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Patient advocacy groups are urging the South African government to reopen an antitrust investigation into Vertex Pharmaceuticals over allegations the company misled authorities into closing a high-profile case last year over access to a cystic fibrosis treatment.

Last December, the Competition Commission ruled that the company had sufficiently provided access to its medication after a patient filed a complaint alleging that Vertex violated the South African Constitution. The petition cited human rights failures — such as a basic right to health — as one justification for the complaint, as well as claims that the company abused its patent status.

Notably, the petition maintained that Vertex, which is the leading purveyor of cystic fibrosis drugs, including a highly effective treatment called Trikafta, had failed to register the medication with regulators. And since Vertex held patent rights in the country, the only available route to obtain Trikafta was to import the medicine from the U.S. at a prohibitive cost, given a list price exceeding $300,000.

Participants

Fourteen healthy TS participants (female = 7, age = 31.71 ± 8.20 years, right-handedness = 13) underwent MRI scans at four different machines (two at the University of Fukui, one at Osaka University, and one at Chiba University) over a three-month period. The study used the TS dataset from the Child Developmental MRI (CDM) project [5] to address measurement bias in each MRI machine. Participants with ADHD were recruited from hospitals of the University of Fukui, Osaka University, and Chiba University in Japan. Children with TD were recruited from the local community and assessed to ensure that none of them had developmental delays, received any special support education, or had a history of epilepsy or other psychiatric disorders. Participants with ADHD fulfilled the diagnostic criteria for ADHD according to the Diagnostic and Statistical Manual of Mental Disorders Fifth Edition (DSM-5). Participants in the current study participated in the experiments from 2014 to 2022. None of the participants had a history of severe head trauma, neurological illness, or potential for hazards associated with MRI examinations (such as the presence of metal on the body surface or internal structures, pregnancy, claustrophobia, or fear of the dark). The demographic data of the participants with ADHD and TD in each MRI machine are summarized in Tables 1 and S1.

MRI data acquisition

Participants were scanned with T1-weighted imaging at the University of Fukui, Osaka University, or Chiba University using a 3T GE Signa PET/MR scanner (General Electric HealthCare, Chicago, Illinois, USA; University of Fukui), 3T GE Discovery MR750 scanner (General Electric HealthCare; University of Fukui or Chiba University), or 3T GE Signa Architect scanner (General Electric HealthCare; Osaka University). The scanning parameters are provided in Table S2.

MRI analysis

The fully automated segmentation procedure implemented in FreeSurfer version 7.3.8 was used to estimate the gray matter volumes of the cortical and subcortical regions (http://surfer.nmr.mgh.harvard.edu/). The structural data were obtained using a standardized processing pipeline. The analysis used the Desikan-Killiany atlas for classifying cortical regions (68 brain regions) and for segmenting subcortical regions (14 brain regions, such as thalamus, caudate, putamen, pallidum, hippocampus, amygdala, and accumbens). Details of the segmentation method are provided by Fischl et al. [19].

Harmonization methods

We followed the TS harmonization method reported by Yamashita et al. [5], which extends a general linear model harmonization using the TS dataset. Python was used to estimate the measurement bias of each MRI machine using the TS dataset and reduce measurement bias from the CDM dataset. We first utilized the TS dataset to calculate scanner differences using ridge regression. The model included dummy variables for both the 4 scanners and the 14 TS participants as follows:

Here, m signifies the measurement bias (4 machines × 1), and p signifies the TS participant factor (14 TS participants × 1).

There is no sampling bias in the TS participants, as participants across different MRI machines do not differ. The TS harmonization method only estimates variations between MRI scanners. Once we estimated the machine differences using the model above, we applied them to the CDM dataset to correct the measurement bias.

ComBat harmonization was also used to control measurement bias for comparison. ComBat was initially developed to correct the batch effect in genomics [20] and has recently been applied to MRI datasets [18]. ComBat corrects a type of multivariate dataset using an empirical Bayesian estimation approach and can be used to analyze datasets obtained using different scanning machines. In the current study, we used the module “neuroCombat” to correct structural brain data using Python [21]. We used ComBat harmonization in the TS dataset and CDM dataset individually. In the TS dataset, we included age, sex, and handedness as covariates for data correction. Whereas, in the CDM dataset, we included age, sex, handedness, and diagnosis (ADHD or TD) as covariates.

Measurement and sampling biases of different harmonization methods

To quantitatively investigate the validity of different harmonization methods in structural brain data, we calculated measurement biases, sampling biases, and disorder factors, following recommendations from Yamashita et al. [17]. We estimate the measurement and sampling biases using the following model:

where m represents the measurement bias (4 machines × 1), s represents the sampling bias of TD (3 sites × 1) and ADHD (3 sites × 1), d represents the disorder factor (ADHD × 1), and p represents the participant factor (43 participants with repeated measures × 1). We used ridge regression to calculate the parameters. We also assessed measurement bias and sampling bias by excluding or including participants as a random intercept in the model, detailed in the Supplementary Material. The brain structures were normalized for ridge regression. The model was tested on raw CDM data, TS-corrected CDM data, and ComBat-corrected CDM data to analyze measurement and sampling bias before and after harmonization. Measurement bias was calculated as the average of the effect sizes of the brain structures across different MRI scanners. The sampling biases in participants with TD and patients with ADHD were defined separately as the average effect sizes of the brain structures across different sites.

Statistical analyses

We used R (version 4.3.1; The R Foundation for Statistical Computing, Vienna, Austria) and Python (version 3.11.6; Python Software Foundation, Wilmington, DE, USA) for statistical analyses. First, we examined the necessity and validity of harmonization. We used a repeated-measures analysis of variance (ANOVA) on the TS dataset to examine the necessity of harmonization. Additionally, we computed the intraclass correlation coefficient (ICC) of the harmonized structural brain of the TS dataset, a descriptive statistic that can be used when quantitative measurements are made on units organized into groups (the individuals in this study) to examine validity [22]. We compared the ICC among the raw, TS-corrected, and ComBat-corrected data of the TS dataset using ANOVA, followed by a post hoc test using Tukey’s Honest Significant Difference (HSD) method with family-wise error rate (FWE) correction. We subsequently adapted TS and ComBat to correct the brain structure data in 178 children with TD and 116 children with ADHD from the CDM project. We calculated the measurement and sampling biases for TD and ADHD and compared these biases among TS-corrected, ComBat-corrected, and raw data using ANOVA and a post hoc test using Tukey’s HSD method with FWE correction.

Additionally, we examined the association between brain structures and ADHD in CDM dataset. First, we adapted a linear mixed-effects model to examine the relationship between brain structures harmonized by TS and ADHD. We analyzed this model using the R-package “lmerTest”. For the mixed-effects model with a group (ADHD or TD) as the independent variable and brain structures as the dependent variable, we considered participants’ age, sex, handedness, intelligence quotient (IQ) measured using the Wechsler Intelligence Scale for Children (WISC), and intracranial volume of the brain as covariates. As some participants participated in the experiment multiple times, the subject ID (used to distinguish whether it was the same person) was modeled as a random effect. Raw brain structural data and brain structures harmonized using ComBat were also used in the mixed-effects model to compare children with ADHD and TD. Additionally, considering the differences in age, sex, and handedness between the ADHD and TD groups, we adapted the propensity score matching method to match the age, sex, and handedness of the TD group with the ADHD group (N = 94) by using the R package “Matching” with caliper = 0.25, and analyzed them similarly [23, 24]. Specifically, after matching, we conducted mixed-effects regressions to examine the differences between ADHD and TD, with group (ADHD or TD) as the independent variable and brain structures as the dependent variable, controlling for IQ and ICV as covariates. In the current study, for analyses involving brain structures, we applied false discovery rate (FDR) correction to 82 brain regions, 68 cortical regions and 14 subcortical regions, for multiple comparisons correction [25].