Modelling paper suggests hydroxychloroquine dosing was too low to be active against COVID-19 and that higher doses would risk toxicity
Simon Collins, HIV i-Base
A paper published on 21 May 2020 in Clinical Infectious Diseases by Fan and colleagues, modelled drug levels of hydroxychloroquine (HCQ) in vitro to show that dosing for human studies was unlikely to be effective. 
It suggests that in vitro EC50/EC90 values for HCQ should be compared to the in vivo free extracellular tissue concentration (which is similar to the free plasma HCQ concentration).
It also concludes that none of the current studies using HCQ as treatment for COVID-19 are/were using a high enough dose to expect to see a significant clinical effect and that dosing any higher would lead to unacceptable toxicity.
The range of ongoing studies registered to use hydroxychloroquine to treat or prevent COVID-19 already shows wide difference on the most appropriate dose. At least one study was stopped early due to excessing overdosing and serious side effects. 
Many other studies have reported no benefit. This includes the UK RECOVERY study, closing this arm of the study and contributing to the International WHO SOLIDARITY study also discontinuing HCQ. [2, 3, 4]
This paper modelling dosing suggests that activity against CoV-2 is unlikely at any of the current doses and that higher doses needed for activity would increase the risk toxicity.
An excellent editorial article by Charles Flexner et al in Clinical Infectious Diseases further explains the complex pharmacokinetics of HCQ and the problems of dosing for different indications. 
This was included in reference to two papers in the same journal using contradictory approaches to study design. [7, 8]
This article was first published online on 23 June 2020.
- Fan J et al. Connecting hydroxychloroquine in vitro antiviral activity to in vivo concentration for prediction of antiviral effect: a critical step in treating COVID-19 patients. Clinical Infectious Diseases, ciaa623. DOI: 10.1093/cid/ciaa623. (21 May 2020).
- High-dose chloroquine study for COVID-19 stopped with worse outcomes: high risk of cardiovascular events. HIV and COVID-19, HTB. (17 April 2020).
- Studies reporting lack of benefit from hydroxychloroquine to treat COVID-19. HIV and COVID-19, HTB. (14 May 2020).
- Collins S. UK RECOVERY study stops hydroxychloroquine (HCQ) for COVID-19: more than 1100 deaths question ethics and safety overall. HTB early access (6 June 2020).
- WHO. “Solidarity” clinical trial for COVID-19 treatments. Update on hydroxychloroquine. (17 June 2020). https://www.who.int/emergencies/diseases/novel-coronavirus-2019/global-research-on-novel-coronavirus-2019-ncov/solidarity-clinical-trial-for-covid-19-treatments
- Flexner C et al. Dose optimization of hydroxychloroquine for COVID-19: do blood concentrations matter? Clinical Infectious Diseases, ciaa691. DOI: 10.1093/cid/ciaa691. (31 May 2020).
- Martin-Blondel G et al. Hydroxychloroquine in COVID-19 patients: what still needs to be known about the kinetics. Clin Infect Dis 2020. [Epub ahead of print]
- Perinel S et al. Towards optimization of hydroxychloroquine dosing in intensive care unit COVID-19 patients. Clin Infect Dis 2020. [Epub ahead of print]