In the industries that involved either chemistry or biology, such as pharmaceutical industries, chemical industries or food industry, the analytical methods are the necessary eyes and hear of all the material produced or used. If the quality of an analytical method is doubtful, then the whole set of decision that will be based on those measures is questionable. For those reasons, being able to assess the quality of an analytical method is far more than a statistical challenge; it's a matter of ethic and good business practices. Many regulatory documents have been releases, primarily ICH and FDA documents in the pharmaceutical industry (FDA, 1995, 1997, 2001) to address that issue.
Deep Dive into Risk management for analytical methods: conciliating objectives of methods, validation phase and routine decision rules.
In the industries that involved either chemistry or biology, such as pharmaceutical industries, chemical industries or food industry, the analytical methods are the necessary eyes and hear of all the material produced or used. If the quality of an analytical method is doubtful, then the whole set of decision that will be based on those measures is questionable. For those reasons, being able to assess the quality of an analytical method is far more than a statistical challenge; it’s a matter of ethic and good business practices. Many regulatory documents have been releases, primarily ICH and FDA documents in the pharmaceutical industry (FDA, 1995, 1997, 2001) to address that issue.
In the industries that involved either chemistry or biology, such as pharmaceutical industries, chemical industries or food industry, the analytical methods are the necessary eyes and hear of all the material produced or used. If the quality of an analytical method is doubtful, then the whole set of decision that will be based on those measures is questionable. For those reasons, being able to assess the quality of an analytical method is far more than a statistical challenge; it's a matter of ethic and good business practices. Many regulatory documents have been releases, primarily ICH and FDA documents in the pharmaceutical industry (FDA, 1995(FDA, , 1997(FDA, , 2001) ) to address that issue.
The objective of a good analytical method is to be able to quantify accurately each of the unknown quantities that the laboratory will have to determine. In other terms, what is expected from an analytical method is that the difference between a measurement (x) and the unknown “true value” (µ T ) of the sample be small or inferior to an acceptance limit, i.e.:
Eq. 1 With λ, the acceptance limit, which can be different depending on the requirements of the analyst or the objective of the analytical procedure. The objective is linked to the requirements usually admitted by the practice (e.g. 1% or 2% on bulk, 5% on pharmaceutical specialties, 15% for biological samples, 30% for ligand binding assays suc as RIA or ELISA, etc.). A procedure is acceptable if it is very likely that the difference between each measurement (x) of a sample and its “true value” (µ T ) is inside the acceptance limits [λ,+λ] predefined by the analyst. The notion of “good analytical procedure” with a known risk can translate itself by the following equation (Boulanger et al. 2000a;2000b):
With β the probability a measure will fall inside the acceptance limits. All analytical methods can be characterized by a “true bias” µ M (systematic error), and a “true precision " σ M (random error). If the “true bias” µ M and a “true precision " σ M are known, then assuming the measurements follow a normal distribution, the probability in Eq. 2 is easy to obtain using the normal distribution classically. This lead to define the Acceptance Region, i.e. the set of (µ M ,σ M ) such that the probability of Eq. 2 is greater than β . Figure 1 shows, inside the curves, the Acceptance Region for various values of β (99%, 95%, 90%, 80% and 66.7%) when acceptance limits are fixed to [-15%,+15%] as recommended by ICH (1995,1997) and FDA (2001) for bioanalytical methods. Logically, as it can be seen on Figure 1, the greater the variance of measure or greater the bias, the less likely a measure will fall within the acceptance limits.
Before an analytical method can be used in routine for qualifying unknown samples, it’s the practice to perform a more or less extensive set of experiments to evaluate if the analytical method will be able to achieve it’s objective as stated above. Those experiments are usually called “pre-study validation” as opposed to the “in-study validation” experiments that required the use of QC samples used in routine and inserted in the unknown samples.
The “true bias” µ M (systematic error), and a “true precision " σ M (random error) are intrinsic properties of all analytical procedures and are unknown. For that reason experiments are required before using the method in routine (pre-study validation) or QC are inserted among the unknown samples (in-study validation) to allow the user to obtain estimates of bias and of precision of the analytical method. These estimates of bias ( M µ ˆ) and variance ( M σˆ) are intermediary but obligatory steps to evaluate if the analytical procedure is likely to provide accurate measure on each of the unknown quantities, i.e. to fulfill it’s objective. Consequently, the objective of the validation phase is to evaluate whether, given the estimates of bias M µ ˆand variance M σˆ, the expected proportion of measures that will fall within the acceptance limits is greater than a predefined level of proportion, say β, as show in Eq. 3:
However there exist no exact solution for Eq. 3. An easy alternative to make a decision as already proposed by other authors (Boulanger et
where the factor k is determined so that the expected proportion of the population falling within the interval is equal to β. If the β-expectation tolerance interval obtained Eq. 4 is totally included within the acceptance limits [-λ,+λ], i.e. if (
then the expected proportion of measurements within the same acceptance limits is greater or equal to β, i.e. Eq. 3 is also verified in that case. Note that the opposite statement is not true, i.e. if either
doesn’t imply that the expected proportion is smaller than β.
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