Recent news stories have highlighted a new “study” suggesting that the actual case fatality rate for H7N9 is lower than the apparent 30% rate. What most of these stories don’t mention is that to achieve these lower rates, the authors of the study must assume that there have been thousands of unreported H7N9 cases in China.
Here’s the math:
Case fatality rate = Deaths / Cases
The reported number of cases is 131.
The reported number of deaths is 39.
39/131 = 29.77%
The new “study” asserts that the case fatality rate is actually between 0.16% and 2.8%. They come to this conclusion by assuming there must be unreported cases. The news stories don’t say how many unreported cases are required to get these lower case fatality rates. I will.
For a case fatality rate of 2.8% we would have:
39/cases = .028
1/cases = .028/39
cases = 39/.028
cases = 1,393
For a case fatality rate of 0.16% we would have:
39/cases = .0016
1/cases = .0016/39
cases = 39/.0016
cases = 24,375
Is it believable that there have been tens of thousands of cases of H7N9 in China – all from contact with birds at poultry markets? This is patently ridiculous. A case fatality rate of 0.16% requires that there be over 24,000 cases which implies efficient human to human spread of H7N9.
A case fatality rate of 2.8% would be similar to the 1918 pandemic – one of the most lethal disease outbreaks in human history. To reduce the apparent case fatality rate to even this level, we must assume over 1,200 unreported cases. This number pushes the limits as to what is believable in terms of bird to human spread of the virus. More likely, there would have to be substantial human to human spread, perhaps limited by the currently unfavorable weather for influenza transmission.
One can make all the assumptions one wants about missing data. However, anyone who repeats these assumptions should do the math and report the implications of these assumptions.
note: I have just found a story that does mention the number of unreported cases:
From Fox News, June 23, 2013
“Human infections with avian influenza A H7N9 virus seem to be less serious than has been previously reported,” they wrote.
But many mild, unreported cases may have occurred — between 1,500 and 27,000 — said the study, urging “continued vigilance and sustained intensive control efforts”.