## Ranking of Competing Treatments for the Same Condition

There are simple ways to improve the presentation and facilitate the clinical interpretation of MTM results. The MTM model fitted within a Bayesian framework provides the opportunity make probabilistic statements about ranks. In each Markov chain Monte Carlo cycle, each treatment is ranked according to the estimated effect size. Then, the proportion of the cycles in which a given treatment ranks first out of the total number of cycles gives the probability that this treatment ‘is the best’. However, this does not convey the entire picture. For example, a treatment may have low probability to be the best, but very high probability to be the second or third best.

Consider again the network of trials comparing twelve antidepressants as in Figure 1. In Figure 3 I present the distribution of (posterior) probabilities for two antidepressants (escitalopram and fluoxetine). On the x-axis is the probability for each antidepressant to be the first best option, second best, third best etc. It looks roughly that escitalopram gets high probability to be among the best treatments whereas fluoxetine among the least effective ones. Quantification of ranking within this probabilistic framework needs further operationalisation; an idea is outlined below.

Instead of taking the ‘probability to be the best’ as a rule, ranking could be possibly based on measures associated with the* cumulative ranking surface. *Probabilities calculated for each treatment to be the best, second best, third best and so on sum to one for each treatment and each rank. For each treatment *i* out of the *n* competing, a vector of cumulative probabilities *cumi,j *for *i* to be among the *j*-best options,* j=1,…,n *can be calculated. Then, the area below the cumulative function is Σ_{j}cum_{i , j}/(n-1). Figure 4 presents the cumulative ranking function for bupropion (red solid line). If a treatment always ranks first, then the cumulative ranking surface is one, and if it always ranks last it is zero. For more details on ranking probabilities and the area below the cumulative function see (Salanti et al., 2010a).

### References

Salanti, G., Ades, A. E., & Ioannidis, J. P. (2010a). Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J. Clin. Epidemiol, J. Clin. Epidemiol 2011, Feb 64 (2):163-71