Abductive statistical methods improve the results of calibration curve bioassays:An example of determining zinc bioavailability in broiler chickens
摘要In this paper,we discuss the theory behind calibration curve experiments and their application to a zinc(Zn)bioavailability study with broiler chickens.Seven replicates of 16 male commercial broiler chicks were fed starter diets for 14 days.Six diets had different levels of a potential Zn source and one was a positive control with standard industry levels of Zn for comparison.Four commonly used methods of calculating bioavailability means and confidence intervals(CI)from a calibration curve(standard curve)experiment to estimate the bioavailability of a new zinc source in broiler chickens were compared.The methods compared were the following:1)the Counter-Intuitive Method uses a multiple-range test to compare unknown test and standard samples;2)the Intuitive Method uses standard linear regression and inverts the equation to predict Zn bioavailability for each replicate of test samples;3)the Abductive Method uses Graybill's Equation,based on theory and observation,to estimate CI's;and 4)the Sophistic Method uses reverse regression,and calculates Zn bioavailability values directly from the equation.The Counter-Intuitive Method only gives information about which standards the test samples are,or are not,significantly different from respectively(average available Zn not predicted).The Intuitive Method ig-nores error about the standard curve and theoretically cannot estimate the CI directly(X±SEM=107.5±15.8 mg Zn/kg).The Sophistic Method underestimates and overestimates the test sample mean values above and below the mean of the standards,respectively(X=96.6 mg Zn/kg).The Abductive Method has an advantage over the other methods:The mean prediction estimation is consistent with theory(107.5±6.1 mg Zn/kg;X±SEM).When test or"unknown"samples are near the mean of the standard samples,the CI is smaller than when near the extremes of the calibration curve.When calibration curve error is small(R2>approximately 0.95),there is little advantage to using the Abductive Method,but when calibration curve error is larger,as in many bioassays with growing ani-mals,the Abductive Method improves the accuracy of the CI calculations.The Abductive Method was used to demonstrate the influence of the number of replicate samples on experimental power and cost.
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