Question

Based on different scenarios, the population prevalence of flu in Toronto ranged from 2.49% (with 95% CI of 1.80% - 3.17%) to 4.16% (with 95% CI of 2.58% - 5.70%). These prevalence estimates are 50 to 85 times more than the number of cases confirmed by the routine tests.

Toronto’s current confirmed infection rate (from the on-going insufficient tests) is 0.113%. Assume there is a consensus among epidemiologists that the confirmed infection rate of 0.113% is many folds underestimated and the true infection rate might be around 3.5%.

You may choose to discuss random sampling design, sample size (you have the concern of time/money cost if the sample is too big; in the meanwhile, you have the concern of the validity of the estimates if the sample is too small.), hypothesis setting, size of the test or other statistical issues you think to be important for such a medical study.

Answer 1

There could be multiple reasons for the infection rate to be found as 0.113%.

One of the main reasons could be that 0.113% could have been miscalculated.This is because the 95% of either of the interval does not include 0.113%. And condidering the width of the intervals, 0.113% will not be included in 99.9% interval as well.

Assuming 0.113% was properly caculated, the possible reasons could be:

1)The population is not random and is a biased sampling or a custer based sampling.

2) The size of the testing could have been a smaller size compared to the ones used to estimate CI.

3)A type 1 error where we may have ignored the posibility of such events.