1) Sounds good to me! We can connect about it over DM.
2) Your reading is right. A priori, a positive correlation means lower cost-effectiveness in expectation. However, I’m not sure if it means anything generally for the median cost-effectiveness (which I tried to work with in my existing CEA), irrespective of the other model parameters. And in my existing setup, if worlds of high spending and high success are more likely co-occur, and worlds with low spending and low success are more likely to co-occur, then I believe the distribution of their product would have been more dispersed, since there would be more values at the extremes (high/high and low/low) then there would be if they were independent. But I’m pretty convinced now that a better approach would have been, as you’ve suggested, to do separate CEAs conditional on various assumed interventions. Rather than change the parameters of independent distributions as I did in the posted analysis, the true next step is probably to re-model under varying assumptions about the covariance of the different variables.
3) I have a different sense of this, but not an overwhelmingly different sense, and I’m going to think about it some more.
1) Sounds good to me! We can connect about it over DM.
2) Your reading is right. A priori, a positive correlation means lower cost-effectiveness in expectation. However, I’m not sure if it means anything generally for the median cost-effectiveness (which I tried to work with in my existing CEA), irrespective of the other model parameters. And in my existing setup, if worlds of high spending and high success are more likely co-occur, and worlds with low spending and low success are more likely to co-occur, then I believe the distribution of their product would have been more dispersed, since there would be more values at the extremes (high/high and low/low) then there would be if they were independent. But I’m pretty convinced now that a better approach would have been, as you’ve suggested, to do separate CEAs conditional on various assumed interventions. Rather than change the parameters of independent distributions as I did in the posted analysis, the true next step is probably to re-model under varying assumptions about the covariance of the different variables.
3) I have a different sense of this, but not an overwhelmingly different sense, and I’m going to think about it some more.