The studies which "are considered adequate by EFSA and FDA to show the safety of APM" are not necessarily considered adequate by scientists in the field, and "do not provide adequate scientific support for APM safety" Soffritti, M., Padovani, M., Tibaldi, E., Falcioni, L., Manservisi, F. and Belpoggi, F. (2014), The carcinogenic effects of aspartame: The urgent need for regulatory re-evaluation. Am. J. Ind. Med. 57:383–397. doi:10.1002/ajim.22296
In general, there's a lack of good evidence for most non-basic ("don't overdo it", "don't get fat") positions taken on (processed/modern) food and drink, see e.g. Steven E. Nissen (2016), U.S. Dietary Guidelines: An Evidence-Free Zone. Ann Intern Med. 164:558–559. doi: 10.7326/M16-0035 : "The lack of high-quality RCTs [randomized, controlled clinical trials] has left dietary advice to cult-like advocates, often with opposite recommendations."
Two things we do know are that there are big downsides to these soft drinks, and that there is no evidence at all that the upsides are real rather than psychologically-induced by marketing: when people have looked at whether e.g. cola makes its drinkers happy (as marketed), "[n]o evidence was found that soft drink consumption has a beneficial effect on either the physical or mental dimensions of HRQL [health-related quality of life]." A Lana, E Lopez-Garcia & F Rodríguez-Artalejo (2015), Consumption of soft drinks and health-related quality of life in the adult population European Journal of Clinical Nutrition 69:1226–1232 doi:10.1038/ejcn.2015.103
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