Thank you @f2harrell. I have searched for mediation analyses of statins on CV disease via lipid metabolism. A sample of what I found suggests much complexity, as expected by @ESMD and me. For example “This study suggests a potential causal pathway between statin and coronary artery calcification or CAC (the positive association of statin on CAC) through HDL-cholesterol as an inhibitor (Investigating potential mediator between statin and coronary artery calcification)” and “The increased risk of dyslipidemia on CAD was partly enhanced by elevated mean platelet volume levels, whose mediating effect was around 20% (https://doi.org/10.3389/fcvm.2022.753171)” and “Lipid plays a partial mediation on the association between smoking and CAD risk (Mediating effects of lipids on the association between smoking and coronary artery disease risk among Chinese | Lipids in Health and Disease | Full Text)” and “Improvement of remnant lipoproteinemia may be an important mediator for the relationship between improvement of endothelial dysfunction and LDL-lowering after statin treatment in patients with CAD (Redirecting)” etc. etc.
We could therefore incorporate some of these mediators as covariates into a RCT and the resulting risk calculation and then assess the performance of different methods when trying to differentiate between people at higher and lower risk and the effect this has on effectiveness of treatment (whereas the overall effect over all levels of risk or odds ratio as assessed by a RCT should be the same). The question is how to make this assessment. My approach with a single variable (the albumin excretion or AER) was to plot a ROC curve and to identify the point where the sensitivity and specificity with respect to the outcome of nephropathy were the same, and to dichotomise the AER data at this threshold.
The threshold was found for the combined data on placebo and treatment in order to identify a point common to both. This allowed the proportions with the outcome in those below the threshold to be found for those on placebo and treatment. The same proportions were found above the threshold. The difference (or ratio) between the proportions above and below the threshold is a measure of the predictive performance of the covariate (the AER in my example). It should be the same for the treatment and control data; therefore a better estimate might be obtained by combining the control and treatment data. The risk and odds ratios between treatment and control can be found above and below the thresholds.
If the probability calculations were based on more than one variable, then the assumptions required might very well create bias in the probability estimates. This could be addressed by regarding the probabilities created as variables in their own right. They (or some transformation of them) could be used to plot a ROC curve and the point identified where the sensitivity equalled the specificity as a threshold. The performance of the multivariable ‘test’ could then be assessed as in the previous paragraph. A comparison could also be made between different methods (e.g. for the three approaches described in my original post no 1 above).
Fitting a logistic regression function to the control and treatment data (or applying an overall odds ratio or risk ratio to the control curve to estimate the treatment curve) is a quite separate issue. Assessing the validity of the resulting theoretical probabilities based on the many assumptions (e.g. assuming that the underlying true curve will be a sigmoid logistic function) would have to be done separately.
Do you all think that this would be a reasonable description of how diagnostic tests should be assessed for use when predicting the probability of outcomes with and without treatment?