Why an ADSM detection chart isn’t a cumulative probability (and shouldn’t be treated as one) - NAVADMC/ADSM GitHub Wiki

Suppose I enter the chart shown in figure 1. This is probably not a realistic chart, but it is simple and it is a perfectly valid input to ADSM.

Figure 1: An example of an ADSM detection chart.

Now suppose ADSM is in the middle of a simulation, and it sees a unit that is on its third day showing clinical signs and has not been detected yet. ADSM will look up the probability of detection on the chart (figure 2). It will then use its random number generator, “roll the dice”, to decide whether the unit gets detected today.

Figure 2: Looking up the probability of detection for a unit on its third day showing clinical signs.

So, given the way ADSM uses this chart, there is a 50% chance that a unit will be detected on the first day it shows clinical signs. If it is not detected on its first day clinical, there is another chance for it to be detected on its second day clinical. If it is not detected on its first or second days clinical, there is another chance for it to be detected on its third day clinical. It is clear that the cumulative probability of detection will increase with each additional day (figure 3).

Figure 3: The cumulative probability of detection that results from this ADSM detection chart.

Another way to look at this situation is to ask what proportion of units will be detected on their first day clinical, their second day clinical, and so on. With the given chart, 50% of the units will be detected on their first day clinical. 50% of the remaining units (the ones that weren’t detected on their first day) will be detected on their second day clinical. 50% of the remaining units (the ones that weren’t detected on their first or second day) will be detected on their third day clinical. The resulting days-to-detection histogram is shown in figure 4.

Figure 4: The days-to-detection histogram that results from this ADSM detection chart.

What happens if you treat the ADSM detection chart as though it were a cumulative probability? Figure 5 shows the result. The red line is a cumulative probability of detection (estimated for dairy farms in the UK, data provided by R. Sanson). The green line shows the cumulative probability that you will get if you input the red line as an ADSM detection chart. You can see that the cumulative probability rises more steeply than what was intended.

Figure 5: The result of mistakenly using a cumulative probability as an ADSM detection chart. The cumulative probability that you will get in the simulation will not be what you intended.