Statistical analyses

3.2.5.1 Brain volume: Patients versus controls. Results from the SIENAX brain

volume estimation (head size-normalised grey matter, white matter and total brain tissue) were entered into SPSS and the TBI and control groups then compared. Independent samples t-tests were used after adjusting for the potentialconfounding effects of age, previously demonstrated to affect the structural integrity of the brain (e.g. Fotenos, Snyder, Girton, Morris, & Buckner, 2005; Schönberger et al., 2009). The brain volumes were first regressed against age and the standardised residuals saved. These residuals were then used as the dependent variables, and the groups compared using t-tests.

3.2.5.2 Brain volume: Relationships with neuropsychological performance.

Statistical relationships between each of the three measures of whole-brain volume (grey matter, white matter, and total brain tissue) and the six neuropsychological measures of interest wereassessed within the patient group.

Relationships of potential confounds (age, severity of injury (mild: +1, moderate/severe: −1), and time since injury) with neuropsychological test performance were first explored by calculating nonparametric Spearman rank correlation coefficients: (a) age significantly correlated with median reaction times on the CRT (rho = .45, p < .01), but not with any of the other cognitive measures, (b) severity of injury significantly correlated with TMT-B – TMT-A completion times (rho = − .48, p < .01) and CRT reaction times (rho = − .42, p < .01), but not with the other measures, and (c) time since injury/months post-injury similarly correlated with performance on the TMT-B – TMT-A (rho = .38, p < .05) and CRT (rho = .57, p < .001), but not with performance on the other measures.

Therefore, whilst relationships between brain volumes and performance were in general investigated using standard Spearman rank correlation coefficients, correlations between brain volumes and TMT and CRT performance were tested using Spearman rank-based partial correlation, controlling for the effects of the confounds identified above. These partial correlations were calculated based on the residuals from the linear regression of the ranks of the variables of interest on the ranks of the variables partialled out.

3.2.5.3 Relationship between anatomical location of brain contusions and cognitive function. Voxel-based Lesion Symptom mapping (VLSM; Bates et al., 2003), part of

MRIcron (http://www.cabiatl.com/mricro/mricron/stats.html), was used to test voxel-wise correlations between brain contusions and neuropsychological performance across the whole brain. Separate analyses were carried out investigating the voxel-based lesion correlates of each of the cognitive variables of interest.

First, patients were divided into two groups at each voxel according to the presence or absence of a lesion affecting that voxel, with voxels affected by lesions in fewer than two patients excluded from the analysis. The patients’ scores on the neuropsychological measures of interest were then compared between these two groups, each in their separate t-test analyses.

Standard t-tests were used instead of the nonparametric Brunner-Munzel rank order test (Rorden, Karnath, & Bonilha, 2007), because the Brunner-Munzel has been shown to inflate the probability of a Type I error if used to test voxels where a very small number (<10) of participants are in either the lesion or the no lesions group (Medina, Kimberg, Chatterjee, & Coslett, 2010). Carrying out the t-test yielded a single-tailed p-value at each voxel, corresponding to how likely a relationship was between the presence of lesion at that voxel and worse neuropsychological performance.

A False Discovery Rate (FDR; Benjamini & Hochberg, 1995) correction for multiple comparisons was implemented to provide reasonable statistical power in this type of whole- brain analysis while guarding against false positives. The threshold to control the FDR was set at pFDR < .01, as recommended by Kimberg (2009), meaning that out of every 1000 voxels

exceeding the threshold for statistical significance, no more than 10 could be false positives. Whilst this is clearly more lenient than traditional family-wise (or map-wise) error rate, controlled at p < .05, it also guards against false negatives, which could be particularly problematic for this type of exploratory data analysis, with high spatial coherence (whereby the lesion status of a given voxel predicts that of the neighbouring voxels) being an inherent property of the lesion maps being analysed (Kimberg, 2009).

Reflecting the convention in VLSM that a higher score indicates better performance, larger voxel-based t-statistics normally mean a stronger effect of the presence of a lesion at that

voxel on behaviour (Bates et al., 2003). However, negative t-statistics were expected to result from analyses of the following cognitive measures, where a lower score indicates better performance: TMT-B – TMT-A, Color-Word Interference test inhibition/switching − baseline, and CRT median reaction time.

3.2.5.4 Relationship between anatomical location of white matter lesions and cognitive function. The effect of the anatomical location affected by white matter lesions (deep/infratentorial vs. lobar only) on the six cognitive indices was tested using independent samples t-tests.

3.2.5.5 Lesion load and cognitive function. Relationships between the six neuropsychological measures and normalised contusion load (total number of voxels across the whole brain) were then explored, as were their relationships with white matter lesion load (total number of microbleeds).

Given the significant correlations between TMT and CRT performance and potential cofound variables (age, severity of injury, and time since injury) the relationships between contusion and white matter lesion load and these two cognitive variables were explored using Spearman rank-based partial correlation, controlling for the relevant confounds. Correlations between lesion load and the remaining four cognitive variables were tested using standard nonparametric correlation.