I recent paper of mine was rejected following statistical review. I am completely unable to parse what the criticism is or what it means and would love to hear your comments or links to teaching materials that explain the supposed error.

For several years now I have liberally used restricted cubic splines, following auditing the regression modelling strategies course by Frank Harrell Jr. A prospective study I was involved in was rejected because of something called “spline approximation error”. I am unable to find anything about this term, or related terms, in RMS or other statistical textbooks, nor through google searching. It should be noted that we did present the regression equation in the supplement, we used restricted cubic splines not B-splines (and this was very clear in the paper), and finally, p-values were not used for any inference in the paper, which makes the comment all the more frustrating. However, if this supposed error exists and I have committed it, it would presumably apply to the confidence intervals as well. The comment is presented below:

“The paper does not present the expression of the logistic model, so it is clear about how the true functional relationship between the log-odd of the outcome and age is specified. Based on the descriptions in the paper, it seems that a nonparametric relationship 𝜃(𝑎𝑔𝑒) is included in the logistic model, where the fully unknown function 𝜃() is approximated by B-splines with four knots. If the above understanding of the modeling is accurate, then statistical inference (and the calculation of p values) conducted in this paper is problematic. This is because in the calculation of p values the splines approximation error isn’t accounted for in the analysis, so the resulting inference is incorrect. This is the well-known fact in the statistical literature. The research team should consult a statistician with proper knowledge of nonparametric regression with the utility of splines.”