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A surrogate endpoint should be a true predictor of disease, not reflection of a co-variable.
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.
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In the case of correlation between a redundant variable and a true predictor, the probability of not selecting a redundant variable was 0.95 to 1 for Bayesian model averaging while for stepwise regression it was between 0.7 and 0.9, depending on the effect size of the true predictor.
We compared the selection methods in terms of the probability of selecting a true predictor and the probability of not selecting a redundant variable.
For each method, we estimated the probability of selecting a true predictor as the proportion of cases where a true predictor was selected and the probability of not selecting a redundant variable as the proportion of cases where a redundant variable was not selected.
The probability of selecting a true predictor depended on effect size of the true predictor.
For the null hypothesis H0 : β i = 0, the probability of selecting a true predictor corresponds to the probability of rejecting H0 given it is false and the probability of not selecting a redundant variable corresponds to the probability of failing to reject H0 given it is true.
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.
Available data thus show that the higher probability of not selecting a redundant variable in Bayesian model averaging compared to stepwise regression does not come at the price of lower probability of selecting a true predictor but instead provides us with similar probability of selecting a true predictor as stepwise regression.
We observed that the probability of selecting a true predictor increased as the effect size of the true predictor increased.
The probability of selecting a true predictor increased as the effect size of the true predictor increased and leveled out at between 0.9 and 1 for stepwise regression, while it leveled out at 1 for Bayesian model averaging.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com