Safety analyses sampling variation

NMR is an incredibly versatile tool that can be used for a wide array of applications, including determination of molecular structure, monitoring of molecular dynamics, chemical analysis, and imaging. NMR has found broad application in the food science and food processing areas (Belton et al., 1993, 1995, 1999 Colquhoun and Goodfellow, 1994 Eads, 1999 Gil et al., 1996 Hills, 1998 O Brien, 1992 Schmidt et al., 1996 Webb et al., 1995, 2001). The ability of NMR to quantify food properties and their spatiotemporal variation in a nondestructive, noninvasive manner is especially useful. In turn, these properties can then be related to the safety, stability, and quality of a food (Eads, 1999). Because food materials are transparent to the radio frequency electromagnetic radiation required in an NMR experiment, NMR can be used to probe virtually any type of food sample, from liquids, such as beverages, oils, and broth, to semisolids, such as cheese, mayonnaise, and bread, to solids, such as flour, powdered drink mixes, and potato chips. 

In the UK the Joint Food Science and Safety Group of the Department of Health and the Ministry of Agriculture, Fisheries and Food have published the results of many analyses for chemical contaminants in food carried out under their Food Surveillance Programme. In many cases the raw data from these surveys are available for analysis. Table 2.1 lists the results of analyses for lead in some samples of cow, sheep and pig kidney obtained in Scotland and England.5 There are clear differences between species and some evidence of differences between sampling locations. What is not clear is the extent to which the variability observed is due to real and consistent differences between species and location or to normal biological variation. 

The results of analysis were compared with the limits specified in the Commission Regulation (Joint MAFF and Department of Health Food Safety and Standards Group, 1999a,b). For the purposes of the survey, and in line with the usual practice followed by UK enforcement authorities, where samples were found to lie outside the statutory limits, an additional tolerance was added to take account of potential variations in the analytical methodology. The Commission Regulation makes it clear that an oil may not be considered to fit its description if any one of its characteristics lies outside the limits laid down. On this basis, the majority of the oils analysed were found to be correctly described and only four samples were found to exceed European Commission limits for one or more chemical criteria used to distinguish and authenticate the different grades of olive oil. 

In discussion of meta-analysis, there is often much attention given to the random effects model versus the fixed effects model. Random effects models assume that the true treatment effects of the individual trials represent a random sample from some population. The random effects model estimates the population mean of the treatment effects and accounts for the variation in the observed effects. It is sometimes stated that the fixed effects model assumes that the individual trial effects are constant. However, this is not a necessary assumption. An alternative view is that the fixed effects model estimates the mean of the true treatment effects of the trials in the meta-analysis. Senn (2000) discussed the analogy with center effects in multicenter trials. In safety, random effects models may be problematic because of the need to estimate between-trial effects with sparse data. Additionally, the random effects model is less statistically powerful than the fixed effects model, albeit the hypotheses are different. In the fixed effects model, the variance estimate should account for trial effect differences either through stratification, conditioning, or modeling of fixed effects. 

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