Assumptions, testing

M. O. Karlsson, E. N. Jonsson, C. G. WUtse, and J. R. Wade, Assumption testing in population pharmacokinetic models illustrated with an analysis of moxonidine data from congestive heart failure patients. J Pharmacokinet Biopharm 26 207-246 (1998). 

The assumptions of the structural model regarding distribution of the random effects should be examined. Most population parameters are modeled assuming the random effects are log-normal. The random effects are assumed to be independent and have a normal distribution with mean 0 and variance co2. These assumptions should be tested. Other assumptions that should be tested include testing the residuals for homoscedasticity, normality, and lack of systematic deviations in the residuals over time. More about assumption testing will be presenting later in the chapter. If the assumptions are violated, remedial measures should be taken. 

Obviously not all assumption tests can be applied at every stage of model development, although many should. At the least, many of these assumptions should be examined once a final covariate submodel or base model is developed. It should also be noted that many of these assumptions are tested by examination of the EBEs. As such, datasets that have few observations per subject will be of less value than datasets with many observations per subject since sparse data tend to produce EBEs that are more model dependent than data dependent. More will be said of the quality of the EBEs later in the chapter. 

Karlsson and Sheiner have provided excellent examples of the varied assumptions that come into play during population pharmacokinetic analysis. The decomposition of the assumptions into common categories and application of assumption testing to actual data sets are important concepts to grasp, and the manuscript itself is an excellent reference. Table 15.4 summarizes the assumptions discussed in Karlsson et al. and lists testing procedures to examine the validity of these assumptions. 

Assumptions and Assumption Testing Options for Population Pharmacokinetic Analyses... 

Hypothesis testing is applicable to all of the above factors. Detection decisions may be made, for example, using the critical level of Student s-t to test for bias, or the critical level of to test an assumed spectral shape or calibration model or error model. For a given measurement design and assumption test procedure, one can estimate the corresponding detection limit for the alternative hypothesis, e.g., the minimum detectable bias. As with analyte detection, the ability to detect erroneous assumptions rests heavily on the design of the experiment and the study of optimal designs is a field unto Itself. 

Based on the results obtained here, it can be seen that, although the model passes all the assumption tests, its predictive capability is not the best. There seems to be some components in the data that is not being reflected in the model. Furthermore, some of the parameter estimate confidence intervals are close to zero, suggesting that those estimates should be excluded from the model. 

To further stress the above-mentioned assumption, tests were performed by adding the nonphosphated purine or the ribose phosphate to the metal-anthocyanin mixture. In both... 

To check this assumption tests were performed that produced the results shown in Figure 14 using the 310,000 polymer at an applied shear rate of y = 0.0533 sec. At the upper end of the temperature scale the stress relaxation curves show the transition as discussed previously with the very long relaxation times at the lower end of the transition region. But as the temperature is further decreased the relaxation times become shorter, and then with a further decrease in temperature the relaxation times begin to increase again. This minimum in the relaxation times as a function of temperature is quite unexpected. 

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