Poor adherence to a drug prescription significantly impacts on the efficacy and safety of a planned therapy. The relationship between drug intake and pharmacokinetics (PK) is only partially known. In this work, we focus on the so-called "inverse problem", concerned with the issue of retracing the patient compliance scenario using limited clinical knowledge. Using a reported Pop-PK model of imatinib, and accounting for the variability around its PK parameters, we were able to simulate a whole range of drug concentration values at a specific sampling point for a population of patients with all possible drug compliance profiles. Using a Bayesian decision rule, we developed a methodology for the determination of the associated compliance profile prior to a given sampling value. The adopted approach allows, for the first time, to quantitatively acquire knowledge about the compliance patterns having a causal effect on a given PK. Moreover, using a simulation approach, we were able to evaluate the evolution of success rate of the retracing process in terms of the considered time period before sampling as well as the model-inherited variability. In conclusion, this work allows, from a probability viewpoint, to propose a solution for this inverse problem of compliance determination.
The pharmacokinetics of baclofen is well delineated in subjects with normal kidney function (KF); however, pharmacokinetics data in patients with chronic kidney disease (CKD) are not and dosage recommendations remain empirical. The effects of CKD on baclofen pharmacokinetics were assessed through a multi-center, open-label, single 5-mg dose, pharmacokinetics study. The KF was measured as the creatinine clearance (CrCL) calculated with the Cockroft-Gault (C-G) equation or as the estimated glomerular filtration rate (eGFR) using subjects' CKD-EPI equation. Subjects were assigned to 1 of 4 groups based on their CrCL (>80 mL/min, 50-80 mL/min; 30-50 mL/min and <30 mL/min). Cmax was not statistically different between the groups, while AUC and T1/2el increased, and CL/F decreased, with increasing severity of CKD. Baclofen's oral clearance and CrCL were statistically significantly correlated, and the trend was the same when classifying subjects either with the CKD-EPI or C-G equations. Linear equations using KF as variable were set to recommend individual dose reduction in CKD patients. Results suggest a mean dose reduction of 1/3, 1/2, and 2/3 in patients with mild, moderate, and severe CKD respectively, in order to achieve baclofen exposure comparable to that observed in healthy subjects.
The objective of this study was to characterize the baseline circadian rhythm of testosterone levels in hypogonadal men. A total of 859 baseline profiles of testosterone from hypogonadal men were included in this analysis. The circadian rhythm of the testosterone was described by a stretched cosine function. Model parameters were estimated using NONMEM® 7.3. The effect of different covariates on the testosterone levels was investigated. Model evaluation was performed using non-parametric bootstrap and predictive checks. A stretched cosine function deeply improved the data goodness of fit compared to the standard trigonometric function (p < 0.001; ΔOFV = −204). The effect of the age and the semester, defined as winter and spring versus summer and fall, were significantly associated with the baseline levels of testosterone (p < 0.001, ΔOFV = −15.6, and p < 0.001, ΔOFV = −47.0). Model evaluation procedures such as diagnostic plots, visual predictive check, and non-parametric bootstrap evidenced that the proposed stretched cosine function was able to model the time course of the diurnal testosterone levels in hypogonadal males with accuracy and precision. The circadian rhythm of the testosterone levels was better predicted by the proposed stretched cosine function than a standard cosine function. Testosterone levels decreased by 5.74 ng/dL (2.4%) every 10 years and were 19.3 ng/dL (8.1%) higher during winter and spring compared to summer and fall.
Abstract. Approximate scale-invariance and local regularity properties of natural terrains suggest that they can be a accurately modeled with random processes which are locally fractal. Current models for terrain modeling include fractional and multifractional Brownian motion. Though these processes have proved useful, they miss an important feature of real terrains: typically, the local regularity of a mountain at a given point is strongly correlated with the height of this point. For instance, young mountains are such that high altitude regions are often more irregular than low altitude ones. We detail in this work the construction of a stochastic process called the Self-Regulated Multifractional Process, whose regularity at each point is, almost surely, a deterministic function of the amplitude. This property makes such a process a versatile and powerful model for real terrains. We demonstrate its use with numerical experiments on several types of mountains.Key words: Digital elevation models, Hölderian regularity, (multifractional) Brownian motion. Motivation and backgroundA digital elevation model (DEM) is a digital representation of ground surface topography or terrain. DEM are widely used for geographic information systems and for obtaining relief maps. In most places, the surface of the earth is rough and rapidly varying. 2D random processes are thus often used as models for DEM. In addition, most terrains possess a form of approximate self-similarity, i.e. the same features are statistically observed at various resolutions. For these reasons, fractal stochastic processes are popular models for DEM.The most widely used set of models is based on fractional brownian motion (fBm) and its extensions. fBm has been used for mountain synthesis as well as in the fine description of the sea floor [PP98]. One of the reasons for the success of fBm is that it shares an important property of many natural grounds: statistically, a natural ground is the same at several resolutions. fBm allows to model this scale-invariance property as well as to control the general appearance of the ground via a parameter H taking values in (0, 1): H close to 0 translates into an irregular terrain, while H close to 1 yields smooth surfaces. More precisely, one can show that, almost surely, the local regularity of the paths of fBm, as measured by the Hölder exponent (see definition 22), is at any point equal to H. A large body of works has been devoted to the synthesis and estimation of fBm from numerical data.A major drawback of fBm is that its regularity is the same at every point. This does not fit into reality: for example, erosion phenomena will smooth parts of a mountain more than others. Multifractional Brownian motion (mBm) goes beyond fBm by allowing H to vary in space. Multifractional Brownian motion simply replaces the real parameter H of fBm with a function, still ranging in (0, 1), with the property that, at each point (x, y), the Hölder exponent 2 Ground modelling using extensions of the fractional Brownian motion. of a re...
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