A semiparametric method for describing noisy population pharmacokinetic data.

We propose a semiparametric method to estimate model-independent pharmacokinetic (PK) measures such as area under concentration-time, peak concentration and time to peak concentration (Tpeak), for noisy population PK data from a sparsely sampled prospectively designed trial. The method is developed within the mixed-effect model framework, for the single-dose and steady-state case. We describe individual concentration vs. time using a longitudinal spline, consisting of a template spline, common to all individuals, and an individual-specific distortion spline accounting for individual differences. We impose a number of constraints on the longitudinal spline, including (i) it has a decreasing tail, (ii) its typical Tpeak is near the modal Tpeak observed in the population data, and (iii) its value is zero at time zero (single dose), or the same nonzero value at the beginning and end of a dosing interval (steady state). We test our method using simulated data and compare its performance to that of a parametric and a nonparametric method. An actual data example is also shown. The performance of the method is as good or better than that of a standard nonparametric method, and when the analysis model is misspecified, the method is superior to a standard parametric one. Since it is often not apparent that an analysis model is correct, we propose this approach as a general method for analysis.