Statistical adjustments for brain size in volumetric neuroimaging studies: Some practical implications in methods

Abstract

Volumetric magnetic resonance imaging (MRI) brain data provide a valuable tool for detecting structural differences associated with various neurological and psychiatric disorders. Analysis of such data, however, is not always straightforward, and complications can arise when trying to determine which brain structures are “smaller” or “larger” in light of the high degree of individual variability across the population. Several statistical methods for adjusting for individual differences in overall cranial or brain size have been used in the literature, but critical differences exist between them. Using agreement among those methods as an indication of stronger support of a hypothesis is dangerous given that each requires a different set of assumptions be met. Here we examine the theoretical underpinnings of three of these adjustment methods (proportion, residual, and analysis of covariance) and apply them to a volumetric MRI data set. These three methods used for adjusting for brain size are specific cases of a generalized approach which we propose as a recommended modeling strategy. We assess the level of agreement among methods and provide graphical tools to assist researchers in determining how they differ in the types of relationships they can unmask, and provide a useful method by which researchers may tease out important relationships in volumetric MRI data. We conclude with the recommended procedure involving the use of graphical analyses to help uncover potential relationships the ROI volumes may have with head size and give a generalized modeling strategy by which researchers can make such adjustments that include as special cases the three commonly employed methods mentioned above.

Introduction

Volumetric magnetic resonance imaging (MRI) studies have been key in identifying structural brain changes associated with many neurological and psychiatric disorders. Such structural changes can manifest in a variety of ways. The challenge of detecting and interpreting these changes has fallen upon neuroanatomists, clinical researchers, and statisticians. The inherently quantitative nature of morphometric MRI data mandates the use of statistical techniques to assess volumetric relationships, often with the goal of detecting subtle differences in regional volumes between or among diagnostic groups.

The questions of primary interest to clinical researchers, however, are not typically as straightforward as simply determining whether a particular brain region is larger or smaller in one group relative to another. In one example from a recent study of microcephaly, despite a decrease in whole-brain volumes only nuclear gray matter was found to differ significantly from controls (Cheong et al., 2008). In studies of autism, macrocephaly is commonly reported in the literature (Lainhart et al., 1997, Fombonne et al., 1999, Fidler et al., 2000, Bolton et al., 2001, McCaffery and Deutsch, 2005, Rice et al., 2005). Most studies in the field have demonstrated that autistic children tend to have larger heads, and MRI studies have found larger brains among children with autism compared with controls. This finding raises an important question: Are brain volumes increased globally in autism (are all structures proportionally bigger?) or locally (is brain overgrowth in autism driven by regionally specific expansion of some brain structures but not others?).

There is not a single, straightforward approach to addressing these questions. For example, one could make a statement about the overall average white matter volume in autistic children relative to controls. Nevertheless, someone with a larger brain is likely to exhibit increased gray and white matter volumes, although not necessarily according to the same proportions (Zhang and Sejnowski, 2000, Changizi, 2001, Bush and Allman, 2003). We could ask whether the amount of white matter is larger in autistic children after adjusting for total brain volume (TBV) or some other measure of head size (Herbert et al., 2003). The answers to these questions could be quite different depending on the methodology employed.

Considerations are further complicated when one asks what is meant by the phrase “adjusting for” in the previous paragraph. Those familiar with statistical literature are accustomed to seeing this phrase and generally have a preconceived notion of what it means. In the volumetric brain imaging literature, however, there are several ways in which one can assess the relative sizes of volumes of particular regions of interest (ROIs) after “adjusting for” differences in overall head size. It is important to note that although we use the term “head size” for the adjustment factor, different metrics can be used for head size. Total brain volume and intracranial volume (ICV) are two commonly measures, but their correlation generally decreases with increased age (Bartholomeusz et al., 2002). Using TBV may be more appropriate when interest is in how an ROI changes with respect to the brain as a whole. However, if interest is in how ROI volume changes with respect to maximal adult brain size, using ICV may be more appropriate. Other body parameters may also be used as adjustment factors (cf. Peters et al., 1998). It is important to note, however, that the issues discussed and the modeling methods recommended in this paper do not change with the choice of the adjustment variable.

The goal of the present article is to bring to light the origins of the three common adjustment methods, the statistical assumptions that underlie them, and to give examples of common pitfalls that researchers must be wary of when analyzing volumetric MRI brain data. Further, we assess the degree to which prevailing methods are concordant in an example data set, and the degree to which anthropometric dependent measures are interchangeable. We conclude with a generalized strategy which researchers may use when modeling volumetric MRI data.