Model dependent method

Given that we in principle can never select a sample of local thick disk stars that is guaranteed to not contain any intervening thin disk stars, I would argue that we should keep the selection schemes as simple and as transparent as possible. In this sense the simplest and most robust selection is based on the kinematics of the stars. This is also the least model dependent method. Of course, should positions be available, i.e. height over the galactic plane, these could, and should, be used. 

Various model-dependent methods for the comparison of two cumulative dissolution data sets have been proposed (21). Usually, these methods involve prior characterization of both profiles by one to three parameters per profile. In some models, these parameters can be interpreted in terms of the kinetics, the shape, and/or the plateau, but in other instances, they have no physical meaning. One issue that requires some attention is that, in cases where more than one parameter is estimated, a multi-variate procedure for the comparison of the parameters must be applied (9,21). 

For formulations not meeting the criterion for very fast release of drug substance, similarity of profiles may be evaluated by model-independent or model-dependent methods as stated in the Guidance for Industry—Dissolution Testing of IR Solid Oral Dosage Forms (1,2). 

I dissolution profiles can also be compared using other model independent or model dependent methods (5). 

To deduce a particle size distribution, the detector response must be deconvoluted by means of a simulation calculation. The scattering particles are assumed to be spherical in shape, and the data are subjected to one of three different computational methods. One system uses the unimodal model-dependent method, which begins with the assumption of a model (such as log normal) for the size distribution. The detector response expected for this distribution is simulated, and then the model parameters are optimized by minimizing the sum of squared deviations from the measured and the simulated detector responses. The model parameters are finally used to modify the originally chosen size distribution, and it is this modified distribution that is presented to the analyst as the final result. 

Figure 15.12. The obtained cross-section pair distribution function p R) as obtained by the indirect Fourier transformation method, where the composition of SDS/DTAB was 80 20. The results almost perfectly correlate with the results obtained by the model-dependent method illustrated in Figure 15.11. (see ref. (32) for further details)...

Experimental data obtained from TG is generally deconvolved to calculate kinetic parameters by either model-independent or model-dependent method. The extent of conversion, a, is extracted from TG data using the following equation. 

Model-dependent method for isothermal experiment Experiments carried out under isothermal conditions are considered to be more reliable than those conducted under non-isothermal conditions because one of the parameters (T) is held constant during each experiment, thereby reducing the number of kinetic parameters that are determined simultaneously by fitting. Methodology adopted for deriving kinetic... 

Model-independent method for non-isothermal experiments Model-dependent methods need prior knowledge of mathematical function of fractional decomposition, f(a) as reported in the literature [45-47]. Iso-conversion method eliminates the need of assumption of a mathematical functional form, f(a) [52-55]. 

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