Novel H1N1 Mortality Rate: Pitfalls in Calculation

Although the crude mortality rate for infection with the novel H1N1 virus has been supplied at this blog (by using raw data from the World Health Organization), there are a number of pitfalls when calculating this value during an epidemic/pandemic. The drawbacks of using the simple equation for the mortality rate—that is, dividing the number of known deaths (the numerator) by the number of known cases (the denominator)*—are outlined in a recent (if somewhat mathematically challenging) article in the BMJ.

Briefly, however, the UK authors highlight 2 general sources of potential error: 1) difficulties with case ascertainment; and 2) inevitable delays between infection onset, death, and subsequent reporting.

Case Ascertainment

Particularly as the pandemic advances (for example, in the hot zones of Mexico and the United States), there is the likelihood of underrecognizing (or simply ignoring) mild cases of infection. Consequently the denominator is underestimated, and the mortality rate is overestimated.

But deaths due to H1N1 may also be unrecognized. For instance, some vascular deaths may not be recognized as caused by influenza. Also, at least in developing areas, hospital surveillance may be poor. Consequently the numerator and the mortality rate are underestimated.

The authors' solution (at least for the underrecognition of cases) is to use closely monitored hospitalization data from the early part of the pandemic and in-hospital mortality data later in the pandemic (when total case ascertainment becomes difficult). The overall mortality rate (or really, the case-fatality ratio) is the hospitalization ratio X the fatality ratio among hospitalized cases.

Of course, this calculation requires sufficient sample sizes. For instance, to obtain 95% confidence intervals for a case-fatality ratio ranging from 0.5 to 1.5, you would need ~1100 cases and ~200 hospitalizations. An important assumption with this solution, the authors stress, is that the hospitalization ratio and the in-hospital death ratio remain constant over the course of the pandemic; but guidelines for the hospitalization of H1N1 cases, in particular, may change as the pandemic advances.

Nevertheless, by using numbers from the CDC, the H1N1 case-fatality ratio can be estimated according to the authors' equation. There were 43,771 confirmed or probable cases of novel H1N1 infection in the United States from April 15 to July 24,** resulting in 5011 hospitalizations. Therefore the hospitalization ratio for this time period was 0.114. As of August 20, there have been 522 deaths among 7982 hospitalizations, for an in-hospital death ratio of 0.65 0.065. The case-fatality ratio in the United States is therefore 0.114 X 0.65 0.065, or 0.0075 (and the mortality rate is 0.75%).

Inevitable Delays

The case-fatality ratio may also be underestimated when there is a delay between the onset of infection and knowledge of the final outcome of the case. This effect, the authors note, is known statistically as censoring—which subsides after the pandemic peaks.

The authors' solution is to divide the number of deaths by the number of cases in which the outcome is known; however, this solution may be problematic when there is a relatively long delay between symptom onset and death, as is typical in cases of influenza.

Their second proposed solution is an estimator, which contains a big, fat sigma (a sigma!), to calculate the case-fatality ratio on a particular day. The estimator also requires knowledge of the time from symptom onset to death to approximate the expected number of deaths on the particular day in question.

The estimator is reproduced here for statisticians, epidemiologists, and the otherwise fanatical. Knock yer-selves out (and feel free to post yer calculation).