![risk probability xbeta risk probability xbeta](https://www.statisticsfromatoz.com/uploads/7/3/2/1/73216723/seesaw-ab-err-table_1_orig.jpg)
![risk probability xbeta risk probability xbeta](http://2.bp.blogspot.com/-McErI5J1EK0/Vd3bB1Jg5GI/AAAAAAAAHwg/w-7KoUDzmyc/w1200-h630-p-k-no-nu/Typical%2BRisk%2BMatrix.png)
Quickly defining the parameters of interest I won’t be using real data from the study that motivated this, but will generate simulated data so that I can illustrate the contrast between marginal and conditional estimates. My goal here is to demonstrate the relative simplicity of estimating the marginal risk difference described in these papers by Kleinman & Norton and Peter Austin. The ultimate consensus on our research team is that the benefits of improved communication outweigh the potential loss of generalizability. The odds ratio, on the other hand, is not dependent on the covariates. (I’ve written about this distinction before.) The marginal risk difference estimate is a function of the distribution of patient characteristics in the study that influence the outcome, so the reported estimate might not be generalizable to other populations. From my perspective, the only possible downside in using a risk difference instead of an OR is that risk difference estimates are marginal, whereas odds ratios are conditional. A collaborator suggested we report the difference in vaccination rates rather than the odds ratio, arguing in favor of the more intuitive measure.
![risk probability xbeta risk probability xbeta](https://spicelogicstorage.blob.core.windows.net/documentation/DecisionTreeAnalyzer/category-84/page-319/cumulative-distribution-of-risk-profile.png)
(There is a method developed by Richardson, Robins, & Wang, that allow analysts to model the risk difference, but I won’t get into that here.)Ĭurrently, I’m working on an NIA IMPACT Collaboratory study evaluating an intervention designed to increase COVID-19 vaccination rates for staff and long-term residents in nursing facilities. Although a difference is very easy to calculate when measured non-parametrically (you just calculate the proportion for each arm and take the difference), things get a little less obvious when there are covariates that need adjusting. One alternative measure of effect is the risk difference, which is certainly much more intuitive. I think it is pretty clear that a very large or small OR implies a strong treatment effect, but translating that effect into a clinical context can be challenging, particularly since ORs cannot be mapped to unique probabilities. It is a ratio of two quantities (odds, under different conditions) that are themselves ratios of probabilities. The odds ratio (OR) – the effect size parameter estimated in logistic regression – is notoriously difficult to interpret.