[show abstract][hide abstract] ABSTRACT: We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second-order two-step method with numerical solutions of differential equations (2orderND), and the second-order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear mixed model at the second step. We apply the proposed methods to the analysis of the Ditropan data, and evaluate their performance using a simulation study. Our results show that the 2orderND method performs well, while the 2orderAD method can yield PK parameter estimators that are subject to considerable biases.
[show abstract][hide abstract] ABSTRACT: Medical studies often collect physiological and/or psychological measurements over time from multiple subjects, to study dynamics such as circadian rhythms. Under the assumption that the expected response functions of all subjects are the same after shift and scale transformations, shape-invariant models have been applied to analyze this kind of data. The shift and scale parameters provide efficient and interpretable data summaries, while the common shape function is usually modeled nonparametrically, to provide flexibility. However, due to the deterministic nature of the shift and scale parameters, potential correlations within a subject are ignored. Furthermore, the shape of the common function may depend on other factors, such as disease. In this article, we propose shape-invariant mixed effects models. A second-stage model with fixed and random effects is used to model individual shift and scale parameters. A second-stage smoothing spline ANOVA model is used to study potential covariate effects on the common shape function. We apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol, a hormone that is affected by stress. We find that patients with Cushing's syndrome lost circadian rhythms and their 24-hour means were elevated to very high levels. Patients with major depression had the same circadian shape and phases as normal subjects. However, their 24-hour mean levels were elevated and amplitudes were dampened for some patients.
[show abstract][hide abstract] ABSTRACT: This article is motivated by an application where subjects were dosed three times with the same drug and the drug concentration profiles appeared to be the lowest after the third dose. One possible explanation is that the pharmacokinetic (PK) parameters vary over time. Therefore, we consider population PK models with time-varying PK parameters. These time-varying PK parameters are modeled by natural cubic spline functions in the ordinary differential equations. Mean parameters, variance components, and smoothing parameters are jointly estimated by maximizing the double penalized log likelihood. Mean functions and their derivatives are obtained by the numerical solution of ordinary differential equations. The interpretation of PK parameters in the model and its flexibility are discussed. The proposed methods are illustrated by application to the data that motivated this article. The model's performance is evaluated through simulation.
[show abstract][hide abstract] ABSTRACT: In this paper penalized weighted least-squares is used to jointly estimate nonparametric functions from contemporaneously correlated data. Under condi-tions generally encountered in practice, it is shown that these joint estimates have smaller posterior variances than those of marginal estimates and are therefore more efficient. We describe three methods: generalized maximum likelihood (GML), gen-eralized cross validation (GCV) and leaving-out-one-pair cross validation (CV) to estimate the smoothing parameters, the weighting parameter and the correlation parameter simultaneously. Based on simulations we conclude that the GML method has smaller mean-square errors for the nonparametric functions and the parame-ters and needs less computational time than the other methods. Also, it does not overfit data when the sample size is small. Our research is motivated by and is applied to the problem of estimating associations between hormones. We find that the circadian rhythms of the hormones ACTH and cortisol have similar patterns and that cortisol lags ACTH.
[show abstract][hide abstract] ABSTRACT: Hormones serve as regulating signals for many biological processes. In recent years, it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern, in addition to the absolute concentration level, is important in regulating biological processes. Consequently, it is necessary to characterize the latent secretion patterns from measurements of concentration levels. The characterization is complicated by the presence of a biological circadian rhythm. When hormone concentrations are plotted over time, the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline. This is a result of a mixture of pulsatile secretions and a circadian rhythm. In this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series. A smoothing spline is used to model the baseline, and a multiprocess dynamic linear model is used to model the pulsatile component. An additive structure is assumed, and both components are estimated simultaneously using a multiprocess Kalman filter. The unknown parameters are estimated by approximate maximum likelihood. The locations and amplitudes of the pulses are also estimated as posterior means via the multiprocess Kalman filter. Bayesian confidence intervals can be constructed for the baseline. This approach is found to be robust in simulated data and effective in modeling hormone time series.
Journal of The American Statistical Association - J AMER STATIST ASSN. 01/1999; 94(447):746-756.
[show abstract][hide abstract] ABSTRACT: Interpatient differences in the oral clearance of cyclosporine (INN, ciclosporin) have been partially attributed to variation in the activity of a single liver enzyme termed CYP3A4. Recently it has been shown that small bowel also contains CYP3A4, as well as P-glycoprotein, a protein able to transport cyclosporine. To assess the importance of these intestinal proteins, the oral pharmacokinetics of cyclosporine were measured in 25 kidney transplant recipients who each had their liver CYP3A4 activity quantitated by the intravenous [14C-N-methyl]-erythromycin breath test and who underwent small bowel biopsy for measurement of CYP3A4 and P-glycoprotein. Forward multiple regression revealed that 56% (i.e., r2 = 0.56) and 17% of the variability in apparent oral clearance [log (dose/area under the curve)] were accounted for by variation in liver CYP3A4 activity (p < 0.0001) and intestinal P-glycoprotein concentration (p = 0.0059), respectively. For peak blood concentration, liver CYP3A4 activity accounted for 32% (p = 0.0002) and P-glycoprotein accounted for an additional 30% (p = 0.0024) of the variability. Intestinal levels of CYP3A4, which varied tenfold, did not appear to influence any cyclosporine pharmacokinetic parameter examined. We conclude that intestinal P-glycoprotein plays a significant role in the first-pass elimination of cyclosporine, presumably by being a rate-limiting step in absorption. Drug interactions with cyclosporine previously ascribed to intestinal CYP3A4 may instead be mediated by interactions with intestinal P-glycoprotein.