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A surrogate endpoint should be a true predictor of disease, not reflection of a co-variable.
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22 Thus, CRP appears to be a true biological predictor, and other components of the response criteria may likewise have independent predictive value.
The sustained predictive ability of the post-treatment, pain-intensity-only model suggests that this variable is very likely a true predictor of future pain and would very likely be predictive of pain intensity in further studies carried out in similar populations.
The exception to the pattern was data generating process 4 when a redundant variable was correlated with a true predictor.
This holds for the other data generating processes when considering redundant variables that are uncorrelated with a true predictor.
Thus for the mouse, the size range was a reliable predictor of true full-length proteins.
The estimated probability of not selecting a redundant variable was between 0.99 and 1 for Bayesian model averaging while approximately 0.95 for stepwise regression when the redundant variable was not correlated with a true predictor.
We noted that Bayesian model averaging with 95% posterior probability threshold is less likely to select a true predictor than Bayesian model averaging with 50% posterior probability threshold.
We varied the effect size by varying sigma because for a fixed β, the effect size of the true predictor (and thus the probability of selecting a true predictor) is dependent on the amount of noise.
For stepwise regression, however, the probabilities of selecting a true predictor are higher for lower complexity of the data generating process and gradually decrease with increasing complexity, whereas the probabilities of selecting a true predictor in Bayesian model averaging with 50% posterior probability threshold does not show this sensitivity to increasing complexity.
The studies mentioned above [ 2, 8, 15] did not present probabilities of selecting a correlated redundant variable but Bayesian Model averaging is known to favor smaller models [ 16] and this supports our notion that Bayesian Model averaging is less likely than stepwise regression to select a redundant variable, be it uncorrelated or correlated with a true predictor.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com