Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.     

Bayesian population dynamics of interacting species: great gerbils and fleas in Kazakhstan

We propose a discrete-time Bayesian hierarchical model for the population dynamics of the great gerbil-flea ecological system. The model accounts for the sampling variability arising from data originally collected for other purposes. The prior for the unknown population densities incorporates specific biological hypotheses regarding the interacting dynamics of the two species, as well as their life cycles, where density-dependent effects are included. Posterior estimates are obtained via Markov chain Monte Carlo. The variance of the observed density estimates is a quadratic function of the unknown density. Our study indicates the presence of a density-dependent growth rate for the gerbil population. For the flea population there is clear evidence of density-dependent over-summer net growth, which is dependent on the flea-to-gerbil ratio at the beginning of the reproductive summer. Over-winter net growth is favored by high density. We estimate that on average 35% of the gerbil population survives the winter. Our study shows that hierarchical Bayesian models can be useful in extracting ecobiological information from observational data.     

Estimation and inference for a spline-enhanced population pharmacokinetic model

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.     

A population pharmacokinetic model with time-dependent covariates measured with errors

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.     

Stage duration distributions in matrix population models

Matrix population models are a standard tool for studying stage‐structured populations, but they are not flexible in describing stage duration distributions. This study describes a method for modeling various such distributions in matrix models. The method uses a mixture of two negative binomial distributions (parametrized using a maximum likelihood method) to approximate a target (true) distribution. To examine the performance of the method, populations consisting of two life stages (juvenile and adult) were considered. The juvenile duration distribution followed a gamma distribution, lognormal distribution, or zero‐truncated (over‐dispersed) Poisson distribution, each of which represents a target distribution to be approximated by a mixture distribution. The true population growth rate based on a target distribution was obtained using an individual‐based model, and the extent to which matrix models can approximate the target dynamics was examined. The results show that the method generally works well for the examined target distributions, but is prone to biased predictions under some conditions. In addition, the method works uniformly better than an existing method whose performance was also examined for comparison. Other details regarding parameter estimation and model development are also discussed.     

Using regression trees to predict alpha diversity based upon geographical and habitat characteristics

Different environmental factors act as driving forces of diversity at different scales of analysis; and also the effect of one environmental factor changes as the scale of analysis changes. Most studies rely on multiple regression models, and such models tend to mix-up the effect of all factors and assume that factors effects are additive. We believe that the effect of environment on diversity should be characterized by a hierarchical structure with coarse scale factors, like geographical tropics to poles gradients, defining the envelope of possible diversity conditions, and other more local factors, like habitat structure, being responsible for the fine tuning of diversity. This structure is most efficiently modeled with regression trees. We show that for six habitat types in Greek protected areas regression tree models were able to describe plant species richness based upon environmental factors considerably more efficiently than multiple regression models. More importantly when the models were extrapolated to other sites in Greece, outside their domain, the differences between the predictive ability of the two approaches was magnified. The tree models picked up important ecological characteristics, and a hierarchical structure that used coarse scale factors, like latitude and longitude, for the coarse scale estimate of alpha diversity, and finer scale factors like fragmentation, for the fine-tuning of the estimation. Therefore, we advocate that the regression tree methodology is most appropriate for modeling the relationship between diversity and environmental factors, and the use of the classical regression approaches might be misleading.     

The platinum-carbon replication of a homogenous population of gold particles makes log-normal distributions of shadow widths and lengths

Gold particles were prepared, dried on grids and shadowed at 45° with a 1.2 nm platinum-carbon (Pt-C) film using the shadowing conditions previously described for the freeze-fracture of gastric parietal cell membranes. The particle diameters and the particle shadow widths and lengths were measured using an image analysis system. Statistical analysis of 2000 diameters, shadow widths and shadow lengths indicated that a homogenous population of particles had a normal frequency distribution of diameters (mean diameter 14.5 ± 1.5 nm) and that the Pt-C shadowing transformed that normal curve into a log-normal frequency distribution of shadow widths. The frequency distribution of shadow lengths was log-normal too. We conclude that a statistical partition of experimental frequency distributions of particle shadow widths and lengths of natural membranes to determine the number and parameters of individual components should involve log-normal subdistributions rather than normal ones.     

Disease mapping and spatial regression with count data

In this paper, we provide critical reviews of methods suggested for the analysis of aggregate count data in the context of disease mapping and spatial regression. We introduce a new method for picking prior distributions, and propose a number of refinements of previously used models. We also consider ecological bias, mutual standardization, and choice of both spatial model and prior specification. We analyze male lip cancer incidence data collected in Scotland over the period 1975-1980, and outline a number of problems with previous analyses of these data. In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters. Spatial ecological regression is a far more hazardous enterprise for two reasons. First, there is always the possibility of ecological bias, and this can only be alleviated by the inclusion of individual-level data. For the Scottish data, we show that the previously used mean model has limited interpretation from an individual perspective. Second, when residual spatial dependence is modeled, and if the exposure has spatial structure, then estimates of exposure association parameters will change when compared with those obtained from the independence across space model, and the data alone cannot choose the form and extent of spatial correlation that is appropriate.     

Capillary electrophoresis for pharmacokinetic studies

Different analytical techniques involving capillary electrophoresis for the determination of drugs and metabolites in biological fluids are described. Pharmacokinetic studies carried out using capillary electrophoresis are presented, as well as the in vitro metabolism investigations. The advantages and the limitations of capillary electrophoresis for pharmacokinetic studies are discussed.     

Molecular genetic studies in Saudi population; identified variants from GWAS and meta-analysis in stroke

IntroductionStroke is a multifactorial and heterogeneous disorder, correlates with heritability and considered as one of the major diseases. The prior reports performed the variable models such as genome-wide association studies (GWAS), replication, case-control, cross-sectional and meta-analysis studies and still, we lack diagnostic marker in the global world. There are limited studies were carried out in Saudi population, and we aim to investigate the molecular association of single nucleotide polymorphisms (SNPs) identified through GWAS and meta-analysis studies in stroke patients in the Saudi population.MethodsIn this case-control study, we have opted gender equality of 207 cases and 207 controls from the capital city of Saudi Arabia in King Saud University Hospital. The peripheral blood (5 ml) sample will be collected in two different vacutainers, and three mL of the coagulated blood will be used for lipid analysis (biochemical tests) and two mL will be used for DNA analysis (molecular tests). Genomic DNA will be extracted with the collected blood samples, and specific primers will be designed for the opted SNPs (SORT1-rs646218 and OLR1-rs11053646 polymorphisms) and PCR-RFLP will be performed and randomly DNA sequencing will be carried out to cross check the results.ResultsThe rs646218 and rs11053646 polymorphisms were significantly associated with allele, genotype and dominant models with and without crude odds ratios (OR’s) and Multiple logistic regression analysis (p < 0.05). Correlation between lipid profile and genotypes has confirmed the significant relation between triglycerides and rs646218 and rs1105364 6polymorphisms. However, rs11053646 polymorphism was correlated with HDLC (p = 0.04). Genotypes were examined in both males' vs. males and females' vs. females in cases and control and we concluded that in rs11053646 polymorphisms with male subjects compared between cases and controls found to be associated with dominant model heterozygote genotypes (p < 0.05).ConclusionThe results of the current study confirmed the SORT1 and OLR1 SNPs were associated in the Saudi population. The current results were in the association with the prior study results documented through GWAS and meta-analysis association. However, other ethnic population studies should be performed to rule out in the human hereditary diseases.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

The effect of azithromycin on ivermectin pharmacokinetics--a population pharmacokinetic model analysis

Background

A recent drug interaction study reported that when azithromycin was administered with the combination of ivermectin and albendazole, there were modest increases in ivermectin pharmacokinetic parameters. Data from this study were reanalyzed to further explore this observation. A compartmental model was developed and 1,000 interaction studies were simulated to explore extreme high ivermectin values that might occur.

Methods and Findings

A two-compartment pharmacokinetic model with first-order elimination and absorption was developed. The chosen final model had 7 fixed-effect parameters and 8 random-effect parameters. Because some of the modeling parameters and their variances were not distributed normally, a second mixture model was developed to further explore these data. The mixture model had two additional fixed parameters and identified two populations, A (55% of subjects), where there was no change in bioavailability, and B (45% of subjects), where ivermectin bioavailability was increased 37%. Simulations of the data using both models were similar, and showed that the highest ivermectin concentrations fell in the range of 115–201 ng/mL.

Conclusions

This is the first pharmacokinetic model of ivermectin. It demonstrates the utility of two modeling approaches to explore drug interactions, especially where there may be population heterogeneity. The mechanism for the interaction was identified (an increase in bioavailability in one subpopulation). Simulations show that the maximum ivermectin exposures that might be observed during co-administration with azithromycin are below those previously shown to be safe and well tolerated. These analyses support further study of co-administration of azithromycin with the widely used agents ivermectin and albendazole, under field conditions in disease control programs.     

Prediction of Growth: A Hierarchical Bayesian Approach

A nonparametric hierarchical growth curve model is proposed. Different levels in the model hierarchy are intended to correspond to different sources of variation in an individual's growth. The nonparametric character of the model offers considerable flexibility in fitting the growth curves to empirical data. Here the emphasis is on prediction, and for this purpose the adopted Bayesian inferential approach seems particularly natural and efficient. A Markov chain Carlo method is used to perform the numerical computations. As an illustration of the techniques, we consider the growth of children, during their first two years.     

Gamma generalized linear models for pharmacokinetic data

Summary .   This article considers the modeling of single-dose pharmacokinetic data. Traditionally, so-called compartmental models have been used to analyze such data. Unfortunately, the mean function of such models are sums of exponentials for which inference and computation may not be straightforward. We present an alternative to these models based on generalized linear models, for which desirable statistical properties exist, with a logarithmic link and gamma distribution. The latter has a constant coefficient of variation, which is often appropriate for pharmacokinetic data. Inference is convenient from either a likelihood or a Bayesian perspective. We consider models for both single and multiple individuals, the latter via generalized linear mixed models. For single individuals, Bayesian computation may be carried out with recourse to simulation. We describe a rejection algorithm that, unlike Markov chain Monte Carlo, produces independent samples from the posterior and allows straightforward calculation of Bayes factors for model comparison. We also illustrate how prior distributions may be specified in terms of model-free pharmacokinetic parameters of interest. The methods are applied to data from 12 individuals following administration of the antiasthmatic agent theophylline.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

The pharmacokinetic profile of a novel fixed-dose combination tablet of ibuprofen and paracetamol

Background  

Ibuprofen and paracetamol differ in their mode of action and related therapeutic effects, suggesting that combined administration may offer improved analgesia. Reported here are the results of two studies on the pharmacokinetic properties of a novel ibuprofen (200 mg) and paracetamol (500 mg) fixed-dose combination tablet.     

Antitumor efficacy,pharmacokinetic and biodistribution studies of the anticancer peptide CIGB‐552 in mouse models

Accumulation of the COMMD1 protein as a druggable pharmacology event to target cancer cells has not been evaluated so far in cancer animal models. We have previously demonstrated that a second‐generation peptide, with cell‐penetrating capacity, termed CIGB‐552, was able to induce apoptosis mediated by stabilization of COMMD1. Here, we explore the antitumor effect by subcutaneous administration of CIGB‐552 in a therapeutic schedule. Outstandingly, a significant delay of tumor growth was observed at 0.2 and 0.7 mg/kg (p < 0.01) or 1.4 mg/kg (p < 0.001) after CIGB‐552 administration in both syngeneic murine tumors and patient‐derived xenograft models. Furthermore, we evidenced that ¹³¹I‐CIGB‐552 peptide was actually accumulated in the tumors after administration by subcutaneous route. A typical serine‐proteases degradation pattern for CIGB‐552 in BALB/c mice serum was identified. Further, biological characterization of the main metabolites of the peptide CIGB‐552 suggests that the cell‐penetrating capacity plays an important role in the cytotoxic activity. This report is the first in describing the antitumor effect induced by systemic administration of a peptide that targets COMMD1 for stabilization. Moreover, our data reinforce the perspectives of CIGB‐552 for cancer targeted therapy. Copyright © 2014 European Peptide Society and John Wiley & Sons, Ltd.     

Persistent random motion: Uncovering cell migration dynamics

In this paper we study analytically the stick-slip models recently introduced to explain the stochastic migration of free cells. We show that persistent motion of cells of many different types is compatible with stochastic reorientation models which admit an analytical mesoscopic treatment. This is proved by examining and discussing experimental data compiled from different sources in the literature, and by fitting some of these results too. We are able to explain many of the ‘apparently complex’ migration patterns obtained recently from cell tracking data, like power-law dependences in the mean square displacement or non-Gaussian behavior for the kurtosis and the velocity distributions, which depart from the predictions of the classical Ornstein-Uhlenbeck process.