Pitfalls in brain age analyses

Abstract

Over the past decade, there has been an abundance of research on the difference between age and age predicted using brain features, which is commonly referred to as the "brain age gap." Researchers have identified that the brain age gap, as a linear transformation of an out-of-sample residual, is dependent on age. As such, any group differences on the brain age gap could simply be due to group differences on age. To mitigate the brain age gap's dependence on age, it has been proposed that age be regressed out of the brain age gap. If this modified brain age gap is treated as a corrected deviation from age, model accuracy statistics such as R² will be artificially inflated to the extent that it is highly improbable that an R² value below .85 will be obtained no matter the true model accuracy. Given the limitations of proposed brain age analyses, further theoretical work is warranted to determine the best way to quantify deviation from normality.

Keywords: age; brain; development; deviation; prediction; residual.

FIGURE 1

Inflated correlation, Corr $\left(A,{\widehat{A}}^M\right)$, is a function of the true correlation, Corr$\left(A,\widehat{A}\right)$. The inflated correlation is the correlation between age and the modified predicted age. The true correlation is the correlation between age and predicted age. To illustrate that the series of transformations that researchers perform is equivalent to Equation (8), correlations using both are plotted. r _func is using Equation (8), and r _trans is using the series of transformations. The identity line is displayed for ease of comparing the axes

FIGURE 2

The inflated correlation finding was replicated in the Philadelphia Neurodevelopmental Cohort. Plotted are values for age (A), predicted age ($\widehat{A}$), the brain age gap (BAG), the modified BAG (MBAG) and the modified predicted age (${\widehat{A}}^M$) in the subset of participants who met screening criteria for an instance of mental illness in their lifetime. Panel (a) displayed the correlation between age and predicted age; Panel (b) the correlation between age and the brain age gap; Panel (c) the correlation between age and the modified brain age gap; and Panel (d) the correlation between age and the modified predicted age. The identity line is displayed in Panels (a) and (d)