When are metabolic ratios superior to absolute quantification? A statistical analysis

Metabolite levels measured using magnetic resonance spectroscopy (MRS) are often expressed as ratios rather than absolute concentrations. However, the inter-subject variability of the denominator metabolite can introduce uncertainty into a metabolite ratio. In a clinical setting, there are no guidelines on whether ratios or absolute quantification should be used for a more accurate classification of normal versus abnormal results based on their statistical properties. In a research setting, the choice of one over the other can have significant implications on sample size, which must be factored in at the study design stage. Herein, we derive the probability distribution function for the ratio of two normally distributed random variables, and present analytical expressions for the comparison of ratios with absolute quantification in terms of both sample size and area under the receiver operator characteristic curve. The two approaches are compared for typical metabolite values found in the literature, and their respective merits are illustrated using previously acquired clinical MRS data in two pathologies: mild traumatic brain injury and multiple sclerosis. Our analysis shows that the decision between ratios and absolute quantification is non-trivial: in some cases, ratios might offer a reduction in sample size, whereas, in others, absolute quantification might prove more desirable for individual (i.e. clinical) use. The decision is straightforward and exact guidelines are provided in the text, given that population means and standard deviations of numerator and denominator can be reliably estimated.