In this study, we conducted an assessment of the safety of the oral intake of L-Arg based on studies targeting healthy people by using SR. The estimation of NOAEL was conducted by w-CPRM, which assumed that the incidence of adverse events until reaching the threshold of the expression is 0 and modified the intercept (Kuramochi et al. 2023).

Among the 34 studies that were targeted for analysis, from the results of meta-analysis on the studies classified into Categories B and C, which reported the existence of AEs, there was no significant association between the reported gastrointestinal symptoms and the intake of L-Arg. There were also no significant results in each group from the subgroup analyses for each singly administered dose category. However, we observed a trend for a dose-dependent increase in RD. Therefore, the rate of occurrence of gastrointestinal AEs might rise upon increasing the one-time dosage of L-Arg, suggesting the need to decide on the upper limit of one-time administered dose.

In the conventional method that was used for the safety assessment of L-Lys, we decided on o-NOAEL from the studies classified into Categories B and C and then estimated NOAEL (Hayamizu et al. 2019). However, as mentioned in the introduction, this dose is the same as OSL (Hathcock et al. 2008). Therefore, we estimated NOAEL by using CPRM, which enables to find the exploration of the threshold, as a novel approach this time.

Most meta-analyses are based on sets of studies that are not exactly identical in terms of their methods and/or the characteristics of the included samples. Such differences may obscure the true effects (Viechtbauer et al. 2010). Meta-analyses generally uses either the fixed effects model or the random effects model. The fixed effects model is a model that assumes the random errors to the difference between studies and the random effects model is a model that inserts the heterogeneity that can't be ignored the difference between studies to the fixed effects model. Therefore, Meta-analyses uses these errors and differences as weight (ω1*i*). For that reason, we considered that the same adjustment would also be needed on CPRM. Here, we used the random effects model considering the differences between studies, which is a problem specific to SR. However, τ2 that denotes variability among the true effects tat sample characteristics may introduce was 0.00 from the result of Fig. 4 (τ2 = 0.03 in the subgroup analysis at doses of 9000 mg or more), and it was interpreted that the heterogeneity among studies was low. Therefore, we thought that the same result could get when using the fixed effects model this time.

In this research, we adopted only RCT, which are generally considered to be the highest-quality study type and assessed the quality of studies. However, variations in both the score of the Cochrane Collaboration tool for assessing the risk of bias (Higgins et al. 2008) and the Jadad score (Jadad et al. 1996) were identified among the studies, suggesting that the studies were not of uniform quality (Tables 1 and 2). Meanwhile, the RoB results are not normally used as a parameter for meta-analysis. For this reason, we thought to reflect the result of RoB into the w-CPRM as weight to find the true NOAEL considering about the heterogeneity of it.

Here, we considered using the result for RoB from Cochrane Collaboration tool for assessing the risk of bias, which is widely used in SR, and integrating it as ω2*i* into w-CPRM.

$${\omega }_{2i}*{y}_{i}={\omega }_{2i}\text{*}{\beta }\text{{\rm I}}\left({\chi }_{i}>{\chi }_{cp}\right)\left({\chi }_{i}-{\chi }_{cp}\right)+{\omega }_{2i}*{\epsilon }_{i}(Eq. 5, \text{M}\text{o}\text{d}\text{e}\text{l} \text{F})$$

The Cochrane assessment has seven items in total, so we regarded a perfect score as 14, with high quality of items as + 2, unclear as + 1, and low quality as 0. We regarded the total score of each study as scorei and we regarded RSi as scorei divided by 14 (reflecting full marks), which we used to adjust ω1*i*.

$${\omega }_{2i}={\omega }_{1i}* {RS}_{i}=\frac{1}{{SE}_{i}^{2}＋\widehat{{\tau }^{2}}}*{RS}_{i}$$

$${RS}_{i}=\frac{{score}_{i}}{14}$$

Here, Model E is a linear regression model weighted by ω2*i*, while Model F is w-CPRM weighted by ω2*i*. The formula of the linear regression model weighted by ω2*i* is:

$${\omega }_{2i}{y}_{2i}={{\omega }_{2i}\beta \chi }_{2i}+{\omega }_{2i}{\epsilon }_{i}(Eq. 6, \text{M}\text{o}\text{d}\text{e}\text{l} \text{E})$$

Models E and F are represented by Eqs. 6 and 5, respectively. The AICs of Models E and F were −38.01 and −61.77, respectively (Table 3). This indicates that L-Arg has NOAEL when using ω2*i* as well as ω1*i*. NOAEL weighted by ω2*i* was calculated 8754 mg/ one-time dose. This was a higher dosage but the AIC was slightly bigger than the one weighted by ω1*i*, that meant the fitting of the model was worse.

Table 3

Summary of models with weight2

model | weight | Xcp | AICmin | slope1 | slope2 | P-value |

E (*Eq. 6*) | \({\omega }_{2}\) | - | -38.01 | 1.058e-05 | - | 0.000259 |

F (*Eq. 5*) | \({\omega }_{2}\) | 8754 | -61.77 | 0 | 2.912e-05 | 2.5e-09 |

When using CPRM, at least three data points on each of two straight lines and over seven data points as a whole are necessary to accurately estimate the dose. We could judge that sufficient data were obtained to apply CPRM because here the target research for the assessment involved 23 studies. However, when applying CPRM that has no weighting (Model C), the straight line after the dose threshold was limited to two points, with 30,000 mg/ one-time dose being the highest reported dose and 15,000 mg/ one-time dose being the next highest (Fig. 6). Therefore, there were fewer data points on the side of higher dosages, which limited the estimation of the dose. However, the result of the estimation of NOAEL using this model did not appear to have been markedly impacted because three or more data points were present on both straight lines in w-CPRM weighted by ω1*i* and ω2*i*.

In this research, there were ten reports corresponding to Category A, which refers to studies with no description of the existence of AEs. We could not use these reports for the meta-analysis and w-CPRM, despite them being target studies for the assessment. As a reason of why these reports in category A exsit, foods are generally considered safe. It also seems that one of the reasons why objective assessment of gastrointestinal symptoms is difficult is that there are less severe than other AEs and cannot be detected by a blood test. Therefore, we thought that there is a limit to estimating NOAEL using only data from SR.

When the L-Arg dose was 4000 mg/ one-time dose, AIC was −52.83 from the AIC plot of w-CPRM weighted by ω1*i*. This was the dose estimated using our conventional method to estimate NOAEL (OSL). AIC was −62.31 when NOAEL was estimated as 7531 mg/ one-time dose which was considered to approach the true value. It was also the same when using w-CPRM weighted by ω2*i*.

However, regarding ω2*i*, which includes the result of RoB, the estimated dose may vary widely depends on the kinds of RoB and how to insert them to weight. Therefore, we consider that there is a need for additional research about these issues.