The question
A validation report sets the limit of quantitation for a 0.01% population based on replicate precision at a convenient acquisition depth. Can a rare-event LOQ be set without accounting for how many events were actually counted?
The analysis
Counting rare events is a Poisson process. The coefficient of variation from counting alone is 1 divided by the square root of the number of rare events counted, before any instrument or analyst variability is added. That puts a floor under precision that no amount of method optimization can lower.
| Population frequency | Total events for 20% CV (25 rare events) | Total events for 35% CV |
|---|---|---|
| 1% | 2,500 | 817 |
| 0.1% | 25,000 | 8,164 |
| 0.01% | 250,000 | 81,633 |
| 0.001% | 2,500,000 | 816,327 |
| Total events | Expected rare events | Theoretical CV | Observed CV, 6 replicates |
|---|---|---|---|
| 100,000 | 10 | 31.6% | 37.8% |
| 250,000 | 25 | 20.0% | 15.2% |
| 500,000 | 50 | 14.1% | 11.6% |
| 1,000,000 | 100 | 10.0% | 6.2% |
Why it matters. At 100,000 events a 0.01% population yields about ten cells, and replicate results scatter widely around the true value. The LOQ is a property of the acquisition depth as much as of the assay, so it has to be stated as a minimum number of events acquired.
What to do
- Define the LOQ as a minimum count of rare events (for example, 25 for 20% CV), and derive the required total events from the lowest frequency that must be reported.
- Build the minimum acquisition into the method and make the result non-reportable when it is not met.
- Confirm with replicate data at the claimed LOQ that observed CV matches or exceeds the counting floor.
How it was done
Theoretical curves from Poisson statistics; replicates simulated as Poisson draws for a 0.01% population at four acquisition depths. Download the data (CSV).