Exercise 6: Post-mortem analysis of an under-powered randomized trial

The randomized clinical trial EOLIA¹ evaluated a new treatment for severe acute respiratory distress syndrome (severe ARDS) by comparing the mortality rate after 60 days among 249 patients randomized between a control group (receiving conventional treatment, i.e. mechanical ventilation) and a treatment group receiving extracorporeal membrane oxygenation (ECMO) — the new treatment studied. A frequentist analysis of the data concluded to a Relative Risk of death of \(0.76\) in the ECMO group compared to controls (in Intention to Treat), with \(CI_{95\%} = [0.55 , 1.04]\) and the associated p-value of \(0.09\).

Goligher et al. (2019) ² performed a Bayesian re-analysis of these data, further exploring the evidence and how it can be quantified and summarized with a Bayesian approach.

1. Write the Bayesian model used by Goligher et al. (2019).

2. Write the corresponding BUGS model, and save it into a .txt file (for instance called goligherBUGSmodel.txt)

3. First create two binary data vectors ycontrol and yecmo (or ycontrol and yecmo that are either 1 or 0, using the rep() R function if you prefer the individual model), to encode the observations from the data table above. Then uses the jags.model() and coda.samples() to replicate the estimation from Goligher et al. (2019) (ProTip: use the function window() to remove the burn-in observation from the output of the coda.samples function.)

4. Check the convergence, and then comment the estimate results (ProTip: look at the effective sample size with the effectiveSize() R function).

5. Change to a more informative prior using a Gaussian distribution for the log(RR), centered on log(0.78) and with a standard deviation of 0.15 in the log(RR) scale (i.e. a precision of \(\approx 45\)). Comment the results. Try out other prior distributions.