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14 changes: 10 additions & 4 deletions docs/api/covidcast-signals/quidel.md
Original file line number Diff line number Diff line change
Expand Up @@ -63,19 +63,25 @@ We estimate p across 3 temporal-spatial aggregation schemes:

**MSA and HRR levels**: In a given MSA or HRR, suppose $$N$$ COVID tests are taken
in a certain time period, $$X$$ is the number of tests taken with positive
results. If $$N \geq 50$$, we simply use:
results.

For raw signals:
- if $$N \geq 50$$, we simply use:

$$
p = \frac{100 X}{N}
$$

If $$N < 50$$, we lend $$50 - N$$ fake samples from its home state to shrink the
For smoothed signals, before taking the temporal pooling average,
- if $$N \geq 50$$, we also use:
$$
p = \frac{100 X}{N}
$$
- if $$25 \leq N < 50$$, we lend $$50 - N$$ fake samples from its home state to shrink the
estimate to the state's mean, which means:

$$
p = 100 \left( \frac{N}{50} \frac{X}{N} + \frac{50 - N}{50} \frac{X_s}{N_s} \right)
$$

where $$N_s, X_s$$ are the number of COVID tests and the number of COVID tests
taken with positive results taken in its home state in the same time period.

Expand Down