This prospective, randomized, equivalence, two-period, and cross-over clinical trial open with blinded evaluation was conducted at three pediatric departments in France. Each of the two one-month periods consisted of oral treatment with betaine at 100 mg/kg/day or 250 mg/kg/day with a one-week wash-out period between the treatment periods. The completion and reporting of the trial have complied with CONSORT 2010 guidelines.

The protocol was approved by national ethics committees (Comité de Protection des Personnes [CPP IDF III], the French National Drug Safety Agency [ANSM, EudraCT 2014-003643-36] and the Franch data protection authority [Comission Nationale de l’Informatique et des Libertés, CNIL]). Funding was provided by the French Health ministry (AOR13016). The trial was registered at ClinicalTrials.gov (NCT02404337).

Patients were eligible for inclusion if aged 1–18 years and diagnosed with either pyridoxine non-responsive CBS (pnrCBS), or cblC deficiencies confirmed enzymatically and/or molecularly, treated continuously for at least one year. Exclusion criteria were pyridoxine-responsive CBS deficient patients and pregnant females.

Subjects were recruited in each center, included in the trial, and then investigated in the same center (Clinical Investigation Center (INSERM CIC1426) at the Robert Debré Hospital, Paris, France). Each patient was randomly assigned to one group. The first trial period was followed by a one-week wash-out period to mitigate the possibility of carry-over effects and reduce the likelihood that treatment from the prior first period influenced outcome measures of the current second period.

From day three until the end of the month, they received betaine at 100 mg/kg/day or 250 mg/kg/day as a twice-daily dose. Fasting blood samples were collected before morning betaine administration at the end of the one-month treatment for each dose. All the patient's usual treatment, including protein restriction (apart from betaine), remained unchanged throughout the protocol.

The primary outcome was plasma concentrations of total homocysteine at one month upon oral treatment with betaine at 100 mg/kg/day compared with 250 mg/kg/day in the same individual.

Secondary outcomes included plasma concentrations of betaine, dimethylglycine, sarcosine, methionine, S-adenosylmethionine (SAM), S-adenosylhomocysteine (SAH), creatine, guanidinoacetate, choline, ethanolamine, methylmalonic acid (MMA) and urinary concentrations of betaine, dimethylglycine, sarcosine, homocysteine, methionine, creatine, guanidinoacetate, and MMA before and after one month of treatment. The known side effects of betaine were also recorded in clinical outcomes, notably gastrointestinal disorders. All laboratory parameters were centralized and analyzed at the Biochemistry laboratory (Robert Debré Hospital, Paris, France).

Blood containing EDTA as an anticoagulant was drawn at different time points and immediately centrifuged. Plasma was subsequently collected and frozen at − 80 °C until analysis. SAM, SAH, choline, d9-choline, betaine, d9-betaine, dimethylglycine (DMG), ethanolamine (EA), sarcosine, d3-sarcosine, methionine, L-homocystine, dithiothreitol (DTT), creatine, d3-creatine, guanidinoacetate (GAA), 13C2-GAA and MMA were obtained from Sigma-Aldrich (Saint Louis, USA). d3-SAM, d6-dimethylglycine, d4-ethanolamine, d3-methionine, and d8-DL-homocystine were purchased from CDN-isotope (Pointe-Claire, Canada). D4-SAHwas bought by cayman chemical (Ann Arbor, USA).

Free choline, ethanolamine, creatine, GAA, and MMA were assayed after deproteinization by an LC–MS/MS method adapted from Holm et al. [19], Imbard et al. [20], and Cognat et al. [21]. The analytical system consisted of an Acuity UPLC I Class system (Waters, Milford, USA) coupled with a Xevo-TQD (Waters, Milford, USA) with an Atlantis HILIC analytical column (2.1 × 100 mm, 3 µm) (Waters, Milford, USA).

SAM, SAH, tHcy, Met, betaine, DMG, and sarcosine were measured using new LC–MS/MS developed in our laboratory (detailed in the Additional file 1).

Sample size calculation was conditional to the number of potentially eligible subjects per year in the three centers for these rare diseases, estimated as 18 subjects.

The treatment sequence (100 then 250 vs. 250 then 100) was randomly allocated via a randomization list, previously established by the Clinical Epidemiology Unit of the Robert Debré Hospital, Paris, France, using random blocks of variable size. Stratification on the type of pathology was applied to limit bias. All biological samples were centralized and frozen, and the measurements taken at the end of the study were blinded from the allocated arm.

Descriptive analysis was used to characterize subjects at baseline (all subjects), then evolution and treatment tolerance during the study (considering two groups among betaine dosage 100 mg/kg/day or 250 mg/kg/day) and by disease type (CBS or cblC deficiency). Data was expressed as medians with [min; max] for continuous variables and numbers with percentages for categorical variables.

Mean differences were calculated and tested to verify the absence of a carryover effect between the two sequences (100 mg/kg/day then 250 mg/kg/day vs. 250 mg/kg/day then 100 mg/kg/day) periods. In the case of significant interaction indicating the presence of carryover, only results from the first period were analyzed.

The ratio of plasma tHcy concentration at 30 days in the 100 mg/kg/day and 250 mg/kg/day groups was calculated to test the primary equivalence outcome. As a sensitivity analysis, a two one-sided tests (TOST) approach was also used to test equivalence [22]. Equivalence was declared if the 90% confidence interval of this ratio was between 0.8 and 1.25, taking into account the logarithm of the dosage.

The evaluation in plasma tHcy measured at one month by oral treatment with betaine between 100 and 250 mg/kg/day was tested using a 2-sided Type 3 F-test of the treatment effect in a linear mixed-effect regression model for repeated measures. The model included fixed effects for treatment dosage (100 or 250), period (1 or 2), the interaction between treatment dosage and period (dosage*period), and the disease type (CBS or cblC deficiency) with random effects for the subject.

Similar linear mixed-effect regression models for repeated measures were used to evaluate the secondary metabolic outcomes.

Analyses were performed on the intention-to-treat basis, with a p-value < 0.05 considered significant. Data management and statistical analysis were performed using SAS software, Institute Inc., Cary, NC, version 9.4.

At the beginning of each one-month period each patient received the daily dosage (100 mg/kg/day or 250 mg/kg/day) in a single administration to evaluate the pharmacokinetics of betaine over 48 h. Samples were collected before betaine administration (H0) and 2 h, 6 h, 12 h, 24 h, and 48 h after the first single-dose betaine administration. Plasma concentrations of betaine, dimethylglycine, sarcosine, and urinary concentrations of betaine, dimethylglycine, and sarcosine were measured.

According to standard procedures, individual concentration–time data of betaine were evaluated using a non-compartmental (NCA) approach (PKsolver, version 2.0, China Pharmaceutical University, Nanjing, China).

The total area under the plasma concentration vs. time curves from zero to 48 h (AUCP, 0–48 h) were calculated using the linear trapezoidal rule. The rate constant kel and corresponding half-lives (t1/2) were estimated by a least-squares fit of data points (log concentration–time) in the terminal phase of the decline. The maximum concentration after the first dose (Cmax) and the time at which it appears (Tmax) were obtained from the observed data. The Cmax and AUC ratios after a 250 mg/kg and 100 mg/kg dose were calculated for each patient.

Apparent total body clearance of betaine (CL/F) was calculated as the ratio between the dose of betaine (Dose) and the corresponding AUCP, 0–48 h, with F, the bioavailability of the molecule. The apparent betaine steady-state volume of distribution (VSS /F) was obtained from (Dose. MRT)/(AUCP, 0–48 h), where MRT is the mean residence time of the molecule (h).