking as a discrete stochastic process • Markov process with a countable state space • every treatment (node) is a state • starts at when we start ’moving’ between the treatment options • movement from to implies that treatment was not satisfying and we select as a potentially more beneficial treatment • the probability of selecting treatment at time (step) • the initial state probability vector

  10. Transition probabilities • the probability of selecting treatment at after having selected treatment at • given that , we define where is the probability that is ‘better’ than with • has a unique stationary distribution with • Ruecker and Schwarzer BMC Med Res Methodol 2015

  11. Incorporating the initial probability distribution • special case of a Markov Chain: at any there is a probability of starting again the process from • the probability that continues at according to and the probability that starts again from • modified transition probabilities, • modified transition matrix • has again a unique stationary distribution with Probability of selecting a treatment to recommend (POST-R)

  12. Graphical representation of the POST-R approach A A B B A Probability to start again from the beginning C C Initial probabilities of selecting each treatment Final probabilities of selecting each treatment B Transition probabilities of moving to another treatment C

  13. Defining the vector • Confidence/certainty/quality of the evidence • evidence on some of the treatments might be less ‘trustworthy’ than for others • Clinical experience • prior information from clinical practice is important and is not always in agreement with study results as the latter may lack power, have a short follow-up period • Safety of treatments • efficacy and safety should always be considered jointly when forming recommendations • Cost of the treatments • cheaper treatments might be preferable if they yield similar outcomes to slightly more effective, but expensive, ones

  14. Defining the probability • Network meta-analysis is (or should be) conducted when there is a need for updating and extending the existing evidence • Not straightforward how to select the 𝑧 value • depends also on the clinical setting and the available data • Sensitivity analysis on range of values • Informed by expert opinion

  15. Application to the psoriasis network

  16. Application to the psoriasis network

  17. Application to the psoriasis network

  18. Application to the psoriasis network

  19. Efficacy combined with Results Confidence in the evidence Clinical experience 0.5 Treatment cost Treatment safety 0.4 0.3 POST-R 0.2 0.1 0 IFX IXE ACI ITO ETA ADA USK MTX PBO FUM APRE TOFA SECU PONE CICLO GUSEL CERTO BRODA TILDRA ALEFACEPT Drug

  20. Limitations • The definition of the vector and the probability is subjective to some degree • The expert opinion was obtained after the publication of the original network meta-analysis and we used only one clinician • There might be additional characteristics affecting treatment selection not considered in our application • Our results our only illustrative of the method and do not aim to draw clinical inferences

  21. Discussion • Treatment ranking should represent the process of considering treatments for selection in clinical practice • The POST-R measure provides rankings that can inform decision-making more efficiently • The implementation of the method in Stata is in progress • It is important that a clear and transparent description of the criteria to be used for the definition of and are available in the protocol. • Our method may target primarily network meta-analyses stating “more well-conducted studies are necessary”

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