Category Archives: Statistical Models

Covid-19 in Quebec versus Ontario: Beware of Statistical Models

I have been tracking the Covid-19 statistics of Canadian provinces for several weeks (from March 16 to be precise). Initially, Ontario and Quebec were doing relatively well and had similar statistics. However, over time the case numbers increased, deaths, especially in care homes were increasing and the numbers were diverging. The situation in Quebec was getting worse and recently the number of deaths relative to the population was higher than in the United States. Like many others, I was surprised and concerned, when the Premier of Quebec announced plans to open businesses and schools sooner than later.

I was even more surprised when I read an article on the CTV website that reported new research that claims the situation in Quebec and Ontario is similar after taking differences in testing into account.

The researchers base this claim on a statistical model that aims to correct for testing bias and that is able to estimate the true number of infections on the basis of positive test results. To do so without a representative sample of tests seems rather dubious to most scientists. So, it would be helpful if the researchers could provide some evidence that validates their estimates. A simple validation criterion is the number of deaths. Regions that have more Covid-19 infections should also have more deaths, everything else being equal. Of course, differences in age structures or infections of care homes can create additional differences in deaths (i.e., the caes-fatality rates can differ), but there are no big differences between Quebec and Ontario in this regard as far as I know. So, is it plausible to assume that Quebec and Ontario have the same number of infections? I don’t think so.

To adjust for the difference in population size, all Covid-19 statistics are adjusted. The table shows that Ontario has 1,234 confirmed positive cases per 1 Million inhabitants while Quebec has 3,373 confirmed positive cases per 1 Million residents. This is not a trivial difference. There is also no evidence that the higher number in Quebec is due to more testing. While Ontario has increased testing lately, testing remains a problem in Quebec. Currently, Ontario has tested more (21,865 per Million tests) than Quebec (19,471 per Million tests). This also means that the positive rate (percentage of positive tests; positives/tests*100) is much higher in Quebec than in Ontario. Most important, there are 741 deaths for 10 Million residents in Ontario and 2157 deaths in Montreal. That means there are 2.91 times more deaths in Quebec than in Ontario. This matches the differences in cases where Quebec has 2.73 times more cases than Ontario. It follows that Ontario and Quebec also have similar case-fatality rates of 6.00% and 6.39%. That is, out of 100 people who test positive, about 6 die of Covid-19.

In conclusion there is absolutely no evidence for the claim that the Covid-19 pandemic has affected Ontario and Quebec to the same extent and that differences in testing produce misleading statistics. Rather, case numbers and deaths consistently show that Quebec is affected three time worse than Ontario. As the false claim is based on the Montreal authors’ statistical model, we can only conclude that their model makes unrealistic assumptions. It should not be used to make claims about the severity of Covid-19 in Ontario, Quebec, or anywhere else.