Below the Validated Range: A Client Wants a Number in 48 Hours
A calibration model was validated on 120 samples spanning 10 to 40 units of analyte, with a root-mean-square error of 2.1 percent and no systematic bias. A long-standing client now needs results at 3 units, below the validated range, within 48 hours. Two preliminary runs at 3 units came back 9 and 11 percent above the reference method, and a third came back 4 percent above. The only available low-concentration reference material expires in three days. A colleague suggests applying a proportional correction factor derived from the two discrepant runs so the client gets a number on time. The client contract requires that results falling outside the validated range be flagged.
1. Evaluate the colleague's proposed correction factor.
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Three observations within a 7-point spread, with n of 3 and two of them close together, do not establish a bias that can be corrected. A correction factor fitted to the same three points that motivated it will always appear to work; there is no independent check left. The proposal also assumes the error is proportional and stable across concentration, which is precisely the assumption that fails when extrapolating below a validated range, where the signal approaches the noise floor and the relationship typically becomes nonlinear.
The deeper problem is that a correction factor converts an acknowledged extrapolation into an unacknowledged one. The client would receive a number that looks like a validated result and has none of the support. If the number is later used in a decision, the provenance is gone. Reject the correction, but reject the reasoning rather than the colleague, who is responding to a real deadline pressure.
2. What do you deliver within 48 hours, and how is it labelled?
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Deliver an estimate, not a result, and label it as such on its face. Include the three measured values, the reference-method comparison, and the direction and magnitude of the observed positive offset, stated as an observation on three runs rather than as a bias.
Recommended wording: "Reported values at 3 units fall outside the validated range of 10 to 40 units. The three available measurements were 4 to 11 percent above the reference method. Results below 10 units are indicative only and are not covered by the method's validation. Expanded uncertainty at this level cannot be stated from current data."
Set the expectation explicitly: the model is not shown to be fit below 10 units, and the observed offset is large enough at this concentration that assuming fitness would be indefensible. Give the client the magnitude of the uncertainty you do have, namely the spread, even though you cannot give a formal interval. An honest range beats a false point estimate.
3. Outline the follow-up plan, including how you handle the contract's flagging requirement and the expiring reference material.
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The expiring reference material is the binding constraint, so use it in the next 72 hours: run as many low-level replicates as the material allows, across at least two concentration levels if possible, and preserve whatever remains under conditions that extend its life if the supplier's instructions permit. Record the expiry date and every run against it; data from expired material is not validation data.
Follow-up: prepare fresh low-level standards, extend the validation to 1 to 5 units with sufficient replicates to state an uncertainty, and test explicitly for nonlinearity at the low end rather than assuming proportionality. Until that completes, every result below 10 units is flagged per the contract, on the report itself and not only in a covering email, because the flag must travel with the number when it is forwarded.
Tell the client the flag is a contract term, not a negotiating position, and that the 48-hour delivery is provisional and will be superseded. Recording the limitation in the method file matters as much as telling the client: the next analyst to run a 3-unit sample will see it.