Caracterización de la UCLV y del proceso de Atención Personalizada al Cadete

summary statistics of the ACE model over the brain region of amygdala, which is a brain region typically associated with emotional processing. We provide inference on the unweighted mean summaries for illustration, which is compared with the results obtained from voxel- and cluster-wise inferences using the maximum statistics.

Real Data Acquisition

A sample ofn= 111 subjects in total from a pre-processed fMRI dataset7 includes nMZ = 32 MZ twins (16 pairs),nDZ= 50 DZ twins (25 pairs) andnS= 29 singletons 8_{. These 111 subjects are all males, aged 10–12, from the Twins Early Development}

7

The access information of this fMRI dataset was provided in an email from Prof. T.E. Nichols ([email protected]) in July 2011.

8

Although we found the statistical power of the effect sizeh2= 0.5 for this small sample is low (less than 20%) using simulations, and nothing significant was found using the voxel-wise inference for this dataset, the use of spatial statistics derived from cluster and summary inferences increases the power of the test at the same significance level.

Figure 3.16: The log transformed p-value image (i.e., −log₁₀(pFWE)) for suprath-

reshold clusters on the observed image with significant suprathreshold cluster size.

Figure 3.17: The log transformed p-value image (i.e., −log₁₀(pFWE)) for suprath-

Study (TEDS)9. There are 50 participants out of 111 with the behavioural prob- lems by SDQ assessment. Hence these 111 participants can be separated into two groups: subjects with behavioural problems (CPCU+), and healthy subjects (Neg- ative). During the experiment, all subjects equally performed an emotional pictures matching task with the pictures from International Affective Picture System (IAPS) (Coan and Allen, 2007). The brain ROI’s considered are left amygdala, right amy- gdala and both amygdalas of overall 286, 269 and 555 in-mask voxels separatively. There are 3 samples including all subjects, CPCU+ (n+= 50 with 14 MZ twins, 30

DZ twins and 6 singletons) and Negative (n−= 61 with 18 MZ twins, 20 DZ twins and 23 singletons) considered for heritability analysis. Both permutation and boot- strapping inferences are utilized to compute the p-values and confidence intervals. Before making the analysis, the inverse Gaussian transformation was implemented with the use of probability integral transform to assure the normality of the response data and remove the possible outliers, which is routinely designed to make the re- sponse data variable with a skewed or non-normal distribution follow a normally distributed pattern.

Results

In Tables 3.3 and 3.4, the results for the three samples of all subjects, the CPCU+ group and the Negative group are shown. For all subjects, the estimates, 95% bootstrapping confidence intervals from 1000 bootstrap replicates, and permutation- based p-values derived using 1000 permutations for different spatially informed test statistics are explicitly listed for the considered brain ROI’s of both amygdalas, left amygdala and right amygdala in Table 3.3. The spatial statistics employed include the unweighted mean summaries of heritability (h2_{) and common environmental}

factor (c2 ₌ 1

K

PK

r=1c2r for all K in-mask voxels, where c2r denotes the common environmental factor for voxel r (r = 1, . . . , K)), and the maximum statistics of maximum LRT statistic (Tmax_p ) from voxel-wise inference, and maximum suprath- reshold cluster size (Kmax_p ) and cluster mass (Mmax_p ) from cluster-wise inference. For CPCU+ and Negative, the estimates and permutation-based p-values derived using 1000 permutation for the above-mentioned spatial statistics are displayed in Table 3.4 for those 3 amygdala ROI’s. In Table 3.4, the difference between these two groups is also shown in terms of the estimate and its 95% bootstrapping confidence interval from 1000 bootstrap replicates.

For all subjects, the cluster-wise statistics of maximum suprathreshold cluster size

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and cluster mass and the unweighted mean statistic of heritability are found to be significant at level α = 0.05 for the 3 considered brain ROI’s, but the voxel-wise statistic (maximum LRT statistic) is only found to be significant for left amygdala. Compared with right amygdala, left amygdala has a lower heritability summary measure (h2_{= 0.4108 for left amygdala vs.h}2_{= 0.4564 for right amygdala), but its}

maximum LRT statistic value is higher than that of right amygdala (Tmax_p = 6.3357 for left amygdala vs. Tmax_p = 5.7304 for right amygdala) although its cluster size statistic is smaller (Kmax_p = 70 for left amygdala vs. Kmax_p = 97 for right amygdala), which reveals that left amygdala has a higher peak voxel while right amygdala has a larger significant cluster.

In Table 3.4, we only find significance using mean heritability summary statistics for those included brain regions for the CPCU+ group, while the evidence for her- itability is found with cluster statistics for the Negative group for right amygdala and both amygdalas, but not for left amygdala. There is no significance found using voxel-wise statistic for either CPCU+ or Negative, which should be accounted for by the reduced statistical power for small samples. Comparing the CPCU+ and Negative groups using their difference, we find that the mean heritability measure of CPCU+ is always smaller than that of Negative, and the values of spatial statist- ics including the voxel-wise peak height and cluster size and mass for CPCU+ are much smaller than those for Negative, indicating that these two groups are distinct regarding heritability on amygdala.

Even for the larger sample of all subjects in Table 3.3, the 95% bootstrapping confidence intervals for c2 _{still contain the tested value of 0, implying that the}

omnibus hypothesis test of zero common environmental factor cannot be rejected. In Table 3.4, even if the estimates of heritability mean summary h2 _{for CPCU+}

are less than those for Negative for all 3 samples,h2 _{is always found significant for}

CPCU+ while insignificant for Negative, which may be due to the smaller mean measure of common environmental factorc2 _{for CPCU+.}