Ratio index variables or ANCOVA? Fisher's cats revisited

Over 60 years ago Ronald Fisher demonstrated a number of potential pitfalls with statistical analyses using ratio variables. Nonetheless, these pitfalls are largely overlooked in contemporary clinical and epidemiological research, which routinely uses ratio variables in statistical analyses. This article aims to demonstrate how very different findings can be generated as a result of less than perfect correlations among the data used to generate ratio variables. These imperfect correlations result from measurement error and random biological variation. While the former can often be reduced by improvements in measurement, random biological variation is difficult to estimate and eliminate in observational studies. Moreover, wherever the underlying biological relationships among epidemiological variables are unclear, and hence the choice of statistical model is also unclear, the different findings generated by different analytical strategies can lead to contradictory conclusions. Caution is therefore required when interpreting analyses of ratio variables whenever the underlying biological relationships among the variables involved are unspecified or unclear.