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.

Transformed symmetric models

For the first time, we introduce a class of transformed symmetric models to extend the Box and Cox models to more general symmetric models. The new class of models includes all symmetric continuous distributions with a possible non-linear structure for the mean and enables the fitting of a wide range of models to several data types. The proposed methods offer more flexible alternatives to Box-Cox or other existing procedures. We derive a very simple iterative process for fitting these models by maximum likelihood, whereas a direct unconditional maximization would be more difficult. We give simple formulae to estimate the parameter that indexes the transformation of the response variable and the moments of the original dependent variable which generalize previous published results. We discuss inference on the model parameters. The usefulness of the new class of models is illustrated in one application to a real dataset.

Quantitative structure-activity relationships for a series of inhibitors of cruzain from Trypanosoma cruzi: Molecular modeling, CoMFA and CoMSIA studies

Human parasitic diseases are the foremost threat to human health and welfare around the world. Trypanosomiasis is a very serious infectious disease against which the currently available drugs are limited and not effective. Therefore, there is an urgent need for new chemotherapeutic agents. One attractive drug target is the major cysteine protease from Trypanosoma cruzi, cruzain. In the present work, comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) studies were conducted on a series of thiosemicarbazone and semicarbazone derivatives as inhibitors of cruzain. Molecular modeling studies were performed in order to identify the preferred binding mode of the inhibitors into the enzyme active site, and to generate structural alignments for the three-dimensional quantitative structure-activity relationship (3D QSAR) investigations. Statistically significant models were obtained (CoMFA. r(2) = 0.96 and q(2) = 0.78; CoMSIA, r(2) = 0.91 and q(2) = 0.73), indicating their predictive ability for untested compounds. The models were externally validated employing a test set, and the predicted values were in good agreement with the experimental results. The final QSAR models and the information gathered from the 3D CoMFA and CoMSIA contour maps provided important insights into the chemical and structural basis involved in the molecular recognition process of this family of cruzain inhibitors, and should be useful for the design of new structurally related analogs with improved potency. (C) 2009 Elsevier Inc. All rights reserved.

Fragment-Based QSAR and Molecular Modeling Studies on a Series of Discodermolide Analogs as Microtubule-Stabilizing Anticancer Agents

Inhibition of microtubule function is an attractive rational approach to anticancer therapy. Although taxanes are the most prominent among the microtubule-stabilizers, their clinical toxicity, poor pharmacokinetic properties, and resistance have stimulated the search for new antitumor agents having the same mechanism of action. Discodermolide is an example of nontaxane natural product that has the same mechanism of action, demonstrating superior antitumor efficacy and therapeutic index. The extraordinary chemical and biological properties have qualified discodermolide as a lead structure for the design of novel anticancer agents with optimized therapeutic properties. In the present work, we have employed a specialized fragment-based method to develop robust quantitative structure - activity relationship models for a series of synthetic discodermolide analogs. The generated molecular recognition patterns were combined with three-dimensional molecular modeling studies as a fundamental step on the path to understanding the molecular basis of drug-receptor interactions within this important series of potent antitumoral agents.

Three-dimensional quantitative structure-activity relationships for a large series of potent antitubercular agents

Comparative molecular field analysis (CoMFA) studies were conducted on a series of 100 isoniazid derivatives as anti-tuberculosis agents using two receptor-independent structural data set alignment strategies: (1) rigid-body fit, and (2) pharmacophore-based. Significant cross-validated correlation coefficients were obtained (CoMFA(1), q(2) = 0,75 and CoMFA(2), q(2) = 0.74), indicating the potential of the models for untested compounds. The models were then used to predict the inhibitory potency of 20 test set compounds that were not included in the training set, and the predicted values were in good agreement with the experimental results.

Quantitative structure-activity studies on a series of migrastatin analogs as inhibitors of cancer cell metastasis

Migrastatin, a macrolide natural product, and its structurally related analogs are potent inhibitors of cancer cell metastasis, invasion and migration. In the present work, a specialized fragment-based method was employed to develop QSAR models for a series of migrastatin and isomigrastatin analogs. Significant correlation coefficients were obtained (best model, q(2) = 0.76 and r(2) = 0.91) indicating that the QSAR models possess high internal consistency. The best model was then used to predict the potency of an external test set, and the predicted values were in good agreement with the experimental results (R(2) (pred) = 0.85). The final model and the corresponding contribution maps, combined with molecular modeling studies, provided important insights into the key structural features for the anticancer activity of this family of synthetic compounds based on natural products.

Classical and hologram QSAR studies on a series of inhibitors of trypanosomatid Glyceraldehyde-3-Phosphate Dehydrogenase

Leishmaniasis and trypanosomiasis are major causes of morbidity and mortality in both tropical and subtropical regions of the world. The current available drugs are limited, ineffective, and require long treatment regimens. Due to the high dependence of trypanosomatids on glycolysis as a source of energy, some glycolytic enzymes have been identified as attractive targets for drug design. In the present work, classical Two-Dimensional Quantitative Structure -Activity Relationships (2D QSAR) and Hologram QSAR (HQSAR) studies were performed on a series of adenosine derivatives as inhibitors of Leishmania mexicana Glyceraldehyde-3-Phosphate Dehydrogenase (LmGAPDH). Significant correlation coefficients (classical QSAR, r(2)=0.83 and q(2) =0.81; HQSAR, r(2)=0.91 and q(2) =0.86) were obtained for the 56 training set compounds, indicating the potential of the models for untested compounds. The models were then externally validated using a test set of 14 structurally related compounds and the predicted values were in good agreement with the experimental results (classical QSAR, r(pred)(2) = 0.94; HQSAR, r(pred)(2) = 0.92).

Fragment-based and classical quantitative structure-activity relationships for a series of hydrazides as antituberculosis agents

Worldwide, tuberculosis (TB) is the leading cause of death among curable infectious diseases. Multidrug-resistant Mycobacterium tuberculosis is an emerging problem of great importance to public health, and there is an urgent need for new anti-TB drugs. In the present work, classical 2D quantitative structure-activity relationships (QSAR) and hologram QSAR (HQSAR) studies were performed on a training set of 91 isoniazid derivatives. Significant statistical models (classical QSAR, q(2) = 0.68 and r(2) = 0.72; HQSAR, q(2) = 0.63 and r(2) = 0.86) were obtained, indicating their consistency for untested compounds. The models were then used to evaluate an external test set containing 24 compounds which were not included in the training set, and the predicted values were in good agreement with the experimental results (HQSAR, r(pred)(2) = 0.87; classical QSAR, r(pred)(2) = 0.75).

Classical and fragment-based hologram structure-activity relationships for a series of analgesic cyclic imides

Cyclic imides have been widely employed in drug design research due to their multiple pharmacological and biological properties. In the present study, two-dimensional quantitative structure-activity relationship (2D QSAR) studies were conducted on a series of potent analgesic cyclic imides using both classical and hologram QSAR (HQSAR) methods, yielding significant statistical models (classical QSAR, q(2) = 0.80; HQSAR, q(2) = 0.84). The models were then used to evaluate an external data test, and the predicted values were in good agreement with the experimental results, indicating their consistency for untested compounds.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

Copula-based regression models: A survey

In this review paper we collect several results about copula-based models, especially concerning regression models, by focusing on some insurance applications. (C) 2009 Elsevier B.V. All rights reserved.

Systematic risk estimation in symmetric models

The aim of this article is to discuss the estimation of the systematic risk in capital asset pricing models with heavy-tailed error distributions to explain the asset returns. Diagnostic methods for assessing departures from the model assumptions as well as the influence of observations on the parameter estimates are also presented. It may be shown that outlying observations are down weighted in the maximum likelihood equations of linear models with heavy-tailed error distributions, such as Student-t, power exponential, logistic II, so on. This robustness aspect may also be extended to influential observations. An application in which the systematic risk estimate of Microsoft is compared under normal and heavy-tailed errors is presented for illustration.

Insights into the Molecular Requirements for the Anti-obesity Activity of a Series of CB1 Ligands

Two-dimensional and 3D quantitative structure-activity relationships studies were performed on a series of diarylpyridines that acts as cannabinoid receptor ligands by means of hologram quantitative structure-activity relationships and comparative molecular field analysis methods. The quantitative structure-activity relationships models were built using a data set of 52 CB1 ligands that can be used as anti-obesity agents. Significant correlation coefficients (hologram quantitative structure-activity relationships: r 2 = 0.91, q 2 = 0.78; comparative molecular field analysis: r 2 = 0.98, q 2 = 0.77) were obtained, indicating the potential of these 2D and 3D models for untested compounds. The models were then used to predict the potency of an external test set, and the predicted (calculated) values are in good agreement with the experimental results. The final quantitative structure-activity relationships models, along with the information obtained from 2D contribution maps and 3D contour maps, obtained in this study are useful tools for the design of novel CB1 ligands with improved anti-obesity potency.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Pedal : identification of models for duodenal administration of levodopa

Backgound and aims: The main purpose of the PEDAL study is to identify and estimate sample individual pharmacokinetic- pharmacodynamic (PK/PD) models for duodenal infusion of levodopa/carbidopa (Duodopa®) that can be used for in numero simulation of treatment strategies. Other objectives are to study the absorption of Duodopa® and to form a basis for power calculation for a future larger study. PK/PD based on oral levodopa is problematic because of irregular gastric emptying. Preliminary work with data from [Gundert-Remy U et al. Eur J Clin Pharmacol 1983;25:69-72] suggested that levodopa infusion pharmacokinetics can be described by a two-compartment model. Background research led to a hypothesis for an effect model incorporating concentration-unrelated fluctuations, more complex than standard E-max models. Methods: PEDAL involved a few patients already on Duodopa®. A bolus dose (normal morning dose plus 50%) was given after a washout during night. Data collection continued until the clinical effect was back at baseline. The procedure was repeated on two non-consecutive days per patient. The following data were collected in 5 to 15 minutes intervals: i) Accelerometer data. ii) Three e-diary questions about ability to walk, feelings of “off” and “dyskinesia”. iii) Clinical assessment of motor function by a physician. iv) Plasma concentrations of levodopa, carbidopa and the metabolite 3-O-methyldopa. The main effect variable will be the clinical assessment. Results: At date of abstract submission, lab analyses were currently being performed. Modelling results, simulation experiments and conclusions will be presented in our poster.