# Covid Forecast Examples

Posted on April 29, 2020

This post looks at a few different things you might see when using the Covid Forecasting Tool and explains how to interpret them. I’ve been getting a few questions about output from the tool and I want to consolidate and expand on my answers here.

## Example 1: When it mostly works first time

First let’s look at a nice example where everything works and things are easy to interpret. Here is a chart of the raw data:

First we look at the impact plot which uses the data up to the date of lockdown to make a forecast. If the actual data since lockdown is very different to the forecast then it is reasonable to conclude that lockdown has had an impact.

You can see that what actually happened (the black line) is very different from what was predicted to happen if lockdown did not occur (the blue line). It is far outside the green zone of “stuff we could reasonably expect to happen”; there is less than a 5% chance of seeing what you actually saw if the forecasting model is correct.

Indeed, Google’s `CausalImpact` method says there is a 99.9% probability of a causal effect! (This effect might not be lockdown, but it did happen on 24th March).

Let’s proceed with the analysis and see what we can say about current trends.

The next part of our process analyses the underlying trend in the metric and looks for points at which the trend changes.

The following three plots are all different ways of visualising this.

The chart above shows the underlying trend. It drops (a lot!) around lockdown but then seems to be rising again early in April.

The “deltas” plot shows the size of the trend change. There are two small, positive deltas (black lines) happening after lockdown which shows the trend has changed in an upwards direction since 24th March.

The trend slope is the number of extra sessions (or whatever metric you choose) per day you can expect compared to the day before, after allowing for weekly and annual seasonality. Around lockdown the slope went very negative; each day was worse than the previous one. But in early April is began moving upwards again and is now above zero; you can expect this metric to keep growing over the coming weeks.

This is a nice example of things all working out really well which makes things dead easy to interpret. Most things in the real world are less clear cut as the next examples show.

## Example 2. Lockdown when?

What the hell is going on here?

Looking at the raw data over a longer period of time helps:

There has clearly been something going on with this site. But the first plot is showing us that what we are currently seeing is within the 95% range of what would have happened if there had been no lockdown.

Part of the problem is that, for this site, the changes started happening for them before the UK lockdown on the 24th March. Even for a UK site this is a common pattern. Changing the lockdown date to the 16th March produced the following impact plot instead:

This is a bit more like what we would expect. It shows the impact of whatever started happening on the 16th March as having an impact on the metric; this is the difference between the blue and the black lines. The forecast (blue line) also looks more reasonable than in the first chart; here it seems to continue on from the previous values rather than popping up out of nowhere.

However, it is still not that simple! The green 95% predictive interval overlaps the black line which means that on any given day there is >5% chance that we are observing something that has nothing to do with changes on March 16th.

I’m not that interested in what might happen on any given day, some days are bad days and some days are good days. When all the days are within the 95% interval and all the days are on the same side of it (the low side) this can still mean there is a very high chance of an effect even if the chance for a single day is small.

You can draw a cumulative impact chart to see this.

This plot isn’t part of the forecasting tool at the moment but I’m thinking of adding it in.

It clearly shows the impact of the 16th March. There is a 97.5% probability of a causal effect.

Another problem is that the model doesn’t know any of the constraints on the value of a metric. For example sessions cannot be less than zero and bounce rates must be between zero and 100 percent. You can see this in the first impact plot where the green area suggests there is a chance it might be negative even though in the real world this is impossible.

I have a fix in the pipeline for this; it will probably only be for a small number of commonly used metrics but that will be better than nothing. Give me your email address if you want an update when I do this:

What does the trend analysis say for this data?

Nothing good I’m afraid:

For this site, they have been hit hard before the official lockdown even happened and there are no signs of any recovery yet. If I had a bit more time I’d do more analysis on finding the best date to say “it all started to go wrong here”; it looks to me like things might have been heading South even before the 16th March. Although, of course, the further back you look for these things the more likely it is that something other than COVID-19 is the cause.

## A success story

Just looking at the next chart with the mark 1 human eyeball is enough to tell this is a very different story from our previous example.

It looks like there might be a positive trend from February onwards. The questions here are more about whether or not lockdown had a positive impact and if that impact is sustained rather than temporary.

There is a 99.9% probability of a causal effect and this effect is positive. This isn’t surprising; just looking at the chart and not worrying about the statistics will tell you the same thing!

The deltas plot shows that, starting in early April, there were some negative changes to the trend slope. This could mean it starts decreasing or it could just mean it isn’t increasing so fast.

Looking at the values of the trend gradient this shows that after rapid growth in the runup to lockdown things might be returning to normal for this site.

## Thank you

Big thanks to Dipesh Shah and other (anonymous) contributors who agreed that their data could be shared in this post.