The fallacy of ratio correction to address confounding factors

Abstract

Scientists aspire to measure cause and effect. Unfortunately confounding variables, ones that are associated with both the probable cause and the outcome, can lead to an association that is true but potentially misleading. For example, altered body weight is often observed in a gene knockout; however, many other variables, such as lean mass, will also change as the body weight changes. This leaves the researcher asking whether the change in that variable is expected for that change in weight. Ratio correction, which is often referred to as normalization, is a method used commonly to remove the effect of a confounding variable. Although ratio correction is used widely in biological research, it is not the method recommended in the statistical literature to address confounding factors; instead regression methods such as the analysis of covariance (ANCOVA) are proposed. This method examines the difference in means after adjusting for the confounding relationship. Using real data, this manuscript demonstrates how the ratio correction approach is flawed and can result in erroneous calls of significance leading to inappropriate biological conclusions. This arises as some of the underlying assumptions are not met. The manuscript goes on to demonstrate that researchers should use ANCOVA, and discusses how graphical tools can be used readily to judge the robustness of this method. This study is therefore a clear example of why assumption testing is an important component of a study and thus why it is included in the Animal Research: Reporting of In Vivo Experiment (ARRIVE) guidelines.

Figure 1. Representative scatter plots to show the correlation between body weight and the DEXA variables.

Data shown are from B6Brd;B6Dnk;B6N-Tyr^c-Brd wildtype female mice for fat mass (A) and lean mass (B).

Figure 2. Boxplot comparisons of the impact of Akt2 genotype (wildtype (WT) controls versus Akt2^tm1Wcs homozygotes (HOM)) on body weight and DEXA variables.

The whiskers extend to the most extreme data point which is no more than 1.5 times the inter-quartile range. Points beyond this are classed as outliers and are shown individually as open circles.

Figure 3. Testing the assumption of homogeneity of variance.

An example scatterplot, from Akt2^tm1Wcs homozygous mice versus control study, of the confounding variable (body weight) against the DEXA variable of interest (lean mass) which has a regression line fitted for each treatment group (control shown with triangles versus knockout shown with circles) visually suggests that the regression line is equivalent between the two groups. An ANCOVA which included an interaction term calculated a p-value for this effect of 0.702, meaning this term would not be considered a significant component of the data and that the slopes are equivalent between the two groups. The ANCOVA calculated a p-value for the body weight as a confounding factor as p <0.000 which indicates it is a highly significant component of the analysis.

Figure 4. Representative standardized residuals scatterplot for the Akt2^tm1Wcs homozygous mice versus control dataset.

In this example, the standardized residuals for the lean mass variable were plotted against body weight. Data from knockout mice are shown with a triangle and controls with a circle.