In veterinary medicine I frequently see papers that use biomarkers such as neutrophil:lymphocyte ratio for diagnostic or prognostic purposes. I recall reading that there are statistical problems with this approach. One I can see is that it actually loses information due to turning two continuous variables into a single dichotomized variable. Are there any other concerns that I can point out to my colleagues?
The papers I’ve seen (e.g. the classic Richard Kronmal paper) relate to specific statistical modeling issues / assumption violations. In terms of pure measurement issues, ratios can work, if you can show that an ultimate outcome can be modeled as y = f(log(r)) + g(d) + h(n) for ratio r with all denominator d coefficients and all numerator n coefficients equal to zero. This takes a lot of luck. Quite often transformations of the numerator or denominator need to be taken before computing the ratio. Sometimes the transformation is just a change of origin (subtraction) in the denominator.
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If the two biomarkers are well correlated then it makes little sense to use ratios (or multiplying them together as I’ve seen).