Stage 2: Population Distillation
The stage 1 model was built with intervention patients only and then used to estimate the probability of engaged participation for all patients in the study population. The estimations from the model are a fixed function of prerandomization covariates, which were applied to both treatment and control groups equally. In the control population, these represent the probability that patients would have engaged had they been randomized to the treatment arm. The ordered probabilities were then divided into deciles, allowing us to narrow the full study population to subsets that were increasingly enriched with likely participants. We defined these distilled subsets based on the top percentage most likely to be engaged participants, ranging from 100% (the full population) to 20% (the 20% most likely to be engaged participants).