Clinical trials with non-adherence and unblinding: a graphical perspective

In clinical trials, it is difficult to learn the causal effect of treatment because patients often fail to take their medicine (called "non-adherence" to the regimen). We would like to perform subgroup analyses, comparing the patients who took the treatment with those who took the placebo (called "per protocol" analyses). However, according to the FDA, such an analysis may be biased, as was demonstrated in the Coronary Drug Project (CDP) trial. I argue that (a) the CDP did not demonstrate such a bias, and (b) that per protocol analyses will be biased if and only if the trial is "unblinded" (i.e. patients or doctors can learn who is receiving which treatment). I develop static and time-series graphical representations of the causal structure of clinical trials, and use them to determine whether intent-to-treat, per protocol, instrumental variables, and front door analyses are biased in the presence of non-adherence and/or unblinding. I argue that all analyses may be biased by unblinding, although not all to the same extent. This is work with Richard Scheines.