Use of prediction methods to assess laboratory bias and mean values associated with an interlaboratory study for method validation and/or proficiency testing.

Two methods of prediction of random variables, best predictor (BP) and best linear unbiased predictor (BLUP), are discussed as potential statistical methods to predict laboratory true mean and bias values using the sample laboratory mean (y(i)) from interlaboratory studies. The predictions developed here require that the interlaboratory and/or proficiency study be designed and conducted in a manner consistent with the assumptions of a one-way completely randomized model (CRM). Under the CRM the individual laboratory true mean and bias are not parameters but are defined to be random variables that are unobservable and considered as realized values that cannot be estimated but can be predicted using methods of "prediction." The BP method is applicable when all salient parameters are known, e.g., the consensus true overall mean (mu) and repeatability and reproducibility components (sigma2(r) and sigma2(R)), while the BLUP method is useful when sigma2(r) and sigma2(R) are known, but mu is estimated by the generalized least square estimator. Although the derivations of predictors are obtained by minimizing the mean-square error under the CRM assumptions, the predictors are the expected laboratory true mean and bias given the sample laboratory mean, i.e., conditional expectation.

Variances and uncertainties of the sample laboratory-to-laboratory variance (S(L)2) and standard deviation (S(L)) associated with an interlaboratory study.

The validation process for an analytical method usually employs an interlaboratory study conducted as a balanced completely randomized model involving a specified number of randomly chosen laboratories, each analyzing a specified number of randomly allocated replicates. For such studies, formulas to obtain approximate unbiased estimates of the variance and uncertainty of the sample laboratory-to-laboratory (lab-to-lab) STD (S(L)) have been developed primarily to account for the uncertainty of S(L) when there is a need to develop an uncertainty budget that includes the uncertainty of S(L). For the sake of completeness on this topic, formulas to estimate the variance and uncertainty of the sample lab-to-lab variance (S(L)2) were also developed. In some cases, it was necessary to derive the formulas based on an approximate distribution for S(L)2.

Determination of operating characteristic, retesting, and testing amount probabilities associated with testing for the presence of Salmonella in foods.

The relatively small perceived probability associated with retesting a food for the presence of Salmonella at low levels is often considered as one of the reasons that a confirmatory or check-analysis tends to disagree in practice with the results of an original test. Given a retesting process where a retest is only performed to confirm an original positive Salmonella test, the probability that both the original and retest will test positive for Salmonella has been traditionally determined by some as the product of the probabilities of a positive Salmonella test for the original and retest samples. When examining the probabilities associated with the retesting process, we found that our results disagreed with those based on intuitions apparently held by others concerning how these probabilities should be calculated. For Salmonella testing, operating characteristic values were computed to demonstrate the protections afforded by the Salmonella sampling plans presented in the U.S. Food and Drug Administration's Bacteriological Analytical Manual and to obtain the probability of a positive Salmonella test. The geometric distribution was examined for possible utility in determining the probabilities associated with testing amounts, i.e., the number of Salmonella tests needed to obtain a positive test.

Determination of a two-tailed 100(1-alpha)% upper limit on the relative error in the laboratory-to-laboratory standard deviation obtained from an interlaboratory study.

For some classes of analytical methods, it is assumed that the error in the laboratory-to-laboratory standard deviation (S(L)) is appreciable. To demonstrate the magnitude of this error in S(L) for such methods, formulas were derived to obtain a two-tailed 100(1-alpha)% upper limit on the relative error in S(L) obtained from an interlaboratory study, assuming that the laboratory-to-laboratory variance (S(L)2) obtained in the validation of an analytical method is approximately normal and/or Chi-square distributed. This 100(1-alpha)% upper limit (delta(1-alpha/2)) is referred to as a margin of relative error in S(L) (MRE(S(L. Monte Carlo simulations were performed, and the results compared satisfactorily with the formula calculations. To aid in designing future interlaboratory studies in which concern is focused on the magnitude of the uncertainty in S(L), expressed as a proportion of the true value (sigma L), a formula was derived to determine the number of laboratories needed to attain a given MRE in S(L) for a stated number of replicates per laboratory.

On using a normal approximation for the noncentral t-distribution in determining upper limits for future sample relative repeatability and reproducibility standard deviations.

Formulas, based on a normal approximation for the noncentral t-distribution, were developed to compute 100p% one-tailed upper limits for future sample relative repeatability and relative reproducibility standard deviations (RSDr,% and RSDR,%) collaboratively obtained under a completely randomized model. The accuracy of the formulas for obtaining a one-tailed upper limit for the future sample RSDr,% was assessed by comparing the computed noncentral t-distribution-based upper limits with the one-tailed upper limits based on a normal approximation for the noncentral t-distribution. The accuracy of the normal approximation formula for obtaining a one-tailed upper limit for a future sample RSDR,% was assessed by comparing the formula-based one-tailed upper limits with those obtained in a Monte Carlo simulation study.

Uncertainties of method performance statistics based on a balanced completely randomized model interlaboratory study.

Using exact and asymptotic distributions, formulas were developed to derive population variances and uncertainties, and their corresponding unbiased estimates, for the method performance statistics, i.e., the sample mean (y..), the repeatability variance and standard deviation and (s2r and sr), and the reproducibility variance and standard deviation (s2R and sR) and obtained from collaborative study of an analytical method.

On using an approximate noncentral t-distribution in determining a one-side upper limit for future sample relative reproducibility standard deviations.

For future sample relative reproducibility standard deviations (RSD(R)), collaboratively obtained under a completely randomized model (CRM), a new formula for determining a one-tailed 100p% upper limit (kappap) for such RSD(R) values was developed based on an approximate noncentral t-distribution with degrees of freedom obtained using Satterthwaite's adjustment. The accuracy of kappap was assessed by comparing kappap and its probability levels with similar values associated with a Monte Carlo simulation and with those obtained using another formula (gammap) that was developed for the same purpose but based on a normal approximation.

Exact one-tailed 100p% upper limits for future sample repeatability relative standard deviations obtained in single- and multilaboratory repeatability studies.

Formulas are derived to obtain exact one-tailed 100p% upper limits (kappa(p) and nu(p)) for future sample repeatability relative standard deviations, based on a noncentral t-distribution, for multi- and single-laboratory repeatability studies, respectively, used in the validation of analytical methods.

Determining a one-tailed upper limit for future sample relative reproducibility standard deviations.

A formula was developed to determine a one-tailed 100p% upper limit for future sample percent relative reproducibility standard deviations (RSD(R),%= 100s(R)/y), where S(R) is the sample reproducibility standard deviation, which is the square root of a linear combination of the sample repeatability variance (s(r)2) plus the sample laboratory-to-laboratory variance (s(L)2), i.e., S(R) = s(L)2, and y is the sample mean. The future RSD(R),% is expected to arise from a population of potential RSD(R),% values whose true mean is zeta(R),% = 100sigmaR, where sigmaR and mu are the population reproducibility standard deviation and mean, respectively.

On determining a 1-tailed upper limit for future sample HorRat values.

Two formulas were developed for use in computing 1-tailed upper limits for future HorRat values obtained from the collaborative study of materials. One formula is applicable when a future sample HorRat value H [formula: see text] is computed based on a known concentration (e.g., C = spike level and RSD(R) is the sample relative reproducibility standard deviation) and the other formula is applicable when the true concentration (C) is unknown and a future sample HorRat value [formula: see text] is computed using the sample mean (e.g., y, the collaborative study overall mean for an analyte). A Monte Carlo simulation procedure was developed using the Statistical Analysis System (SAS) software to assess the accuracy of the 2 developed formulas. Based on the degree of closeness between the simulated and calculated limits, the formulas for computing upper limits for future sample HorRat values will prove to be useful to Study Directors in determining worst case scenarios concerning a method's reproducibility precision relative to that predicted using the "Horwitz equation". We also define the current empirical HorRat limits as 1-tailed 100p% upper limits to assess the statistical consequence, in a probability sense, of their application as an analytical methods screening tool.

Sample sizes needed for specified margins of relative error in the estimates of the repeatability and reproducibility standard deviations.

Sample size formulas are developed to estimate the repeatability and reproducibility standard deviations (Sr and S(R)) such that the actual error in (Sr and S(R)) relative to their respective true values, sigmar and sigmaR, are at predefined levels. The statistical consequences associated with AOAC INTERNATIONAL required sample size to validate an analytical method are discussed. In addition, formulas to estimate the uncertainties of (Sr and S(R)) were derived and are provided as supporting documentation. Formula for the Number of Replicates Required for a Specified Margin of Relative Error in the Estimate of the Repeatability Standard Deviation.

Multi-Laboratory Study of Five Methods for the Determination of Brevetoxins in Shellfish Tissue Extracts.

A thirteen-laboratory comparative study tested the performance of four methods as alternatives to mouse bioassay for the determination of brevetoxins in shellfish. The methods were N2a neuroblastoma cell assay, two variations of the sodium channel receptor binding assay, competitive ELISA, and LC/MS. Three to five laboratories independently performed each method using centrally prepared spiked and naturally incurred test samples. Competitive ELISA and receptor binding (96-well format) compared most favorably with mouse bioassay. Between-laboratory relative standard deviations (RSDR) ranged from 10 to 20% for ELISA and 14 to 31% for receptor binding. Within-laboratory (RSDr) ranged from 6 to 15% for ELISA, and 5 to 31% for receptor binding. Cell assay was extremely sensitive but data variation rendered it unsuitable for statistical treatment. LC/MS performed as well as ELISA on spiked test samples but was inordinately affected by lack of toxin-metabolite standards, uniform instrumental parameters, or both, on incurred test samples. The ELISA and receptor binding assay are good alternatives to mouse bioassay for the determination of brevetoxins in shellfish.

Landau-Kleffner Syndrome: Localization of Epileptogenic Lesion Using Wavelet- Cross-Correlation Analysis.

Magnetoencephalographic findings in a 6-year-old patient suffering from acquired aphasia with convulsive disorder (Landau-Kleffner Syndrome, LKS) are presented. The data were analyzed using wavelet-cross-correlation analysis, a nonstationary analysis method developed to analyze the localization of an epileptogenic lesion and the propagation of epileptiform discharges. The results indicate that LKS might be a disorder of the primary temporal cortex, and that the auditory neural network may function as the circuit for the epileptic discharge propagation.