## Simon Cook

# Working out length of hospital stay for Covid patients: a technical note

Length of hospital stay is a crucial metric, but hard to do with much accuracy unless each patient is certified Omicron or Delta. The closest proxy we have right now is information on patient stay and there are graphs for two cohorts: those admitted from 1 May (third wave) and from 1 December. The graphs were published in the CO-CIN study dated 22nd Dec (Fig 8). The younger age groups are at the top. Those who were discharged on the left, those who died on the right. The line drawn on each chart shows 14 days on, and indicates what percent of patients were discharged or had died by that point. First, those from 1 May…

And the December ones are below. From simply looking at the charts, there seems to be a shift towards lower values. The bottom left chart, for example, shows discharged over-80s. The one above (for those after 1 May) says 63pc were discharged after day 14, but in the post-December version (bottom left, below) that rises to 99%. For those in their 70s it rises from 75pc to 98pc. For those aged 50-70, it rises from 83pc to 100pc. So clearly, something is going on. The question is whether we can express this in a simpler format: the average stay (in days).

So how to come up with an average? These graphs are probability density functions. So you can find the *probability* of a hospital stay being between (let’s say) two and three days by finding the area under the curve between those points. This can be done numerically - simply doing it in a spreadsheet gives a good approximation - and the median is a line drawn where 50pc of the area of the graph is on the left, and 50pc on the right.

Drilling into this data is harder given how few SAGE reports come with the data attached (unlike the OBR where every graph has a downloadable dataset). But these can be approximated using scanning software to estimate the numerical data from the graph images. It’s a relatively new tool, and useful in data journalism where sources are reluctant to release the data used for the graphs in public debate.

The median is better than the common arithmetic mean in this case because, while the vast majority of patients leave hospital within 14 days, there will be the occasional patient who stays for months and this will distort the mean. The median gives a much better idea of a typical value.

As our figures were derived from scans, we present them as estimates. It would of course be much better for everyone if SAGE published the underlying data tables in the same way that other bodies like ONS and UKHSA do for their reports. Or, even better, published its own estimate for the all-important length of hospital stay.

And a final note: cohorts are patients from all over the UK admitted from 1 December, not just Omicron. If Omicron patients are being discharged earlier, that effect would be heavily mixed with Delta patients - so the chart should not be seen as Delta vs Omicron. It’s likely that a more precise Omicron estimate is on its way to us soon, but the above tables give us an interesting sign of what might be to come.