Application of robust regression in translational neuroscience studies with non-Gaussian outcome data

Abstract

Linear regression is one of the most used statistical techniques in neuroscience, including the study of the neuropathology of Alzheimer's disease (AD) dementia. However, the practical utility of this approach is often limited because dependent variables are often highly skewed and fail to meet the assumption of normality. Applying linear regression analyses to highly skewed datasets can generate imprecise results, which lead to erroneous estimates derived from statistical models. Furthermore, the presence of outliers can introduce unwanted bias, which affect estimates derived from linear regression models. Although a variety of data transformations can be utilized to mitigate these problems, these approaches are also associated with various caveats. By contrast, a robust regression approach does not impose distributional assumptions on data allowing for results to be interpreted in a similar manner to that derived using a linear regression analysis. Here, we demonstrate the utility of applying robust regression to the analysis of data derived from studies of human brain neurodegeneration where the error distribution of a dependent variable does not meet the assumption of normality. We show that the application of a robust regression approach to two independent published human clinical neuropathologic data sets provides reliable estimates of associations. We also demonstrate that results from a linear regression analysis can be biased if the dependent variable is significantly skewed, further indicating robust regression as a suitable alternate approach.

Keywords: Alzheimer’s disease; Gaussian distribution; linear regression; normal distribution; normality assumption; robust regression.