  Recent work has focused on the very common practice of prediction-based
inference: that is, (i) using a pre-trained machine learning model to predict
an unobserved response variable, and then (ii) conducting inference on the
association between that predicted response and some covariates. As pointed out
by Wang et al. (2020), applying a standard inferential approach in (ii) does
not accurately quantify the association between the unobserved (as opposed to
the predicted) response and the covariates. In recent work, Wang et al. (2020)
and Angelopoulos et al. (2023) propose corrections to step (ii) in order to
enable valid inference on the association between the unobserved response and
the covariates. Here, we show that the method proposed by Angelopoulos et al.
(2023) successfully controls the type 1 error rate and provides confidence
intervals with correct nominal coverage, regardless of the quality of the
pre-trained machine learning model used to predict the unobserved response.
However, the method proposed by Wang et al. (2020) provides valid inference
only under very strong conditions that rarely hold in practice: for instance,
if the machine learning model perfectly estimates the true regression function
in the study population of interest.
