Page 444 - Contributed Paper Session (CPS) - Volume 2

CPS1917 Trijya S.
2 as initial estimates. We have also included the mean absolute percent error
(MAP E) of each method, which is given by

̂
1 |( ) − ( )|

= ∑ × 100.
( )

=1

This measures the predictive power of the method. The estimates of the
asymptotic standard errors of the estimates obtained using the `nls' R package
are also given within parentheses in Table 1.

4. Discussion and Conclusion
Shah (1973) suggested a regression-difference equation method for
obtaining initial parameter estimates needed to start an iterative estimation
procedure in the case of a mixture of exponential distributions. However, this
method is of limited use since it is applicable only to equally spaced data. In
pharmacokinetic analysis, observations are rarely measured at equal intervals.
Our proposed methods are not only applicable to unequally spaced
observations, but have also been shown to yield remarkably lower RSS and
MAPE values compared to Shah's method, as is evident from Table 1.
Moreover, important pharmacokinetic parameters of interest like drug
transfer rates, volume of a drug in a patient's blood stream at time t and
clearance of the drug from the body are all functions of A, B, as
discussed in Appleton (1995). Hence, these parameters need to be estimated
with as much precision as possible. A close examination of the RSS and MAPE
values in Table 1 also reveals that although initial estimates obtained by all
methods give convergence to same optimum values, the performance of the
method incorporating information regarding tail behavior (that is, method 2)
is better. The initial estimates of parameters obtained using method 2 are, in
general, closer to the optimum values compared to those obtained by Shah's
method or method 1 and, as such, convergence is attained in a much smaller
number of iterations for method 2.
An undesirable feature which has been noticed in the findings is that the
fitted values corresponding to the first time point are negative for Shah's
method and method 1. This is another reason that method 2 should be used
in preference to method 1 or Shah's method in order to obtain initial
estimates.

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