D. Kratzer, R. Littell
Apr 30, 2006
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Abstract
Kratzer and Ash(1996) presented Experimentation Science as a process to accomplish the Scientific Method with a complete protocol including relevant statistical design and analyses The first principal to sound Experimentation Science is the principle of Relevance. This is a case study primarily of Relevance in Experimentation Science. In our consulting work we found a so called “performance” design as not relevant because of the use of null hypothesis testing to promote a concept of equivalence. The best alternative involves equivalence testing, more replication and representative-ness. Secondly we found a dose response design for two products where non-linear asymptotic regression is misused in applying Bioassay techniques to estimate a single relative biological efficacy (RBV) because the basic assumption of sameness of mathematical form does not hold. We offer a relevant model which involves predicted differences in the relevant zone of commercial use (VazquezAñón, M et al, 2006b, GonzalesEsquerra et al, 2007). Introduction There are two primary product forms of supplemental L-methionine (L-met) activity commercially available for supplementation of Met deficient diets; DL-2-hydroxy-4-(methylthio) butanoic acid (HMTBa) most commonly available as an 88% solution with 12% water (ALIMET® feed supplement, registered trademark of Novus International, Inc, St. Louis, MO; Rhodimet AT-88®, registered trademark of Adisseo, Paris, France; Sumimet-L®, registered trademark of Sumitomo Chemical, Tokoyo, Japan), and dry DL-methionine, (DLM, 99% powder). While these compounds both provide L-met activity to avian and mammalian species alike, they are chemically different in that HMTBa has a hydroxyl group at the asymmetric carbon whereas DLM has an amino group. Clearly, HMTBa is not an amino acid as presented to the animal and not a nutrient, but a nutrient precursor. This results in a substantial number of metabolic differences between these products once they are made available for absorption in the gastrointestinal tract of the animal (Dibner, 2003, Lobley et al, 2005, Wester et al., 2005). These compounds have been commercially available and used in animal production systems for over 50 years; however, there remains controversy and confusion with respect to the relative bioavailability value of HMTBa and DLM (i.e. bioavailability of a nutrient in relation to a response obtained with a standard reference material with known bioavailability or relative bioavailability value; RBV). This situation is fueled by continued publication of individual product comparisons in relatively small experiments as well as compilations i.e. “desk studies” of published results with apparently conflicting conclusions (Jansman et al. 2003; Vazquez-Anon et al, 2006a). Experimental Designs (65% design) Conference On Applied Statistics In Agriculture 67 Conference on Applied Statistics in Agriculture Kansas State University New Prairie Press https://newprairiepress.org/agstatconference/2006/proceedings/6 One experimental design called the “performance or 65%” design has been used to compare responses to HMTBa in its commercial form and DLM on a product basis without accounting for the12% water contained in the product. A variety of these types of comparisons between HMTBa and DLM have been previously described (Peak et al, 2002). It appears that this approach was initially based on the fact that HMTBa in commercial form contained 65% to 69 % HMTBa monomer, with 16% to 18% HMTBa dimer and 2 to 3% HMTBa trimer while DLM is 99% monomer. These ester linkages between HMTBa molecules are the result of reducing the water content to 12% in the commercial form of HMTBa liquid and like normal fatty acid esters, have been shown to be hydrolyzed in the intestine to monomer and available for use as a methionine source (Martin-Venegas et al, 2006). Regardless of its origin, the 65% design is constructed using a ratio of 65% DLM (DLM65) to 100% of 88% HMTBa and 12% water (ALIMET100). The stated objective is to demonstrate DLM65 is equivalent to ALIMET100. Diets are formulated with this assumption and if the results show no difference in ALIMET100 versus DLM65 then it is concluded that the product Alimet must be 65% of the product DLM. For example: Alimet is added at 0.326% of diet which results in 0.88*0.326% = 0.286 % added methionine for ALIMET100. DLM is added at 0.65*0.326 =0.212% which results in 0.99*0.212% = 0.21% added methionine for DLM65. Figure 1 shows where to expect the responses of these two groups in commercial broiler performance. There are two main talking points that can be addressed when faced with this trial. First the objective to demonstrate equivalence is not relevant in a test for difference. Second, in practical industry diets at one location with limited replication of experimental units, there is probably not enough power to show a statistically detectable difference for ALIMET100 versus formulating DLM65, especially if the Alimet100 group results in an over supplementation on the plateau. This bias may be further exaggerated if the dose response curves are more quadratic than asymptotic as suggested by Vasquez-Anon et al (2006) and ALIMET100 occurs on the downward portion of a quadratic response curve. Statements from these 65% designs such as “no significant difference p > .05” provides no evidence for equivalence and this statement is easily misinterpreted as being the power of the test rather than the failure of the experiment to distinguish between the two groups. The Journal of Animal Science, Journal of Dairy Science (2006) Guidelines and the FDA Global Harmonization of Statistical Principles (1997) reiterate the fallacy of such statements. A clearer interpretation of the 65% experiment would be reflected by presenting confidence intervals on the differences or Least Significant Differences to indicate the lack of precision of such studies. Experimental Designs (Dose Response Designs) Another experimental design used to compare these two forms of MET is a factorial arrangement of 2 sources (Alimet and DLM) by n doses. Usually n equals 3 or more added levels starting with zero up to adequate nutritional levels. They usually have one or more nutritionally deficient, commercially irrelevant levels, which have been justified as necessary to show significant differences using a non-linear common plateau asymptotic regression (NLCPAR) model to compare the two Met sources i.e. they add irrelevant treatment groups to conform to a model. The longstanding controversy with respect to HMTBA and DLM efficacy is due at least in part to the misapplication of bioassay methodology for estimation of a single RBV with the NLCPAR model. The validity of approach is predicated on certain specific assumptions. In this case, 68 Kansas State University Conference on Applied Statistics in Agriculture Kansas State University New Prairie Press https://newprairiepress.org/agstatconference/2006/proceedings/6 Finney (1978) defined the technique as the comparison of a standard product ‘S’ to a test dilution ‘T’. The implicit assumption in nutritional studies is that the active compounds being compared are the same and that in the case of the two Met sources, DLM was considered the standard product ‘S’ and HMTBA the test dilution ‘T’. Littell et al. (1997) indicated that to be a valid comparison S and T must have the same mathematical form of dose response. Finney (1978) describes this further by stating that: “even a small discrepancy between the forms of the two curves would prove invalidity” and “in particular, if the S response curve asymptotically approaches a limiting value, that T must have the same asymptote”. In other words, for a valid comparison of HMTBA and DLM using Finney’s relative potency methodology, one product must function as a dilution of the other. That is, there is a dilution factor k such that the mean response to a dose ‘x’ of the standard product is the same as the mean response to a dose ‘kx’ of the test product. The value of k is the potency of the test product relative to the standard product. More technically, if f(x) and g(x) are the response curves for products S and T, respectively, then for any dose x, f(x) = g(kx). This condition is impossible unless the two response curves have the same asymptote. Before properly applying the NLCPAR bioassay method, some effort must be made to test the validity of the model’s basic assumptions. It appears that such tests of assumptions have not routinely been examined. A recently prepared meta-analysis sought to resolve the Met source RBV controversy for poultry and swine and employed the NLCPAR methodology as a primary means of evaluating published Met source comparisons (Jansman et al, 2003). Indeed, no reference was made to the basic assumptions of the model when the authors reported relative HMTBA:DLM efficacy estimates of 77%, 82% 83% and 83-101% for broilers, pigs, layers and turkeys respectively. These single values were based on averages across several studies to which the authors applied either NLCPAR models or linear models depending on set criterion. The report indicated that of the approximately 132 broiler citations surveyed (representing the majority of published data comparing these two compounds) 17 experiments fit the selection criteria for inclusion in the compilation with respect to BWG response to the two Met sources. Of those 17 citations, four studies were not appropriate for nonlinear analyses since the response curves showed no curvature, probably due to the low levels of supplementation used in those experimental designs. The remaining 13 broiler studies with curvature were used to evaluate validity of the basic assumptions required for application of the NLCPAR method. Each of these experimental designs had at least three non-zero supplemented doses of the Met sources and an un-supplemented control and all had suboptimal doses of both HMTBA and DLM. In order to t