Voxel-Based Morphometry in Individual Patients: A Pilot Study in Early Huntington Disease

Patients

Data and images were derived from routine diagnostics of our HD outpatient clinic. The group consisted of 22 gene-positive subjects in early stages of HD (women, 12; CAG repeats: range, 40–48; mean ± SD, 45 ± 2; age range, 35–61 years; mean ± SD, 44 ± 8 years). The motor score of the Unified Huntington's Disease Rating Scale ranged from 0 (no motor symptoms in 3 patients) to 43 (considerable motor symptoms) with a mean value of 17 and an SD of 15.

Control Group

Images were derived from volunteers who had participated in imaging studies as healthy control subjects at our department. In these studies, subjects were interviewed before scanning by an experienced neurologist and were only included if there was no indication for any neurologic or psychiatric disorder. Moreover, all images were screened by an experienced neuroradiologist and were excluded if there were unusual or abnormal findings. We could recruit the images of 133 subjects (women, 62; age range, 27–74 years; mean ± SD, 55 ± 12 years).

Matched Control Subjects

Of the 133 control subjects, we chose 22 matched control subjects (ie, 1 matched control subject per patient). For each patient, the control of the same sex with the age closest to the respective patient was chosen (age differences: <1 year, 13 pairs; 1–2 years, 6 pairs; 2–3 years, 2 pairs; 5 years, 1 pair).

MR Imaging Acquisition

Each subject underwent MR imaging in the same scanner (magnetic field intensity, 1.5T; scanner, Magnetom Symphony [Siemens, Erlangen, Germany]; sequence, T1 magnetization-prepared rapid acquisition of gradient echo; TR, 11.1 ms; TE, 4.3 ms; TI, 800 ms; voxel size, 1 × 1 × 1 mm³; flip angle, 15°; sagittal sections, 160; FOV, 256 × 256 mm).

Which Statistical Test Should Be Used?

We made no effort to apply nonparametric tests because, here, ranks are considered exclusively. The comparison of a single patient to a group of 133 control subjects can, at best, yield rank 134 for the patient corresponding to an uncorrected P value of 0.0075 (1/134), so that it seems very unlikely to provide results that remain significant after correction for multiple statistical tests as required for hypothesis-free whole-brain analyses. Instead, we tested 2 parametric approaches.³⁰ For both approaches, we assumed a t distribution of the data of the control group. With respect to the variance of the test “group” (containing only 1 subject), we tested 2 approaches:

The first approach is based on the assumption that the patient's value constitutes the mean value of a (hypothetical) population with a variance equal to that of the control group. This approach is implemented by default in most programs for the analyses of neuroimaging data such as statistical parametric mapping and has been the method of choice so far, though, to the best of our knowledge, this issue has never been discussed explicitly. This “conventional approach” corresponds to the 2-sample t test with the “pooled” estimate of variance and results in the following equation for the T value: 1) with

Here the common variance is calculated by weighting each group variance by the number of observations in that group, thus, giving more weight to larger groups (because they are better estimates). Given N_p is one, equation 1 reduces to 2)

The “alternative approach” does not assume any variance from the patient. Instead, the patient is regarded as a unique single case and, hence, is treated as a fixed effect. This complies with the 1-sample t test where a test value ρ (eg, from a patient) is compared with the values of a sample of N controls with the mean value μ and the SD σ. The T value is estimated as follows: 3)

Note that the 2-sample t test for unequal variances (Welch t test) does not apply because the degrees of freedom cannot be estimated.

It is obvious that the 2-sample t test (with a “pooled” estimate) of the conventional approach (equation 2) yields lower T values than the 1-sample t test of the alternative approach (equation 3) and is hence more conservative. It is noteworthy that this more conservative approach has also been suggested recently for the neuropsychologic assessment of single patients.³¹ However, both approaches are based on different statistical assumptions so that neither of them can primarily be regarded correct or incorrect. Accounting for the problem of statistical assumptions when comparing a single subject with a group, it has been proposed to empirically validate the statistical approach by comparing each healthy subject to the remainder and by relating these findings to the type 1 error probability.³² Applying a significance threshold of P less than .05 corrected, we expect to (erroneously) detect GM decrease in 5% of the healthy control subjects, that is in approximately 1 of the 22 matched control subjects analyzed in our study. More precisely, the number of matched control subjects with GM decrease identified should range from 0 to 3 (χ² test: P > .05).

Following the proposal of an empiric validation, we could clearly falsify the alternative approach on the basis of the 1-sample t test because it yielded GM decrease in every control subject. Therefore, we concentrated on the conventional approach on the basis of the 2-sample t test (with a “pooled” estimate of variance).

Accounting for Age and Sex

Before our study, we had made extensive attempts to generate statistical parametric maps of single subjects with various neuropsychiatric diseases compared with populations other than the one analyzed in this study. It is intriguing that when increasing the number of control subjects, we saw more significant and more plausible results at first. However, when including additional control subjects of ages more different from the subject under investigation, significance decreased. It is notable that significance increased again after accounting for age and sex. This is well conceivable because age and sex considerably influence regional and global GM values in healthy subjects.^11,33,34 Therefore, we accounted for age and sex by including these parameters in our model and extended the 2-sample t test to an analysis of covariance (ANCOVA).

Preprocessing and Distributional Assumptions

For normalization and segmentation, default settings of VBM5 (http://dbm.neuro.uni-jena.de/), an extension of SPM5 (http://www.fil.ion.ucl.ac.uk/spm/software/spm5/), were applied. Apart from the unified segmentation as implemented in SPM5,³⁵ VBM5 applies a hidden Markov random field model. ³⁶ This segmentation procedure minimizes the noise level by removing isolated voxels of 1 tissue class, which are unlikely to be a member of this tissue class. For smoothing, we used a Gaussian kernel of 12-mm full width at half maximum, which is necessary to fulfill the distributional assumptions of VBM, especially for the analysis of single subjects.³⁷

Voxels Included in the Analyses (“Explicit Masking”)

We analyzed only voxels that were likely to represent GM according to the probability maps of SPM5 (“priors”) for GM, white matter (WM), and CSF that have been derived from a large cohort of healthy control subjects. Therefore, a voxel was only included if it displayed a GM value greater than both the corresponding WM and CSF values. Accounting for the existence of another class apart from the 3 tissue classes, the background class, we also applied an absolute voxel threshold of a GM value greater than 0.2 (range, 0–1).

Correction for Multiple Statistical Tests

To correct for multiple statistical tests, we applied the false discovery rate (FDR) predicated on the procedure of Benjamini and Hochberg.^38,39 We set a whole brain significance level of P less than .05.

No Systematic Shifts of MR Imaging Parameters with Time

All subjects underwent MR imaging examinations from September 2000 to September 2003 and were almost evenly distributed during the scanning period. In most VBM studies, the dates of MR imaging scans have assumingly also overlapped between the groups under investigation, though this is rarely stated explicitly. To certainly exclude that the statistical parametric maps of single subjects result from shifts of MR imaging parameters with time, we performed multiple regression analyses with the smoothed GM images. Here, the date of MR imaging and the age and sex of the subjects served as covariates. This analysis yielded age-related GM loss and sex-related differences in GM as described previously⁴⁰ but did not yield significant results with respect to the date of MR imaging scanning. This finding indicates that statistical parametric maps of single subjects reported in our study did not result from systematic shifts of MR imaging parameters with time, but we cannot certainly exclude an influence of unsystematic changes (ie, instability) of MR imaging parameters.

How Many Control Subjects Are Necessary?

Finally, we tried to estimate the effect of smaller control groups. To this end, we repeated all analyses with control groups of 33, 66, and 99 subjects. All groups were matched for age and sex so that mean and SD did not differ significantly from the control group of 133 subjects. To estimate sensitivity, we determined the size of the largest cluster overlapping with the striatum for each single-patient analysis. For comparison of the cluster sizes derived from different numbers of control subjects, the volumes were assigned to 4 classes (0, 1–99, 1000–9999, >9999 voxels) and plotted against the percentage of patients.