Biomarker levels with seasonal variation

What is the best way to include a biomarker as a predictor that varies seasonally? Should it simply be included as an interaction term?

Say more. Are you thinking that the biomarker varies seasonally? Is this variation such that (1) it’s real and doesn’t modify the impact on outcome of the marker or (2) it’s real and modifies the impact on outcome, e.g. in one season the marker runs high and this reflects a completely unrelated phenomenon that should not be useful in predicting the outcome?

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Its a marker (ACTH) that is higher during the autumn months (in horses) used to diagnose Cushings disease of pituitary origin. I am interested in seeing if it can be used in a prediction model to predict mortality as well as a significant adverse outcome known as laminitis. The marker will go back down in the winter and spring/summer months. Currently the diagnosis of the disease is based on thresholds which are adjusted based upon season.

There are diseases and markers where adjustment of thresholds undoes the biology and makes decisions worse. An example is age-adjusted thresholds for PSA in prostate cancer detection. A way to demonstrate the validity of seasonal adjustments for forced-choice ACTH thresholds and to derive optimal adjustments is through modeling a large cohort with marker x calendar time interaction, the interaction being modeled as two transformations (sine and cosine). Need for seasonal adjustment would be demonstrated by getting better diagnoses when the interaction terms are present.

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If I retained ACTH as a continuous variable does this method seem valid? Restricted cubic splines for modelling periodic data (plos.org)

That’s a wonderful paper. For the cosinor method see also General Multi-parameter Transformations in rms

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The R package mgcv also has built-in support for both cyclic cubic regression splines and cyclic p-splines. With tensor product terms you can also add smooth interaction terms that enforce periodicity on seasonality, but not on the biomarker. All of these smooths can be used in model with random effects and a huge variety of “beyond-glm” outcomes. Definitely worth looking into as well!

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