Biomarker ratios

From these references some potential problems: Ratios only “normalize” when the relationship passes through the origin. A ratio Y/X controls for X only if Y vs. X is a straight line through zero. For NLR and most biomarker ratios, this assumption is biologically implausible and rarely tested — so the ratio fails at its stated purpose.

1. Mathematical coupling creates spurious associations. Even when numerator and denominator are independent, the ratio is correlated with the denominator by construction. Any “association” between NLR and an outcome may be partially an artifact of this coupling rather than real biology.

2. Ratios conflate distinct underlying realities. A group difference in NLR is consistent with at least three different scenarios — different intercepts, different slopes, or genuine ratio differences in the N–L relationship — and the ratio cannot distinguish among them. ANCOVA or unconstrained regression can.

3. The ratio imposes an untested functional-form constraint. Using log(N/L) forces β_neutrophil = −β_lymphocyte. Fitting log(N) and log(L) as separate predictors lets the data show whether that constraint holds — and a likelihood ratio test can confirm or reject it.

4. Measurement error and dichotomization compound the damage. Noisy lymphocyte counts (especially at low values) destabilize the ratio precisely in the lymphopenic patients where high NLR is considered diagnostic. Subsequent dichotomization at data-derived cutpoints loses additional information and biases effect estimates.

References

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Allison DB, Paultre F, Goran MI, Poehlman ET, Heymsfield SB. Statistical considerations regarding the use of ratios to adjust data. Int J Obes. 1995;19:644–652.

Carroll RJ, Ruppert D, Stefanski LA. Measurement Error in Nonlinear Models. Chapman & Hall, 1995.

Curran-Everett D. Explorations in statistics: the analysis of ratios and normalized data. Adv Physiol Educ. 2013;37(3):213–219.

Kim JS. Spurious correlation between ratios with a common divisor. Stat Probab Lett. 1999;44:383–386.

Kronmal RA. Spurious correlation and the fallacy of the ratio standard revisited. J R Stat Soc A. 1993;156(3):379–392.

Pearson K. Mathematical contributions to the theory of evolution — on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc R Soc Lond. 1897;60:489–498.

Royston P, Altman DG, Sauerbrei W. Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med. 2006;25(1):127–141.

Tanner JM. Fallacy of per-weight and per-surface area standards, and their relation to spurious correlation. J Appl Physiol. 1949;2(1):1–15.