# Medical Section meeting: The Case Fatality Ratio

Written by Nathan Green on . Posted in Sections and local group meeting reports

Thursday 5 December, the Medical Section held a meeting titled ‘The Case Fatality Ratio – How can estimating a proportion be complicated?’ at the Royal Statistical Society in London. It was presented by Professor Christl Donnelly of the University of Oxford and Imperial College London.

Professor Donnelly started by asking the question: Estimation of CFR should be easy, right? The answer, we found out in the course of the presentation, is unfortunately not.

Professor Donnelly has worked on many interesting and important diseases in her research career, from foot and mouth disease (FMD) in 2001, SARS in 2003, Pandemic influenza 2009, as well as MERS, Ebola and Zika in recent years.

The focus of the talk was on SARS, Ebola and MERS.

For SARS in 2003, more people than expected were dying of what was originally called atypical pneumonia. The University of Hong Kong contacted Professor Anderson’s group at Imperial College London to advise on data collection and to collaborate on the analysis and interpretation of epidemiological data. At the time the World Health Organisation (WHO) provided daily reports of the number of deaths divided by number of cases (D/C). Professor Donnelly added that what this should have said was 'deaths so far' since this was a substantial under-estimation in the presence of a large amount of censoring.

Two naïve estimators were available for estimating CFR. Method 1 was simply D/C. Method 2 was D/(D+R) where R is the number of recovered. Professor Donnelly explained that this second method is appropriate when the distribution of times from clinical onset to death is similar to times from clinical onset to recovery. But there was no reason to think that this was actually the case here.

So the group developed a third method which used hazard functions of the competing risks of survival and discharge to yield dual Kaplan-Meier curves. In a retrospective analysis of the three methods, the third method, that they thought might outperform the others, performed similarly to the D/(D+R) estimator.

For MERS, most cases were in Saudi Arabia and there was some evidence of under-reporting within the region. Why were visitors leaving the Middle East infected when there were so few cases reported inside of it? So the group estimated the number of cases using the person-days present in Saudi Arabia to get a ten-fold increased estimate which went from approximately 100 reported cases to almost 1000.

Finally, Professor Donnelly talked about her experience working on Ebola in West Africa.

They discovered a number of different biases. For example, the CFR looks smaller if you’re better at picking up survivors and vice-versa. In Guinea and Liberia the first cases were all deaths from Ebola so the CFR was 100% and in Sierra Leone the first cases had all recovered so the CFR was 0%. And there are several factors that affect CFR estimates including treatment and delays to admission. Furthermore, when considering relative CFR in two or more groups this also may include confounding and survivorship bias amongst others.

With PhD student Alpha Forna and colleagues, Professor Donnelly introduced a machine learning approach for imputing survival outcomes when there is considerable missingness. Using Boosted Regression Trees she showed that when considering nearly 40 predictors, four were found to explain most of the variation (age, reporting delay, country and fever). The next phase in the work is to investigate spatial correlation in the CFR residuals to identify missing covariates.

The event was preceded by the AGM of the RSS Medical Section, which saw two committee members stand down and the two nominated new members confirmed. A special mention was given to Robin Mitra, lecturer at Lancaster University, as the retiring section chair.

View slides from this event (PPTX).

Medical section