Assessing and selecting gene expression signals based upon the quality of the measured dynamics

<p>Abstract</p> <p>Background</p> <p>One of the challenges with modeling the temporal progression of biological signals is dealing with the effect of noise and the limited number of replicates at each time point. Given the rising interest in utilizing predictive mathematical models to describe the biological response of an organism or analysis such as clustering and gene ontology enrichment, it is important to determine whether the dynamic progression of the data has been accurately captured despite the limited number of replicates, such that one can have confidence that the results of the analysis are capturing important salient dynamic features.</p> <p>Results</p> <p>By pre-selecting genes based upon quality before the identification of differential expression via algorithm such as EDGE, it was found that the percentage of statistically enriched ontologies (p < .05) was improved. Furthermore, it was found that a majority of the genes found via the proposed technique were also selected via an EDGE selection though the reverse was not necessarily true. It was also found that improvements offered by the proposed algorithm are anti-correlated with improvements in the various microarray platforms and the number of replicates. This is illustrated by the fact that newer arrays and experiments with more replicates show less improvement when the filtering for quality is first run before the selection of differentially expressed genes. This suggests that the increase in the number of replicates as well as improvements in array technologies are increase the confidence one has in the dynamics obtained from the experiment.</p> <p>Conclusion</p> <p>We have developed an algorithm that quantifies the quality of temporal biological signal rather than whether the signal illustrates a significant change over the experimental time course. Because the use of these temporal signals, whether it is in mathematical modeling or clustering, focuses upon the entire time series, it is necessary to develop a method to quantify and select for signals which conform to this ideal. By doing this, we have demonstrated a marked and consistent improvement in the results of a clustering exercise over multiple experiments, microarray platforms, and experimental designs.</p

Evaluation of α2-Integrin Expression as a Biomarker for Tumor Growth Inhibition for the Investigational Integrin Inhibitor E7820 in Preclinical and Clinical Studies

E7820 is an orally active inhibitor of α2-integrin mRNA expression, currently tested in phases I and II. We aimed to evaluate what levels of inhibition of integrin expression are needed to achieve tumor stasis in mice, and to compare this to the level of inhibition achieved in humans. Tumor growth inhibition was measured in mice bearing a pancreatic KP-1 tumor, dosed at 12.5–200 mg/kg over 21 days. In the phase I study, E7820 was administered daily for 28 days over a range of 0–200 mg, followed by a 7-day washout period. PK-PD models were developed in NONMEM. α2-Integrin expression measured on platelets, corresponding to tumor stasis at t = 21 in 50% and 90% of the mice (Iint,50, Iint,90) were calculated. It was evaluated if these levels of inhibition could be achieved in patients at tolerable doses. One hundred nineteen α2-Integrin measurements and 210 tumor size measurements were available from mice. The relationship between PK and α2-integrin expression was modeled using an indirect-effect model, subsequently linked to an exponential tumor growth model. Iinh,50 and Iinh,90 were 14.7% (RSE 7%) and 17.9% (RSE 8%). Four hundred sixty two α2-integrin measurements were available from 29 patients. Using the schedule of 100 mg qd (MTD), α2-integrin expression was inhibited more strongly than the Iint,50 and Iint,90 in greater than 95% and greater than 50% of patients, respectively. Moderate inhibition of α2-integrin expression corresponded to tumor stasis in mice, and similar levels could be reached in patients with the dose level of 100 mg qd

A model of hypertension and proteinuria in cancer patients treated with the anti-angiogenic drug E7080

Hypertension and proteinuria are commonly observed side-effects for anti-angiogenic drugs targeting the VEGF pathway. In most cases, hypertension can be controlled by prescription of anti-hypertensive (AH) therapy, while proteinuria often requires dose reductions or dose delays. We aimed to construct a pharmacokinetic–pharmacodynamic (PK–PD) model for hypertension and proteinuria following treatment with the experimental VEGF-inhibitor E7080, which would allow optimization of treatment, by assessing the influence of anti-hypertensive medication and dose reduction or dose delays in treating and avoiding toxicity. Data was collected from a phase I study of E7080 (n = 67), an inhibitor of multiple tyrosine kinases, among which VEGF. Blood pressure and urinalysis data were recorded weekly. Modeling was performed in NONMEM, and direct and indirect response PK–PD models were evaluated. A previously developed PK model was used. An indirect response PK–PD model described the increase in BP best, while the probability of developing proteinuria toxicity in response to exposure to E7080, was best described by a Markov transition model. This model may guide clinical interventions and provide treatment recommendations for E7080, and may serve as a template model for other drugs in this class

Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics

Handling Data Below the Limit of Quantification in Mixed Effect Models

The purpose of this study is to investigate the impact of observations below the limit of quantification (BQL) occurring in three distinctly different ways and assess the best method for prevention of bias in parameter estimates and for illustrating model fit using visual predictive checks (VPCs). Three typical ways in which BQL can occur in a model was investigated with simulations from three different models and different levels of the limit of quantification (LOQ). Model A was used to represent a case with BQL observations in an absorption phase of a PK model whereas model B represented a case with BQL observations in the elimination phase. The third model, C, an indirect response model illustrated a case where the variable of interest in some cases decreases below the LOQ before returning towards baseline. Different approaches for handling of BQL data were compared with estimation of the full dataset for 100 simulated datasets following models A, B, and C. An improved standard for VPCs was suggested to better evaluate simulation properties both for data above and below LOQ. Omission of BQL data was associated with substantial bias in parameter estimates for all tested models even for seemingly small amounts of censored data. Best performance was seen when the likelihood of being below LOQ was incorporated into the model. In the tested examples this method generated overall unbiased parameter estimates. Results following substitution of BQL observations with LOQ/2 were in some cases shown to introduce bias and were always suboptimal to the best method. The new standard VPCs was found to identify model misfit more clearly than VPCs of data above LOQ only