I am building a model with a highly significant interaction. This interaction was one of our main hypotheses. It is clear, however, that the form that the interaction takes does not represent a meaningful change across levels of either variable (one of which is time). The interaction is of 2 quadratic terms (and all lower order terms). Less terms in the model do not fit the data well. Higher order terms do not improve fit. With the quadratic interaction, we see the predicted trends for different levels of covariates begin together for early time, diverge slighlty for middle timings, and then reconverge for late time values. At most, the differences in the ranges of our data are not clinically meaningful. And the convergence at the end of the time range indicates that subjects end up in the same place anyways. Our best explanation for the divergence in the middle time is a change in selection criteria for entry into the study (not well documented, just possibility).
We have categorized the 2 predictors and tested that interaction, so as not to force a functional form. The predicted values for this show some similar trends to the quadratic interaction initially modeled, but is not as rigid or uniform. Additionally, we tested the interaction in a smaller, independently collected sample and found nothing indicating an interaction.
In short, my question is what more do we need to officially write off this interaction? The trouble I see is that this was pretty much what we wanted to test, and we found something statistically significant, yet it appears to not be the greatest fit for the data, nor offer a clinically important interpretation.