Extended least squares curve fitting: A comparison of SIPHAR and MKMODEL

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Abstract
SIPHAR and MKMODEL in their extended least squares modes have been compared when fitting a triexponential declining function to simulated data. The data were simulated on SAS incorporating normally distributed random error, having coefficients of variation (CV) of 5, 10, 15, and 25 per cent. At each error level 100 data sets, consisting of 21 data pairs, were simulated. Non‐parametric tests were used to compare the accuracy and precision of the estimates produced by the packages. The comparison was repeated with two different sets of exponent values incorporating error at the 15 per cent level. MKMODEL was also compared to ELSFIT and ELSMOS at the same error level. SIPHAR was consistently less accurate and less precise than MKMODEL in estimating the structural model parameters. SIPHAR was also sensitive to the concentration units used for the input data. Estimates of the variance model power produced by SIPHAR were very variable while those from MKMODEL covered a much tighter range. For both packages there was generally a linear increase in the CV on each mean parameter estimate with increase in the CV on the error model. Good agreement was observed between MKMODEL, ELSFIT, and ELSMOS. The presence of an additive constant in the variance model used in SIPHAR was shown to be responsible for its poorer accuracy and precision.