STATISTICAL CONSIDERATIONS REGARDING THE USE OF RATIOS TO ADJUST DATA

OBJECTIVE: The use of ratios to adjust data (i.e. 'index' variables) i s common in obesity and related research. The rationale for the use of ratios often seems to be the desire to control or eliminate the influ ence of the variable in the denominator, The purpose of this paper is to gain a greater appreciation of the statistical assumptions underlyi ng ratios and their impact on data interpretation. RESULTS: We demonst rate the limitations of the indiscriminant use of ratios to adjust dat a, Specifically, we show that: (1) given linearity, a zero intercept b etween the numerator and denominator are necessary and sufficient cond itions for a ratio to remove the confounding effects of the denominato r; (2) seemingly minor departures from a zero intercept can have major consequences on the ratio's ability to control for the denominator; ( 3) the ratio of two normally distributed variables cannot be normally distributed, and this may violate the assumptions of subsequent parame tric statistical analyses; (4) the use of ratios affects the error dis tribution of the data which may also violate the assumptions of subseq uent parametric statistical analyses; (5) the use of ratios cannot eas ily take nonlinear effects between the numerator and denominator into account; (6) the use of ratios can introduce spurious correlations amo ng the ratios and other variables; (7) the use of ratios can create in terpretive difficulties, We also clarify that the mean of ratios is no t necessarily equivalent to the ratio of the means of the numerator an d denominator. Finally, we present and discuss formulae for the reliab ility of ratios and residuals. CONCLUSION: Because of the above issues , we question the indiscriminant use of ratios and advocate that inves tigators consider regression-based approaches as alternatives.