Fig. 1
From: Evaluation of randomized controlled trials: a primer and tutorial for mental health researchers
Potential and observed outcomes in RCTs. Note: Going from top to bottom, this diagram illustrates the hidden “machinery” inside an RCT. The top panel (A) shows the potential outcomes for each person in our sample if we provide a new treatment (T = 1) or not (T = 0). In our example, “0” means that a person does not suffer from a depressive episode after several weeks, while “1” means that the person still suffers from depression. The potential outcomes are hypothetical; since they are based on counterfactuals, it is impossible to observe both at the same time, and so the true causal effect τi of our treatment also remains unobservable. Going down one step, panel B shows the process of randomization, which lets chance decide which potential outcome is realized, and which one is missing (“?”). Loss to follow-up (panel C) adds another layer of missingness. Here, it is much less plausible that the missings are added “completely at random”. As analysts, all we end up having are the observed outcomes at the end of this process, which we need to use to estimate the unobservable causal effect τ on top as closely as possible. Legend: Ti = treatment allocation of patient i (Ti = 0 for no treatment, Ti = 1 for treatment); τi = causal treatment effect of patient i; Yi = outcome of patient i: “1” (red box) if the patient still suffers from depression after several weeks, or “0” (green box) if the patient does not suffer from depression after several weeks; “?” (gray box) if the outcome was not recorded; Yiobs = observed outcomes of the trial