Distributions, selection likelihood-ratio test

The selection of the appropriate population pharmacokinetic base model was guided by the following criteria a significant reduction in the objective function value (p < 0.01,6.64 points) as assessed by the Likelihood Ratio Test the Akaike Information Criterion (AIC) a decrease in the residual error a decrease in the standard error of the model parameters randomness of the distribution of individual weighted residuals versus the predicted concentration and versus time post start of cetuximab administration randomness of the distribution of the observed concentration versus individual predicted concentration values around the line of identity in a respective plot. 

A common form of model selection is to maximize the likelihood that the data arose under the model. For non-Bayesian analysis this is the basis of the likelihood ratio test, where the difference of two -2LL (where LL denotes the log-Ukelihood) for nested models is assumed to be approximately asymptotically chi-squared distributed. A Bayesian approach— see also the Schwarz criterion (36)—is based on computation of the Bayesian information criterion (BIC), which minimizes the KuUback-Leibler KL) information (37). The KL information relates to the ratio of the distribution of the data given the model and parameters to the underlying true distribution of the data. The similarity of the KL information expression (Eq. (5.24)) and Bayes s formula (Eq. (5.1)) is easily seen ... 

Model selection is based on the likelihood ratio test with p < 0.001 and diagnostic plots. The difference in minus twice the log of the likelihood -ILL) between a fuU and a reduced model is asymptotically distributed with degrees of freedom equal to the difference in the number of parameters between two models. At p < 0.001, a decrease of more than 6.6 in -ILL is significant. Asymptotic standard errors are obtained from the asymptotic covariance matrix. Alternatively, confidence intervals on parameters can be computed for this very nonlinear situation from the likelihood profile plot (24). 

The selection of the structural PK model and residual error models was based on the goodness-of-fit plots and on the difference in NONMEM objective function (approximately -2 x log likelihood) between hierarchical models (i.e., the likelihood ratio test). This difference is asymptomatically distributed with a degree of freedom equal to the number of additional parameters of the full compared to the reduced model. A p-value of 0.05 was chosen for one additional parameter, corresponding to a difference in the objective function of 3.84. Potential covariates were selected by univariate analysis, testing the addition of each covariate on each of the relevant PK parameters. When a set of covariates, identified by the... 

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