Power interaction

[iuri_leite]

Dear Colleagues,

I am running a logistic model where the dependent variable is the logit of the probability of a patient being diagnosed with COVID-19. The dataset comprises 4,908 patients, of whom 1,729 tested positive for COVID-19. The dataset includes demographic and clinical information about the patients and information on the predominant variant (original, Gamma, Delta, and Omicron) at the time these patients sought care. In the final model, we identified three statistically significant interactions between the symptoms (runny nose, sore throat, and loss of smell) and the variant type.
I would like to know how to calculate these interactions' power.
Thank you in advance.
Best regards,
Iuri

[StatDave]

Define what exactly you mean by "power". I assume you don't mean the statistical power of the test of their parameters or that you mean their significance since that is given right in the parameter estimates table. If you mean their effects on the diagnosis probability, then you might mean their marginal effects which you could get from the Margins macro (http://support.sas.com/kb/63038).

[iuri_leite]

Dear Dave,

I submitted a paper, and one of the reviewers raised a concern about the lack of a reported power calculation for the sample size: “No formal power calculation/sample size is reported. Given the number of predictors and interactions, it would be helpful to know if the study was adequately powered.”

I would like to discuss the best approach to calculate the power. In fact, we did not select a sample; we used data from all patients who sought assistance at a Primary Care Unit.

Therefore, I would like to find the best way to solve this problem.

Regard

[StatDave]

So you do apparently want statistical power. Power and sample size analysis can be done in PROC POWER for a planned study to be analyzed using a logistic model. See the example in the PROC POWER documentation. Note that PROC POWER is for prospective power analysis, not for a retrospective study that has already been designed and analyzed. Results from such a prospective analysis done in advance of you collecting data is apparently what your reviewer is asking for.

[Season]

Here is a webpage on power analysis of regression models with interactions that I have found: Power Analyses for Interaction Effects in Cross-Sectional Regressions • InteractionPoweR.

By the way, the analysis of power is a rather tricky aspect of regression. Research on this field has generally be confined to very simple cases. For instance, despite the popularity of comparing three and more survival curves in survival analysis, the version of SAS I am using (9.4 M5) only supports calculation of power of the test of comparing of two survival curves. So it would be better if you first searched for the method suitable for your problem on the Internet and then posted them here for questions of the implementation of this method in SAS. Also, be prepared that maybe there isn't a solution to your problem yet.