Population one-compartment pharmacokinetic analysis with missing dosage data.

OBJECTIVE: Our objective was to develop a population 1-compartment pharmacokinetic (PK) method of analysis to deal with suspect or missing prior dosage history. METHODS: Population PK data from a 1-compartment model with first-order elimination and absorption, described by PK parameters clearance, volume of distribution, and absorption rate constant, are simulated. A PK sample is drawn just before a test dose (Dt), followed by a (varying) number of additional samples over 1 interdose interval (tau). For 60% of the subjects, the true history of the scheduled dose (Ds) preceding Dt differs from that prescribed, whereas doses taken before Ds do not. Two settings are evaluated: considerable accumulation of drug in the body (typical drug half-life t1/2 approximately equal to tau) and very little such accumulation (t1/2 approximately equal to tau/5). Precision and bias of several PK analysis methods--Missing Dose Method (MDM), Missing Dose Mixture Method (MDMM) and Extrapolation-Subtraction Method (ESM), all of which essentially do not use prior dose history--are compared with those of the Prescribed Dose Method (PDM), which assumes nominal dosage, and an Ideal Method (IDM), which uses true (but unknown) pre-test dose history. RESULTS: At t1/2 approximately equal to tau, MDM and MDMM are the most precise methods. The accuracy of ESM and PDM is poor. At t1/2 approximately equal to tau/5, no significant differences, in terms of precision or bias, are observed between methods. Misspecification of the structural or statistical model seems not to influence these results. The results of analysis of a real (caffeine) data set are compatible with the findings from the simulations. CONCLUSION: When a test dose is given and a predose baseline observation is taken as part of an "intensive" PK study during outpatient therapy of a 1-compartment drug, an analysis that assumes that the nominal dose history is correct is not robust to past dosage history misspecification, whereas methods that do not do this are robust and reliable.

Mixed effects modeling of weight change associated with placebo and pregabalin administration.

OBJECTIVE: To characterize change from baseline weight over time for pregabalin and placebo administration. METHODS: Asymptotic fraction of baseline weight was modeled with a nonmixture model and a mixture model as a function of baseline weight, exposure, time, covariate effects, and subject-specific random effects. Model fit was assessed using standard diagnostic plots. Predictive performance was assessed using both data similar to the original data, and open-label data. RESULTS: The nonmixture model indicated that a typical patient (baseline weight 82 kg) receiving placebo or 300 mg/day pregabalin approached an asymptotic fractional change from baseline weight of [mean (95% prediction interval for typical individual)] 0.7% (-5.5% to 7.4%) or 2.5% (-3.8% to 9.1%), respectively, with a half-life of 17 days. Substantial between-subject variability is observed, with some drug-treated subjects remaining weight neutral or losing weight, at all levels of exposure. Structural fixed effects parameters for the two submodels (mixture model) were in close agreement with each other and with those for the nonmixture model. The mixture model described two subpopulations differing in interindividual variability. No significant interindividual-varying covariates influencing the mixture probabilities were identified other than exposure. Both models had adequate fit; both models performed well during external validation. Predictive performance (nonmixture model) was adequate to ~900 days. CONCLUSIONS: The weight of a typical 82-kg patient receiving placebo or pregabalin (300 mg/day) approaches an asymptotic fractional change from baseline weight of 0.7%, or 2.5%, respectively, with a half-life of 17 days. Substantial between-subject variability remains unexplained.

Conditioning on certain random events associated with statistical variability in PK/PD.

In PK/PD data analysis, statistical models involving random variables are developed. At times an analysis can be carried out by conditioning on certain random events involving these variables. This paper attempts to clarify issues regarding conditioning. In particular, conditioning is examined as it relates to a number of disparate practical matters: missing covariate values, dose titration, BQL data, "no change from baseline" data, and the use of a truncated intraindividual probability distribution for PK observations.

Use of prior information to stabilize a population data analysis.

When modeling new data with a complex population pharmacokinetic/pharmacodynamic model, there may not be sufficient information to obtain estimates of all parameters. In this case information from previous studies can also be used to help stabilize estimation. Using simulated data, we explored three different ways to do this. (i) Some parameter values were fixed to estimates obtained from earlier data. (ii) The earlier data were combined with the current data. (iii) The objective function based on the current data was augmented by a penalty function expressing summary information obtained from the earlier data. This last method is similar to the use of a Bayesian prior. It may be particularly useful when either the combined data set of method (ii) is very large and leads to large computation times or when the early data are not readily available. With this method, two different types of penalty functions were used. With our examples, the three methods all resulted in stabilized estimation. Methods (ii) and (iii) gave similar results for parameter and standard error estimation, especially with respect to fixed effects parameters. For hypothesis testing, results obtained with method (i) are very problematic. There are also problems with the results obtained with method (iii), but they are much less severe, and when the design for the earlier data is known, they can be corrected by using a computer-intensive simulation test procedure.

Simultaneous vs. sequential analysis for population PK/PD data I: best-case performance.

Dose [-concentration]-effect relationships can be obtained by fitting a predictive pharmacokinetic (PK)-pharmacodynamic (PD) model to both concentration and effect observations. Either a model can befit simultaneously to all the data ("simultaneous" method), or first a model can befit to the PK data and then a model can be fit to the PD data, conditioning in some way on the PK data or on the estimates of the PK parameters ("sequential" method). Using simulated data, we compare the performance of the simultaneous method with that of three sequential method variants with respect to computation time, estimation precision, and inference. Using NONMEM, under various study designs, observations of one type of PK and one type of PD response from different numbers of individuals were simulated according to a one-compartment PK model and direct Emax PD model, with parameters drawn from an appropriate population distribution. The same PK and PD models were fit to these observations using simultaneous and sequential methods. Performance measures include computation time,fraction of cases for which estimates are successfully obtained, precision of PD parameter estimates, precision of PD parameter standard error estimates, and type-I error rates of a likelihood ratio test. With the sequential method, computation time is less, and estimates are more likely to be obtained. Using the First Order Conditional Estimation (FOCE) method, a sequential approach that conditions on both population PK parameter estimates and PK data, estimates PD parameters and their standard errors about as well as the "gold standard" simultaneous method, and saves about 40% computation time. Type-I error rates of likelihood ratio test for both simultaneous and sequential approaches are close to the nominal rates.

Simultaneous vs. sequential analysis for population PK/PD data II: robustness of methods.

A model can be fit to joint PK/PD data (concentration and effect) either simultaneously or sequentially. The results of a companion paper suggested that when the data-analytic and true models agree, a particular sequential approach is computationally faster than the simultaneous one, yet produces hardly less precise PD parameter estimates, and for suitable designs, about as accurate PD standard error estimates. In this paper, we compare the performance of various methods for the case that the data-analytic model is misspecified. We illustrate these methods by applying them to a set of real data. Using NONMEM, population PK/PD observations were simulated under various study designs according to a one- or two-compartment PK model and direct Emax or sigmoid Emax model. A one-compartment PK model and Emax PD model were fit to the simulated observations by simultaneous and sequential methods. Predictive performance (interpolation and extrapolation) of PD and the type-I error rate of a likelihood ratio test are compared. The real data set consists of PK and (more frequent) PD observations after administration of the muscle relaxant vecuronium. When only the PK data-analytic model is misspecified, the simultaneous method has greater precision than the sequential methods. However a sequential method that uses a non-parametric PK model performs better than both other methods when PK model misspecification is severe. When the PD data-analytic model is misspecified, sequential and simultaneous methods perform similarly. The analysis of the real data shows that the PK fitted with the simultaneous method can be quite sensitive to PD model misspecification, yielding a possible diagnostic for this type of misspecification.