Convert GeMTC posterior samples for the log odds-ratio to samples for the log risk-ratio using an assumed baseline probability. The baseline could also be a vector of samples from a distribution for the baseline probability. For the given example probability (p = 0.3), the LRR and LOR differ substantially. For p = 0.01 they are nearly identical.

lor.to.lrr.R

network <- ... # wherever your network comes from
model <- mtc.model(network)
result <- mtc.run(model)
result <- relative.effect(result, t1="A") # make sure everything is relative to the same reference

# transform the LOR to the LRR using an assumed probability for the reference treatment A
lor.to.lrr <- function(lor, p.A) {
  lo.A <- log(p.A / (1 - p.A))
  lo.B <- lo.A + lor # absolute log-odds of B
  p.B <- exp(lo.B) / (1 + exp(lo.B)) # inverse logit: absolute probability of B
  log(p.B / p.A) # the log-RR
}

p <- 0.3 # assume a 30% probability of treatment response with A

# Calculate the log-RR
lrr.samples <- as.mcmc.list(lapply(result$samples, function(chain) {
  cols <- grep("^d\\.", colnames(chain)) # find the "difference (d.X.Y)" parameters
  chain[, cols] <- lor.to.lrr(chain[, cols], p)
  as.mcmc(chain)
}))
summary(lrr.samples)