Approximations of the Fisher information for the construction of efficient experimental designs in nonlinear mixed effects models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

Modeling of transfer kinetics at the serum-cerebrospinal fluid barrier in rabbits with experimental meningitis: application to grepafloxacin

The goals of the present study were to model the population kinetics of in vivo influx and efflux processes of grepafloxacin at the serum-cerebrospinal fluid (CSF) barrier and to propose a simulation-based approach to optimize the design of dose-finding trials in the meningitis rabbit model. Twenty-nine rabbits with pneumococcal meningitis receiving grepafloxacin at 15 mg/kg of body weight (intravenous administration at 0 h), 30 mg/kg (at 0 h), or 50 mg/kg twice (at 0 and 4 h) were studied. A three-compartment population pharmacokinetic model was fit to the data with the program NONMEM (Nonlinear Mixed Effects Modeling). Passive diffusion clearance (CL(diff)) and active efflux clearance (CL(active)) are transfer kinetic modeling parameters. Influx clearance is assumed to be equal to CL(diff), and efflux clearance is the sum of CL(diff), CL(active), and bulk flow clearance (CL(bulk)). The average influx clearance for the population was 0.0055 ml/min (interindividual variability, 17%). Passive diffusion clearance was greater in rabbits receiving grepafloxacin at 15 mg/kg than in those treated with higher doses (0.0088 versus 0.0034 ml/min). Assuming a CL(bulk) of 0.01 ml/min, CL(active) was estimated to be 0.017 ml/min (11%), and clearance by total efflux was estimated to be 0.032 ml/min. The population kinetic model allows not only to quantify in vivo efflux and influx mechanisms at the serum-CSF barrier but also to analyze the effects of different dose regimens on transfer kinetic parameters in the rabbit meningitis model. The modeling-based approach also provides a tool for the simulation and prediction of various outcomes in which researchers might be interested, which is of great potential in designing dose-finding trials.

Population pharmacokinetics and clinical response for artemether-lumefantrine in pregnant and nonpregnant women with uncomplicated Plasmodium falciparum malaria in Tanzania.

Artemether-lumefantrine (AL) is the first-line treatment for uncomplicated malaria in the second and third trimesters of pregnancy. Its efficacy during pregnancy has recently been challenged due to altered pharmacokinetic (PK) properties in this vulnerable group. The aim of this study was to determine the PK profile of AL in pregnant and nonpregnant women and assess their therapeutic outcome. Thirty-three pregnant women and 22 nonpregnant women with malaria were treated with AL (80/480 mg) twice daily for 3 days. All patients provided five venous plasma samples for drug quantification at random times over 7 days. Inter- and intraindividual variability was assessed, and the effects of covariates were quantified using a nonlinear mixed-effects modeling approach (NONMEM). A one-compartment model with first-order absorption and elimination with linear metabolism from drug to metabolite fitted the data best for both arthemether (AM) and lumefantrine (LF) and their metabolites. Pregnancy status and diarrhea showed a significant influence on LF PK. The relative bioavailability of lumefantrine and its metabolism rate into desmethyl-lumefantrine were, respectively, 34% lower and 78% higher in pregnant women than in nonpregnant patients. The overall PCR-uncorrected treatment failure rates were 18% in pregnant women and 5% in nonpregnant women (odds ratio [OR] = 4.04; P value of 0.22). A high median day 7 lumefantrine concentration was significantly associated with adequate clinical and parasitological response (P = 0.03). The observed reduction in the relative bioavailability of lumefantrine in pregnant women may explain the higher treatment failure in this group, mostly due to lower posttreatment prophylaxis. Hence, a modified treatment regimen of malaria in pregnancy should be considered.

Spatial Learning and Stress Response of Male Rats Prenatally Exposed to Dexamethasone

Dexamethasone is routinely administered to women at risk for a preterm birth in order to enhance fetal lung development and reduce uterine contractions. Research has demonstrated possible behavioral abnormalities in adulthood as a result of dexamethasone treatment. Using nonlinear mixed effects modeling, this study found thatprenatal dexamethasone treatment impaired spatial learning and memory of adult male Sprague-Dawley rats. Prenatal dexamethasone treatment also led to more anxiety related behaviors on Elevated Plus Maze testing 1.5 hours after a stress challenge. Because theassumptions underlying the independent samples t-test were violated, the randomization test was used to compare groups on the Elevated Plus Maze.

Population pharmacokinetics of metformin in late pregnancy

The pharmacokinetic disposition of metformin in late pregnancy was studied together with the level of fetal exposure at birth. Blood samples were obtained in the third trimester of pregnancy from women with gestational diabetes or type 2 diabetes, 5 had a previous diagnosis of polycystic ovary syndrome. A cord blood sample also was obtained at the delivery of some of these women, and also at delivery of others who had been taking metformin during pregnancy but from whom no blood had been taken. Plasma metformin concentrations were assayed by a new, validated, reverse-phase HPLC method, A 2-compartment, extravascular maternal model with transplacental partitioning of drug to a fetal compartment was fitted to the data. Nonlinear mixed-effects modeling was performed in'NONMEM using FOCE with INTERACTION. Variability was estimated using logarithmic interindividual and additive residual variance models; the covariance between clearance and volume was modeled simultaneously. Mean (range) metformin concentrations in cord plasma and in maternal plasma were 0.81 (range, 0.1-2.6) mg/L and 1.2 (range, 0. 1-2.9) mg/L, respectively. Typical population values (interindividual variability, CV%) for allometrically scaled maternal clearance and volume of distribution were 28 L/h/70 kg (17.1%) and 190 L/70 ka (46.3%), giving a derived population-wide half-life of 5.1 hours. The placental partition coefficient for metformin was 1.07 (36.3%). Neither maternal age nor weight significantly influenced the pharmacokinetics. The variability (SD) of observed concentrations about model-predicted concentrations was 0.32 mg/L. The pharmacokinetics were similar to those in nonpregnant patients and, therefore, no dosage adjustment is warranted. Metformin readily crosses the placenta, exposing the fetus to concentrations approaching those in the maternal circulation. The sequelae to such exposure, ea, effects on neonatal obesity and insulin resistance, remain unknown.

Population pharmacokinetics and pharmacodynamics of lumefantrine in young Ugandan children treated with artemether-lumefantrine for uncomplicated malaria

Background. The pharmacokinetics and pharmacodynamics of lumefantrine, a component of the most widely used treatment for malaria, artemether-lumefantrine, has not been adequately characterized in young children. Methods. Capillary whole-blood lumefantrine concentration and treatment outcomes were determined in 105 Ugandan children, ages 6 months to 2 years, who were treated for 249 episodes of Plasmodium falciparum malaria with artemether-lumefantrine. Results. Population pharmacokinetics for lumefantrine used a 2-compartment open model with first-order absorption. Age had a significant positive correlation with bioavailability in a model that included allometric scaling. Children not receiving trimethoprim-sulfamethoxazole with capillary whole blood concentrations <200 ng/mL had a 3-fold higher hazard of 28-day recurrent parasitemia, compared with those with concentrations >200 ng/mL (P =. 0007). However, for children receiving trimethoprim-sulfamethoxazole, the risk of recurrent parasitemia did not differ significantly on the basis of this threshold. Day 3 concentrations were a stronger predictor of 28-day recurrence than day 7 concentrations. Conclusions. We demonstrate that age, in addition to weight, is a determinant of lumefantrine exposure, and in the absence of trimethoprim-sulfamethoxazole, lumefantrine exposure is a determinant of recurrent parasitemia. Exposure levels in children aged 6 months to 2 years was generally lower than levels published for older children and adults. Further refinement of artemether-lumefantrine dosing to improve exposure in infants and very young children may be warranted. © 2016 The Author.

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenarios

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

Preclinical modeling of multi-drug cancer therapies

Anticancer drugs typically are administered in the clinic in the form of mixtures, sometimes called combinations. Only in rare cases, however, are mixtures approved as drugs. Rather, research on mixtures tends to occur after single drugs have been approved. The goal of this research project was to develop modeling approaches that would encourage rational preclinical mixture design. To this end, a series of models were developed. First, several QSAR classification models were constructed to predict the cytotoxicity, oral clearance, and acute systemic toxicity of drugs. The QSAR models were applied to a set of over 115,000 natural compounds in order to identify promising ones for testing in mixtures. Second, an improved method was developed to assess synergistic, antagonistic, and additive effects between drugs in a mixture. This method, dubbed the MixLow method, is similar to the Median-Effect method, the de facto standard for assessing drug interactions. The primary difference between the two is that the MixLow method uses a nonlinear mixed-effects model to estimate parameters of concentration-effect curves, rather than an ordinary least squares procedure. Parameter estimators produced by the MixLow method were more precise than those produced by the Median-Effect Method, and coverage of Loewe index confidence intervals was superior. Third, a model was developed to predict drug interactions based on scores obtained from virtual docking experiments. This represents a novel approach for modeling drug mixtures and was more useful for the data modeled here than competing approaches. The model was applied to cytotoxicity data for 45 mixtures, each composed of up to 10 selected drugs. One drug, doxorubicin, was a standard chemotherapy agent and the others were well-known natural compounds including curcumin, EGCG, quercetin, and rhein. Predictions of synergism/antagonism were made for all possible fixed-ratio mixtures, cytotoxicities of the 10 best-scoring mixtures were tested, and drug interactions were assessed. Predicted and observed responses were highly correlated (r2 = 0.83). Results suggested that some mixtures allowed up to an 11-fold reduction of doxorubicin concentrations without sacrificing efficacy. Taken together, the models developed in this project present a general approach to rational design of mixtures during preclinical drug development. ^