Error-in-variables nonlinear regression

The same caveats that apply to linear models when the predictor variables are measured with error apply to nonlinear models. When the predictor variables are measured with error, the parameter estimates may become biased, depending on the nonlinear model. Simulation may be used as a quick test to examine the dependency of parameter estimates within a particular model on measurement error (Fig. 3.14). The SIMEX algorithm, as introduced in the chapter on Linear Models and Regression, can easily be extended to nonlinear models, although the computation time will increase by orders of magnitude. 

Often in pharmacokinetics the analyst has data on more than one individual. In a typical Phase 1 clinical trial, there might 12-18 subjects who have pharmacokinetic data collected. Applying a compartmental model to each individual s data generates a vector of parameter estimates, each row of which represents a realization from some probability distribution. For example, 

Given a vector of parameter estimates, 0 = 1, 2. 0n, one estimator for the population mean (0) is the arithmetic mean, which is calculated using the well-known equation 

However, most pharmacokinetic parameters tend to be skewed in a log-normal manner since their lower bound 

the geometric mean is the exponentiated arithmetic mean of the log-transformed values. Once the mean is calculated, an estimate of the variance of the parameter ft is usually estimated by 

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