Matrix-matched calibration

Matrix-matched calibration estimates the response–amount relationship using standards whose sample matrix reproduces relevant measurement conditions of the unknown samples. Matching is intended to control an analytical matrix effect, rather than merely to make a standard look similar. A calibration is a relationship under given conditions; transferring it requires those conditions to remain appropriate.^[ref]

For an original local model, let the sample response be $y=b_M+s_{M}c$. Standards in a matching matrix estimate $b_M$ and $s_M$, giving $\hat{c}=(y-b_M)/s_M$. Choose $b_M=3$, $s_M=1.2$ and true $c=10$, hence $y=15$. The matched calibration gives10. A neat-reference model with $b_0=1$, $s_0=2.5$ instead gives $(15-1)/2.5=5.6$.

A partial match can still fail. If the actual sample slope is $1.5$ while its offset remains3, the same true $c=10$ now gives $y=18$. Applying the nominal matrix-matched slope $1.2$ gives $(18-3)/1.2=12.5$, a25% overestimate. The name of the calibration method is not evidence that all samples share one slope.

Where standards enter the workflow matters. Standards prepared before extraction can incorporate preparation loss into their response–amount relationship. Standards added after preparation primarily characterize the final-extract response. Applying an additional recovery correction to a calibration that already incorporates the same loss can double-count it.

A suitable analyte-free matrix may be unavailable. A surrogate sample matrix can then be evaluated, but similarity must be tested rather than assumed. An analytical blank constrains particular background contributions, and an internal standard can compensate only for response changes it follows appropriately. Assess matching across the intended sample types, analyte levels and preparation conditions.