When does brain aging accelerate? Dangers of quadratic fits in cross-sectional studies

Abstract

Many brain structures show a complex, non-linear pattern of maturation and age-related change. Often, quadratic models (β 0 + β 1 age + β 2 age 2 + ε) are used to describe such relationships. Here, we demonstrate that the fitting of quadratic models is substantially affected by seemingly irrelevant factors, such as the agerange sampled. Hippocampal volume was measured in 434 healthy participants between 8 and 85 years of age, and quadratic models were fit to subsets of the sample with different age-ranges. It was found that as the bottom of the age-range increased, the age at which volumes appeared to peak was moved upwards and the estimated decline in the last part of the age-span became larger. Thus, whether children were included or not affected the estimated decline between 60 and 85 years. We conclude that caution should be exerted in inferring age-trajectories from global fit models, e.g. the quadratic model. A nonparametric local smoothing technique (the smoothing spline) was found to be more robust to the effects of different starting ages. The results were replicated in an independent sample of 309 participants. © 2010 Elsevier Inc. All rights reserved. IntroductionOver the past few years, research has demonstrated that most brain structures undergo a complex pattern of maturation and agerelated change. For instance, the hippocampus shows a marked nonlinear pattern of change throughout the lifespan (Allen et al., 2005;Jernigan and Gamst, 2005;Kennedy et al., 2008;Walhovd et al., 2005). Very often, non-linearity of age relationships is tested using quadratic or other polynomial models. A quadratic term is added to the list of predictors in a regression analysis, yielding a higher order polynomial function. If the quadratic term is significant, the brain structure in question can be said to have a non-linear age-trajectory (Allen et al., 2005;Good et al., 2001;Jernigan and Gamst, 2005;Kennedy et al., 2008;Lupien et al., 2007;Sowell et al., 2003;Sullivan et al., 1995;Terribilli et al., 2009;Walhovd et al., 2005). In addition, the trajectory of the curve may be used to describe the relationship between age and the brain structure, e.g. to determine when the hippocampus reaches its maximum volume, or how steep the subsequent decline is. This, however, may be problematic: First, to say that a relationship is nonlinear is not the same as saying that it is quadratic. This is an example of a specification effect. Second, if the same quadratic model is fit to different sets of data, one will get different results. For example, the observed peaks of quadratic functions will inherently depend on the age range sampled. This can lead to completely erroneous inferences about features of the trend, for example the location of peaks. This is a localization effect. The aim of this report is to demonstrate biases associated with quadratic model fits, and hint at possible solutions.The quadratic function is always a parabola, and the basic shape only differs in curvature and direction (whether it has a peak or a dip). Thus...

Transcallosal Connectivity Changes from Infancy to Late Adulthood: An Ex Vivo Diffusion Spectrum Imaging Study of Macaque Brains

“…Poisson model considers varying slops for connectivity changes in both developmental and aging periods. In contrast, the quadratic regression model assumes even slops across both the periods (Fjell et al, 2010), though the quadratic regression model provides a simple way to account for the correlated terms over most of the age range (Allen et al, 2005;Lebel and Beaulieu, 2011). As illustrated in Figure 4, the transcallosal connectivity for different cortical areas changed faster in the developmental period than in the aging period, suggesting that the neural fibers maturate quickly during brain development but degenerate slowly during aging, in good agreement with previous studies (Lebel et al, 2010).…”

Brain functional connectivity in regions that exhibit age-related cortical thinning

“…In our results, illustrated in Figure 4.1, the right pallidum did not significantly diminish with age, and the left pallidum displayed a small rate of atrophy. Amygdalae and caudate nuclei also had small rates of atrophy, alongside the hippocampi, though there exists strong evidence the hippocampi follow a nonlinear trajectory at advanced age, and therefore our linear model incurs some bias (FJELL et al, 2010b). The volumetric increase of ventricular structures we reported is consistent with the literature as well (FJELL et al, 2013;WALHOVD et al, 2011).…”

“…These findings have been widely reported in the literature (BAKKOUR et al, 2013;FJELL et al, 2009aFJELL et al, , 2009cFJELL et al, , 2010aFJELL et al, , 2010bFJELL et al, , 2013FJELL et al, , 2014aFJELL et al, , 2014bFJELL et al, , 2015dGOODRO et al, 2012;HARADA;NATELSON LOVE;TRIEBEL, 2013;LEMAITRE et al, 2012;LOCKHART;DECARLI, 2014;MEIER-RUGE et al, 1992;DUCHESNE, 2017a;SALAT et al, 2004;SCAHILL et al, 2003;SOWELL et al, 2007;STORSVE et al, 2014;THAMBISETTY et al, 2010;WALHOVD et al, 2011;WESTLYE et al, 2009;ZHOU et al, 2013;ZIELINSKI et al, 2014). While almost the whole cortex present evidence for age-related thinning, frontal gyri, superior and middle temporal gyri, the temporoparietal junctions and pre-and postcentral gyri display highly consistent thinning across samples, with relative sparing of inferior temporal lobes and anterior cingulate cortices (FJELL et al, 2009a).…”

“…Hippocampal volume follows a nonlinear age trajectory, with a break point nearing the end of the fourth decade of life (FJELL et al, 2010b). Coincidently, hippocampal volume loss is a neuromarker of AD (SCHUFF et al, 2009) and memory performance in normal subjects ( VAN PETTEN, 2004).…”

Prism: Multiple spline regression with regularization, dimensionality reduction, and feature selection

“…While linear and quadratic regression are often used (e.g., Sowell et al (2003); Hogstrom et al (2013); Madan and Kensinger (2016)), it has been shown that non-linear (spline) regression is more appropriate (Fjell et al 2010;). …”