Accounting for event sequence: the 1|1|1 rule and the backdating exercise
The backdating exercise is a simple way to correct new cases curves for the sequence of events they reflect: a ”case” is typically the report of a diagnostic test indicating the patient is infected. But the epidemiologically important event is the contagion event: the moment the patient contracted the virus, which is normally unobserved. To find out when the contagion event happened we have to backdate from the reported test to the contagion event. The 1|1|1 rule and the backdating exercise give us a quick way to do this.
This is dedicated to Todd LaPorte who taught me everything about zero-tolerance environments.
In a dynamic environment, we are watching echoes of past events, and it is important to shift these events back in time to avoid oversteering after the fact. Belated oversteering is the #2 reason why dynamic systems with information cascades become volatile and eventually collapse.
In a rapidly evolving scenario all incoming information is out of place and out of time, so it is important to put it into context. In particular, it is important to backdate information from when we receive an echo of an event to the event itself. In an epidemic, this is the contagion event. The echos of that event are the publicly visible signals: test reports, hospital statistics, and similar.
1|1|1: the simple version
A person gets infected, some time later gets tested — positive or negative — and if positive will receive treatment.
This treatment can involve a number of steps: hospitalization, intensive care, or at any stage the patient recovers: gets healthy again and gets discharged from the treatment. Unfortunately, a number of the patients die.
This model simplifies this process by assuming the time from getting infected to testing is one week, the time from testing to hospitalization is one week, and the time from hospitalization to final stage (death or release) is also one week. These numbers simplify the model but are not arbitrary. They are based on scientific estimates of the Covid-19 infection cycle.
This is the 1|1|1 rule.
Examples of backdating exercises
Three early hotspots in LOMBARDY (orange) and Lombardy overall. Shifting back one week from reported testing, the contagion cycle peaked in late February, before lockdown.
The contagion cycle in CODOGNO, close to the original contagion at Casalpusterlengo, seems to have peaked in mid February, a week before the original eleven towns went into lockdown on February 22.
ITALY. The tail end of the curve is still unclear, but we are mostly interested in the peak here. Peak contagion around March 3.
GERMANY with interesting symptomatic and asymptomatic curves. The symptomatic cycle is through, now they are testing mostly asymptomatic comers. Peak March 4-7, before any interventions.
Note that the German Robert Koch Institut has a very peculiar backdating protocol in place.
SOUTH KOREA, contagion peak in February. A very clean response.
SWITZERLAND with small numbers problem, but I can show the effect of correcting for testing ramp-up. In this case, not much. Testing ramp-up should typically in a phantom fat tail (and phantom late peaks), not so much in a shift of the first peak.
SPAIN is very problematic since it never released testing data, and has all kinds of problems stemming from an overmatched disaster response system, but we can recognize that an end is in sight.