There are many criticisms and anomalies, but a few notes about the Australian data. The authors reported 609 admissions and 73 deaths in 5 Australian hospitals on 21 April.
Curiously, no Australian data were included in a previous paper on cardiovascular disease by the same authors in the @NEJM (10.1056/NEJMoa2007621) using the same database to 28 March
However, the state breakdown of deaths was NSW 29, VIC 15, TAS 8, WA 7, QLD 6, SA 4, ACT 3. So even if the four hospitals had treated for all the people who had died in the states with the most deaths (unlikely), this wouldn't be possible. https://www.covid19data.com.au/deaths 
Additionally, the authors reported that 49 patients had received CQ and 50 had received HCQ. CQ isn't currently available in Australia.
CQ can be imported under the Special Access Scheme in Australia, but it would seem unlikely that large numbers of patients would have received CQ when HCQ is available. https://www.tga.gov.au/form/special-access-scheme
There have been other observational studies of HCQ and CQ. But these are all likely to have various biases - treatment tends to be given to those more seriously unwell, but patients need to survive long enough to receive it.
Ultimately, we'll need a randomized controlled trial to know if CQ or HCQ have any effect on the time to recovery or mortality. It would be a pity if these trials were stopped in response to these data.
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