In vitro-in vivo relationships for oral extended-release drug products

It is of interest to predict the in vivo behavior of an oral extended-release drug product based on its in vitro dissolution profile. In some cases a suitable convolution-based prediction model can be found. We present a methodology for developing statistical models of in vitro-in vivo relationships under the framework of the mixed-effects nonlinear model and discuss methods for assessing the validity and strength of the relationship. These methods are illustrated and contrasted with a level A in vitro-in vivo correlation using data from a study involving four different formulations of an oral extended-release drug product.     

Late feedback effects of hypothalamic-pituitary-adrenal axis hormones in healthy subjects

The main aims of the present study were to establish an in vitro/in vivo correlation for multiple-unit capsules of paracetamol by means of statistical prediction models and to investigate the effect of a number of in vitro variables on the discussion rate of paracetamol from the formulation. A fractional factorial screening design was used to investigate the effects of the variables agitation, pH, osmolality, viscosity, and the presence of bile salt on the dissolution rate of paracetamol. The effects were evaluated in two separate partial least-squares models, in which the responses were expressed as the cumulative percentage of paracetamol dissolved at specified time-points (model I) and as the shape (beta) and scale (eta) parameters according to the Weibull function (model II). It was concluded that agitation and viscosity had significant effects on the dissolution rate of paracetamol. Statistical models based on the responses from models I and II were then used to predict the in vitro conditions most closely correlated with the in vitro dissolution of paracetamol after administration of the formulation to 10 healthy volunteers. The predicted optimal in vitro conditions were similar for the two models and not too far from what is expected from the gastrointestinal tract. The experimental verification of the in vitro conditions showed that both models were equally good, and contributed to high degrees of correlation with the in vivo dissolution behavior of the formulation during 9 hr. The relationships obtained when plotting the percentage dissolved in vitro versus in vivo were y = 1.1x (r2 = 0.98) and y = 1.1x (r2 = 0.94) for models I and II, respectively. Based on these results, it is difficult to state a preference for one of the models. Finally, the use of statistical prediction models to develop critical in vitro tests is a successful approach in the establishment of associations between dissolution behavior in vitro and in vivo for oral extended-release systems.     

Multiple-layer, direct-compression, controlled-release system: in vitro and in vivo evaluation

A new approach to achieve controlled drug delivery is demonstrated for a triple-layer tablet, which simultaneously combines the principles of diffusion and dissolution. Heckel's equation was used to characterize the compression behavior of formulation components. A balanced proportion of each component and a model drug (theophylline) were selected to avoid lamination after ejection and ensure coherent compaction. In vitro release profiles over a period of 10 h in different dissolution media and hydrodynamic conditions were similar and resulted in an n value of 0.786, signifying anomalous release kinetics. The n value is calculated from a curve fit to the empirical equation: Mt/Minfinity = Ktn, where Mt and Minfinity denote the amount of drug released at time t and at infinite time, respectively, K denotes the proportionality constant, and n characterizes the type of release mechanism operative during the dissolution process. In vivo study in human subjects after administration of the experimental triple-layer system exhibited a steady rise in plasma concentration up to 7 h. The actual amount of drug absorbed by the body was calculated by the Wagner-Nelson technique, and a linear relationship was observed between the percentage absorbed in vivo and the percentage dissolved in vitro. The proposed triple-layer model appears to provide good correlation between in vitro and in vivo results with maximum flexibility with respect of dose, duration range, and ease of production.     

Time and change: Using survival analysis in clinical assessment and treatment evaluation.

Survival analysis is a set of statistical techniques that is useful for modeling the types of changes commonly encountered in clinical assessment and treatment evaluation. This article provides a practical, comprehensive, mathematically sound yet nontechnical introduction to survival methods. After discussing study design and data, a complete example data set from a fictitious study of alcohol relapse patterns is introduced to illustrate commonly used survival analysis procedures, including the life-table method, the Kaplan–Meier procedure, the Cox proportional hazards model, and fully parametric survival models. These methods are used to describe the general survival and hazard functions, compare survival probabilities for groups of patients, develop multivariate hazard models, model the shape of the hazard function over time, and use diagnostic tools to check statistical assumptions. Complete SAS and SPSS programs are included in Appendix B. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Assessment of statistical and neural networks methods in NMR spectral classification and metabolite selection

Magnetic resonance spectroscopy opens a window into the biochemistry of living tissue. However, spectra acquired from different tissue types in vivo or in vitro and from body fluids contain a large number of peaks from a range of metabolites, whose relative intensities vary substantially and in complicated ways even between successive samples from the same category. The realization of the full clinical potential of NMR spectroscopy relies, in part, on our ability to interpret and quantify the role of individual metabolites in characterizing specific tissue and tissue conditions. This paper addresses the problem of tissue classification by analysing NMR spectra using statistical and neural network methods. It assesses the performance of classification models from a range of statistical methods and compares them with the performance of artificial neural network models. The paper also assesses the consistency of the models in selecting, directly from the spectra, the subsets of metabolites most relevant for differentiating between tissue types. The analysis techniques are examined using in vitro spectra from eight classes of normal tissue and tumours obtained from rats. We show that, for the given data set, the performance of linear and non-linear methods is comparable, possibly due to the small sample size per class. We also show that using a subset of metabolites selected by linear discriminant analysis for further analysis by neural networks improves the classification accuracy, and reduces the number of metabolites necessary for correct classification.     

Development and internal validation of an in vitro-in vivo correlation for a hydrophilic metoprolol tartrate extended release tablet formulation

PURPOSE: To develop and validate internally an in vitro-in vivo correlation (IVIVC) for a hydrophilic matrix extended release metoprolol tablet. METHODS: In vitro dissolution of the metoprolol tablets was examined using the following methods: Apparatus II, pH 1.2 & 6.8 at 50 rpm and Apparatus I, pH 6.8, at 100 and 150 rpm. Seven healthy subjects received three metoprolol formulations (100 mg): slow, moderate, fast releasing and an oral solution (50 mg). Serial blood samples were collected over 48 hours and analyzed by a validated HPLC assay using fluorescence detection. The f2 metric (similarity factor) was used to analyze the dissolution data. Correlation models were developed using pooled fraction dissolved (FRD) and fraction absorbed (FRA) data from various combinations of the formulations. Predicted metoprolol concentrations were obtained by convolution of the in vivo dissolution rates. Prediction errors were estimated for Cmax and AUC to determine the validity of the correlation. RESULTS: Apparatus I operated at 150 rpm, and pH of 6.8 was found to be the most discriminating dissolution method. There was a significant linear relationship between FRD and FRA when using either two or three of the formulations. An average percent prediction error for Cmax and AUC for all formulations of less than 10% was found for all IVIVC models. CONCLUSIONS: The relatively low prediction errors for Cmax and AUC observed strongly suggest that the metoprolol IVIVC models are valid. The average percent prediction error of less than 10% indicates that the correlation is predictive and allows the associated dissolution data to be used as a surrogate for bioavailability studies.     

From multiple regression analysis to logistic model, proportional hazard model and log linear model. Its concept and application

Recently logistic model, proportional hazard model and log linear model have been used frequently in the medical literatures. Here, each model is reviewed briefly from basics to its application, pointing out pitfalls in its application, some of which are common to any regression analysis. The logistic model is especially useful for the analysis of retrospective data where odds ratio is utilized to evaluate the outcome probability. On the other hand, proportional hazard model is useful when we analyze censored data, utilizing hazard function. Log linear model has been used where contingency table has more than three independent variables, the situation where its applicability in clinical medicine is wide. Familiarity with these statistical methods would enable us to evaluate data more effectively and efficiently and ultimately to read literature more easily.     

Semiology and subtyping of panic disorders

OBJECTIVES: To review the appropriateness of the prevalence odds ratio (POR) and the prevalence ratio (PR) as effect measures in the analysis of cross sectional data and to evaluate different models for the multivariate estimation of the PR. METHODS: A system of linear differential equations corresponding to a dynamic model of a cohort with a chronic disease was developed. At any point in time, a cross sectional analysis of the people then in the cohort provided a prevalence based measure of the effect of exposure on disease. This formed the basis for exploring the relations between the POR, the PR, and the incidence rate ratio (IRR). Examples illustrate relations for various IRRs, prevalences, and differential exodus rates. Multivariate point and interval estimation of the PR by logistic regression is illustrated and compared with the results from proportional hazards regression (PH) and generalised linear modelling (GLM). RESULTS: The POR is difficult to interpret without making restrictive assumptions and the POR and PR may lead to different conclusions with regard to confounding and effect modification. The PR is always conservative relative to the IRR and, if PR > 1, the POR is always > PR. In a fixed cohort and with an adverse exposure, the POR is always > or = IRR, but in a dynamic cohort with sufficient underlying follow up the POR may overestimate or underestimate the IRR, depending on the duration of follow up. Logistic regression models provide point and interval estimates of the PR (and POR) but may be intractable in the presence of many covariates. Proportional hazards and generalised linear models provide statistical methods directed specifically at the PR, but the interval estimation in the case of PH is conservative and the GLM procedure may require constrained estimation. CONCLUSIONS: The PR is conservative, consistent, and interpretable relative to the IRR and should be used in preference to the POR. Multivariate estimation of the PR should be executed by means of generalised linear models or, conservatively, by proportional hazards regression.     

Analysis of clustered data in receiver operating characteristic studies

Clustered data is not simply correlated data, but has its own unique aspects. In this paper, various methods for correlated receiver operating characteristic (ROC) curve data that have been extended specifically to clustered data are reviewed. For those methods that have not yet been extended, suggestions for their application to clustered ROC studies are provided. Various methods with respect to their ability to meet either of two objectives of the analysis of clustered ROC data are compared to consider a variety of ROC indices and their accessibility to researchers. The available statistical methods for clustered data vary in the range of indices that can be considered and in their accessibility to researchers. Parametric models permit all indices to be considered but, owing to computational complexity, are the least accessible of available methods. Nonparametric methods are much more accessible, but only permit estimation and inference about ROC curve area. The jackknife method is the most accessible and permits any index to be considered. Future development of methods for clustered ROC studies should consider the continuation ratio model, which will permit the application of widely available software for the analysis of mixed generalized linear models. Another area of development should be in the adoption of bootstrapping methods to clustered ROC data.     

Mathematical modelling of the release of drug from porous, nonswelling transdermal drug-delivery devices

A general model is presented for the release of drug from porous nonswelling, transdermal drug-delivery devices and it is shown to reduce to previously proposed models in suitable limits. The processes which govern the release of drug are considered to be diffusion of dissolved drug and dissolution of dispersed drug, both in the body of the device and in the device pores, and transfer of drug between the two domains. In the classical limit of large dissolution rates, the problem reduces to one of the moving-boundary type, and solution of this problem in the case where the initial drug loading is much greater than the drug solubility in the device yields expressions for the flux of drug to a perfect sink (modelling in vitro conditions). It is shown that behaviour greatly differing from the classical first-order drug delivery (alpha t 1/2) may be exhibited, depending upon the parameter regime. In some situations the dissolution rates may not be so large and solutions of the general model are derived in the case where the dispersed drug is considered to be undepleted and the diffusivity in the solvent-filled pores is much larger than in the body of the delivery device. Numerical studies are undertaken, and the coupling of delivery device and skin-diffusion models (in order to model the complete transdermal drug-delivery process) is also considered.     

Maintenance of ions, proteins and water in lens fiber cells before and after treatment with non-ionic detergents

The proportional odds model is illustrated in the analysis of two efficacy scales used in a phase II clinical trial involving 81 schizophrenic patients. The proportional odds model preserves the discrete, ordinal nature of one of the scales. The analysis of this data suggested that the relationship between the two scales is not captured by a linear proportional odds model. A linear model and a piecewise linear model for the explanatory variable were therefore compared using likelihood-based analyses. Residuals from both models were compared. Predicted probabilities for the ordinal categories were constructed from the estimated model. Extensions and limitations of the model for interpretation of other trials and for the planning of future trials are discussed.     

Correlation between the pharmacokinetics of oxindanac and inhibition of serum thromboxane B2 in calves

The pharmacokinetics and pharmacodynamics of the non-steroidal antiinflammatory drug, oxindanac, were assessed simultaneously in calves after intravenous (i.v.) administration at dose rates of 0.5, 1, 2, 4 and 8 mg/kg. Plasma pharmacokinetic data were fitted to either two or three compartment open models. The elimination t1/2 was constant in the dose range 0.5 to 4 mg/kg (20.2-22.8 h) and shorter at 8 mg/kg (14.7 h). The pharmacodynamics of oxindanac were assessed by its inhibition of serum TxB2, an index of platelet cyclo-oxygenase activity. Plots of total plasma oxindanac concentration vs. inhibition of serum TxB2 fitted in all cases a sigmoidal Emax equation. There were no significant differences in the estimates for ED50 (1.6-1.9 micrograms/ml), Hill constant (1.3-2.7) or Emax between the doses used in the in vivo studies or when blood was spiked with oxindanac in vitro. Plots of inhibition of serum TxB2 vs. time were prepared from the pharmacokinetic model equations in each calf in combination with a single sigmoidal Emax plot generated in vitro. These data were not significantly different from the results produced in vivo. It is concluded that oxindanac causes reversible inhibition of platelet cyclo-oxygenase in calves. Its inhibition of serum TxB2 can be predicted from total plasma drug concentration, as described by a multicompartmental model, and sigmoidal Emax enzyme kinetics. It was not necessary to take into account factors such as drug equilibration between plasma and its target site, free vs. total drug concentration or chirality. This simple model may be useful for predicting the pharmacodynamics of oxindanac in other species.     

Tests of Race Models for Reaction Time in Experiments with Asynchronous Redundant Signals

We propose an extended hazard regression model which allows the spread parameter to be dependent on covariates. This allows a broad class of models which includes the most common hazard models, such as the proportional hazards model, the accelerated failure time model and a proportional hazards/accelerated failure time hybrid model with constant spread parameter. Simulations based on sub-classes of this model suggest that maximum likelihood performs well even when only small or moderate-size data sets are available and the censoring pattern is heavy. The methodology provides a broad framework for analysis of reliability and survival data. Two numerical examples illustrate the results.     

A biophysically based dermatopharmacokinetic compartment model for quantifying percutaneous penetration and absorption of topically applied agents. I. Theory

We present a general comprehensive mathematical model to stimulate and predict percutaneous absorption and subsequent disposition of chemicals in vivo that is chiefly based on biophysical parameters estimated or measured with in vitro and ex vivo perfused skin preparations. Current physicochemical principles of drug diffusion and partitioning across the skin barrier, solute and solvent concentration dynamics, the influence of solute and solvent on the stratum corneum barrier, and dynamic vascular perfusion effects are integrated in this model. Such a comprehensive approach is necessary to achieve optimal biological relevance in a quantitative model of percutaneous absorption, particularly when a chemical is applied as a binary (solute and solvent) or more complex formulation or chemical mixture. The proposed model should have applications in (a) designing drugs and permeation enhancers for passive or active (e.g., electrically assisted) transdermal drug delivery, (b) assessing the systemic exposure of topical drugs used in dermatology, and (c) integration into other mathematical models being developed to assess the risk after topical exposure to mixtures of environmental pollutants. We also have included experimental data to provide a preliminary illustration of the performance of the model.     

Pharmacokinetic and pharmacodynamic models of the antistaphylococcal effects of meropenem and cloxacillin in vitro and in experimental infection

The efficacies of meropenem (MPM) and cloxacillin (CLC) against two Staphylococcus aureus strains were established in vitro. A pharmacodynamic model equation, based on the concept that the killing rate depends on concentration and time, was fitted to the numbers of CFU. The parameters of the equation are maximum killing rate, time point of maximum killing, and 50% effective concentration (EC50). The EC50s for the two strains were 0.047 and 0.040 mg/liter, respectively, for MPM and 0.105 and 0.121 mg/liter, respectively, for CLC. Calculated values of the parameters were used to predict the numbers of CFU at exponentially decreasing concentrations in vitro as well as in an experimental infection model. The prediction for in vitro conditions gave a satisfactory fit (R2, between 0.862 and 0.894). In vivo the numbers were predicted with the assumption that killing rate in vivo is proportional to that in vitro (R2, between 0.731 and 0.973). The proportionality factor ranged between 0.23 and 0.42; this variation was due mainly to covariation with growth rates in control animals, without other significant differences between antibiotics or strains.     

New approaches to studying problem behaviors: A comparison of methods for modeling longitudinal, categorical adolescent drinking data.

Analyzing problem-behavior trajectories can be difficult. The data are generally categorical and often quite skewed, violating distributional assumptions of standard normal-theory statistical models. In this article, the authors present several currently available modeling options, all of which make appropriate distributional assumptions for the observed categorical data. Three are based on the generalized linear model: a hierarchical generalized linear model, a growth mixture model, and a latent class growth analysis. They also describe a longitudinal latent class analysis, which requires fewer assumptions than the first 3. Finally, they illustrate all of the models using actual longitudinal adolescent alcohol-use data. They guide the reader through the model-selection process, comparing the results in terms of convergence properties, fit and residuals, parsimony, and interpretability. Advances in computing and statistical software have made the tools for these types of analyses readily accessible to most researchers. Using appropriate models for categorical data will lead to more accurate and reliable results, and their application in real data settings could contribute to substantive advancements in the field of development and the science of prevention. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical analysis of repeated measures data using SAS procedures

Mixed linear models were developed by animal breeders to evaluate genetic potential of bulls. Application of mixed models has recently spread to all areas of research, spurred by availability of advanced computer software. Previously, mixed model analyses were implemented by adapting fixed-effect methods to models with random effects. This imposed limitations on applicability because the covariance structure was not modeled. This is the case with PROC GLM in the SAS System. Recent versions of the SAS System include PROC MIXED. This procedure implements random effects in the statistical model and permits modeling the covariance structure of the data. Thereby, PROC MIXED can compute efficient estimates of fixed effects and valid standard errors of the estimates. Modeling the covariance structure is especially important for analysis of repeated measures data because measurements taken close in time are potentially more highly correlated than those taken far apart in time.     

A comparison of two latent variable causal models for adolescent drug use.

Compared the competing simplex (involvement) and common factor models for youthful drug use using causal modeling with latent variables methods with 1,634 students in Grades 7–9. Latent variables of alcohol, marihuana, and other illicit drug use were confirmed and causally interconnected in a set of states. The confirmatory factor and the simplex stage models were found to be acceptable representations of the observed data according to both statistical and psychometric criteria. Results are discussed in terms of their implications for theories of emerging life-styles including drug use, methodology, and policy about psychoactive substances. (44 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An evaluation of methods to assess the effect of antimicrobial residues on the human gut flora

1. Barrier effect. Relevant models should include an anaerobic dominant flora that antagonizes minor bacterial populations such as drug resistant E. coli. 2. Anaerobes vs. aerobes. Aerobe counts are more precise and much less time consuming than anaerobe counts. Minor populations of drug resistant aerobes are sensitive markers of the ecosystem balance, and are directly relevant to the potential risk of antimicrobial residues. 3. MIC vs. plate counts. The determination of minimum inhibitory concentrations (MIC) of selected clones in time consuming, does not detect subdominant resistance (less than 1%), and the MIC shift is difficult to test statistically. In contrast, direct counts of bacteria on drug supplemented media allows a rapid measure of minor resistant populations. 4. Statistics: Most published designs do not include adequate statistical evaluation. This is critical for trials made in conventional humans and animals, where data are highly variable. 5. Human trials: The lowest concentration of antibiotic tested in human volunteers (2 mg oxytetracycline/d for 7d in 6 subjects) significantly increased the proportion of resistant fecal enterobacteria (P = 0.05). However, the huge day-to-day and interindividual variations of human floras make this evidence rather weak. 6. Gnotobiotic mice inoculated with human flora are living isolated models in which the effect of any antimicrobial on the human gut flora can be tested. This in vivo model does include the barrier effect of dominant anaerobes. Interindividual and day-to-day variations of bacterial populations are lower in those mice than in humans. 7. Most resistant enterobacteria in the human gut of untreated people come from bacterial contamination of raw foods. The relative contribution of residues in selecting antibiotic resistance seems to be low when compared to bacterial contamination.     

Pharmacokinetic analysis program based on tank-in-series model, MULTI(TIS), for evaluation of capacity-limited local disposition

A pharmacokinetic analysis program based on a tank-in-series model, MULTI(TIS), was developed for the evaluation of dose-dependency in the local disposition of a drug. The program written in FORTRAN was constructed by expanding MULTI(RUNGE). The reliability of MULTI(TIS) was verified by analyzing the experimental data based on linear and nonlinear tank-in-series models. Linear one- and two-compartment tank-in-series models were adopted to analyze outflow time profiles in single-pass hepatic perfusion following a pulse input of 5'-deoxy-5-fluorouridine (DFUR). The estimated parameters agreed well with those by MULTI(FILT) which is widely used for linear kinetic analysis. The nonlinear models adopted were one-compartment model with Michaelis-Menten elimination and two-compartment models with Michaelis-Menten elimination from central and peripheral compartments. Oxacillin was used as a model drug, because time courses of oxacillin show a capacity-limited hepatic disposition following a pulse input in high doses to the liver (300, 1000, 3000 and 5000 microg). The hepatic recovery ratio (F(H)) of oxacillin increased with dose, whereas the mean transit time (tH) was almost constant. The maximum elimination rate constant (Vmax) and Michaelis constant (Km) of oxacillin were estimated to be 1980 microg/ml/min and 54.1 microg/ml, respectively. Thus, the reliability of MULTI(TIS) was demonstrated for the analysis of nonlinear local disposition, especially, capacity-limited elimination in the liver.