A cogent technique to circumvent the use of (some) ratio measures in physiology

Physiologists often express the change in the value of a measurement made on two occasions as a ratio of the initial value. This is usually motivated by an assumption that the absolute change fails to capture the true extent of the alteration that has occurred in attaining the final value - if there is initial variation among individual cases. While it may appear reasonable to use ratios to standardize the magnitude of change in this way, the perils of doing so have been widely documented. Ratios frequently have intractable statistical properties, both when taken in isolation and when analysed using techniques such as regression. A new method of computing a standardized metric of change, based on principal components analysis (PCA), is described. It exploits the collinearity within sets of initial, absolute change and final values. When these sets define variables subjected to PCA, the standardized measure of change is obtained as the product of the loading of absolute change onto the first principal component (PC1) and the eigenvalue of PC1. It is demonstrated that a sample drawn from a population of these standardized measures: approximates a normal distribution (unlike the corresponding ratios); lies within the same range; and preserves the rank order of the ratios. It is also shown that this method can be used to express the magnitude of a physiological response in an experimental condition relative to that obtained in a control condition. KEY POINTS: The intractable statistical properties of ratios and the perils of using ratios to standardize the magnitude of change are well known. A new method of computing a standardized metric, based on principal components analysis (PCA), is described, which exploits the collinearity within sets of initial, absolute change and final values. A sample drawn from a population of these PCA-derived measures: approximates a normal distribution (unlike the corresponding ratios); lies within the same range as the ratios; and preserves the rank order of the ratios. The method can also be applied to express the magnitude of a physiological response in an experimental condition relative to a control condition.