Theory Based on Monte Carlo Simulation

Sheiner and Beal (1983) presented the first study on the role of experimental design in one of their seminal papers on nonlinear mixed effects models. They showed that increasing the number of subjects improves parameter estimation accuracy, but that increasing the number of samples per subject subjects does not improve estimation to the same degree when the data were simulated from a 1-compartment model. Hence, it is better to have sparse data from more subjects than intensive pharmacokinetic data with fewer subjects. They also showed that relatively accurate and precise parameter estimates (except for residual variance) can be obtained using FO-approximation with as few as 50 subjects having a single sample collected per subject. Keep in mind, however, this was a very simple pharmacokinetic model with only two estimable parameters. 

Acceptable bias and precision in the structural model parameters were observed with two samples per subject across any two time points. However, better precision and accuracy in estimating clearance was obtained when the second sample was collected at later times. Volume of distribution was not as affected by the choice of sample times. Across all time points, the variance components were often significantly underestimated with the range of estimates being quite large. 

When the number of samples per individual was increased to three, regardless of where the middle point was collected in time, the structural model parameters remained unbiased but the bias in the variance components was removed. When the number of subjects was increased to 100 and then 150, the bias and precision in the structural model parameters remained unchanged, but improved the estimation of the variance components. Hence, under these conditions, neither more data per subject nor more subjects improved the estimates of the fixed effects in the model. What were affected were the variance components. Both more data within a subject and more subjects resulted in better variance component estimation. 

Breant et al. (1996) followed up the work of Al-Banna, Kelman, and Whiting and used Monte Carlo simulation to determine the number of subjects and samples per subject needed to obtain accurate and precise parameter estimates with a drug that showed monoexponential disposition kinetics. They found that for a 1-compartment model, concentration data from 15 to 20 subjects with two samples per subject produced reasonable parameter estimates. Although the authors did not use NONMEM, their results should be applicable to NONMEM analyses. 

Jonsson, Wade, and Karlsson (1996) used Monte Carlo simulation to examine the consequences of collecting two samples per visit instead of one per visit when the drug followed a 1-compartment model with first- 

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