Assessment of pulsatile insulin secretion derived from peripheral plasma C-peptide concentrations by nonparametric stochastic deconvolution.

The characteristics of pulsatile insulin secretion are important determinants of type 2 diabetes pathophysiology, but they are understudied due to the difficulties in measuring pulsatile insulin secretion noninvasively. Deconvolution of either peripheral C-peptide or insulin concentrations offers an appealing alternative to hepatic vein catheterization. However, to do so, there are a series of methodological challenges to overcome. C-peptide has a relatively long half-life and accumulates in the circulation. On the other hand, peripheral insulin concentrations reflect relatively fast clearance and hepatic extraction as it leaves the portal circulation to enter the systemic circulation. We propose a method based on nonparametric stochastic deconvolution of C-peptide concentrations, using individually determined C-peptide kinetics, to overcome these limitations. The use of C-peptide (instead of insulin) concentrations allows estimation of portal (and not post-hepatic) insulin pulses, whereas nonparametric stochastic deconvolution allows evaluation of pulsatile signals without any a priori assumptions of pulse shape and occurrence. The only assumption required is the degree of smoothness of the (unknown) secretion rate. We tested this method first on simulated data and then on 29 nondiabetic subjects studied during euglycemia and hyperglycemia and compared our estimates with the profiles obtained from hepatic vein insulin concentrations. This method produced satisfactory results both in the ability to fit the data and in providing reliable estimates of pulsatile secretion, in agreement with hepatic vein measurements. In conclusion, the proposed method enables reliable and noninvasive measurement of pulsatile insulin secretion. Future studies will be needed to validate this method in people with type 2 diabetes.

Systemic Exposure of Rituximab Increased by Ibrutinib: Pharmacokinetic Results and Modeling Based on the HELIOS Trial.

INTRODUCTION: In the HELIOS trial, bendamustine/rituximab (BR) plus ibrutinib (BR-I) improved disease outcomes versus BR plus placebo in previously treated chronic lymphocytic leukemia/small lymphocytic lymphoma. Here, we describe the pharmacokinetic (PK) observations, along with modeling to further explore the interaction between ibrutinib and rituximab. METHODS: 578 subjects were randomized to ibrutinib or placebo with BR (6 cycles). Ibrutinib PK samples and tumor measurements were obtained from all subjects; a subset was evaluated for bendamustine and rituximab PK. Population rituximab PK was assessed using nonlinear mixed-effects modeling. RESULTS: Dose-normalized plasma concentration-time bendamustine data were comparable between the arms. Systemic rituximab exposure was higher with BR-I versus BR; mean trough serum concentrations were 2- to 3-fold higher in the first three cycles and 1.2- to 1.7-fold higher subsequently. No relevant safety differences were observed. In the modeling, including treatment arm as a categorical covariate and tumor burden as a continuous time-varying covariate on overall rituximab clearance significantly improved fitting of the data. CONCLUSIONS: BR-I led to higher dose-normalized systemic rituximab exposure versus BR and more rapid steady-state achievement. The modeling data suggest that rituximab disposition is, at least in part, target mediated. Determining the clinical significance of these findings requires further assessments. TRIAL REGISTRATION: This study is registered at https://clinicaltrials.gov/ct2/show/NCT01611090 .

MPBPK-TMDD models for mAbs: alternative models, comparison, and identifiability issues.

The aim of the present study was to evaluate model identifiability when minimal physiologically-based pharmacokinetic (mPBPK) models are integrated with target mediated drug disposition (TMDD) models in the tissue compartment. Three quasi-steady-state (QSS) approximations of TMDD dynamics were explored: on (a) antibody-target complex, (b) free target, and (c) free antibody concentrations in tissue. The effects of the QSS approximations were assessed via simulations, taking as reference the mPBPK-TMDD model with no simplifications. Approximation (a) did not affect model-derived concentrations, while with the inclusion of approximation (b) or (c), target concentration profiles alone, or both drug and target concentration profiles respectively deviated from the reference model profiles. A local sensitivity analysis was performed, highlighting the potential importance of sampling in the terminal pharmacokinetic phase and of collecting target concentration data. The a priori and a posteriori identifiability of the mPBPK-TMDD models were investigated under different experimental scenarios and designs. The reference model and QSS approximation (a) on antibody-target complex were both found to be a priori identifiable in all scenarios, while under the further inclusion of QSS approximation (b) target concentration data were needed for a priori identifiability to be preserved. The property could not be assessed for the model including all three QSS approximations. A posteriori identifiability issues were detected for all models, although improvement was observed when appropriate sampling and dose range were selected. In conclusion, this work provides a theoretical framework for the assessment of key properties of mathematical models before their experimental application. Attention should be paid when applying integrated mPBPK-TMDD models, as identifiability issues do exist, especially when rich study designs are not feasible.

Temporal pharmacokinetic/pharmacodynamic interaction between human CD3ε antigen-targeted monoclonal antibody otelixizumab and CD3ε binding and expression in human peripheral blood mononuclear cell static culture.

Otelixizumab is a monoclonal antibody (mAb) directed to human CD3ε, a protein forming part of the CD3/T-cell receptor (TCR) complex on T lymphocytes. This study investigated the temporal interaction between varying concentrations of otelixizumab, binding to human CD3 antigen, and expression of CD3/TCR complexes on lymphocytes in vitro, free from the confounding influence of changing lymphocyte frequencies observed in vivo. A static in vitro culture system was established in which primary human peripheral blood mononuclear cells (PBMCs) were incubated over an extended time course with titrated concentrations of otelixizumab. At each time point, free, bound, and total CD3/TCR expression on both CD4+ and CD8+ T cells and the amount of free otelixizumab antibody in the supernatant were measured. The pharmacokinetics of free otelixizumab in the culture supernatants was saturable, with a shorter apparent half-life at low concentration. Correspondingly, a rapid, otelixizumab concentration-, and time-dependent reduction in CD3/TCR expression was observed. These combined observations were consistent with the phenomenon known as target-mediated drug disposition (TMDD). A mechanistic, mathematical pharmacokinetic/pharmacodynamic (PK/PD) model was then used to characterize the free otelixizumab-CD3 expression-time relationship. CD3/TCR modulation induced by otelixizumab was found to be relatively fast compared with the re-expression rate of CD3/TCR complexes following otelixizumab removal from supernatants. In summary, the CD3/TCR receptor has been shown to have a major role in determining otelixizumab disposition. A mechanistic PK/PD model successfully captured the PK and PD in vitro data, confirming TMDD by otelixizumab.

Biomarker- versus drug-driven tumor growth inhibition models: an equivalence analysis.

The mathematical modeling of tumor xenograft experiments following the dosing of antitumor drugs has received much attention in the last decade. Biomarker data can further provide useful insights on the pathological processes and be used for translational purposes in the early clinical development. Therefore, it is of particular interest the development of integrated pharmacokinetic-pharmacodynamic (PK-PD) models encompassing drug, biomarker and tumor-size data. This paper investigates the reciprocal consistency of three types of models: drug-to-tumor, such as established drug-driven tumor growth inhibition (TGI) models, drug-to-biomarker, e.g. indirect response models, and biomarker-to-tumor, e.g. the more recent biomarker-driven TGI models. In particular, this paper derives a mathematical relationship that guarantees the steady-state equivalence of the cascade of drug-to-biomarker and biomarker-to-tumor models with a drug-to-tumor TGI model. Using the Simeoni TGI model as a reference, conditions for steady-state equivalence are worked out and used to derive a new biomarker-driven model. Simulated and real data are used to show that in realistic cases the steady-state equivalence extends also to transient responses. The possibility of predicting the drug-to-tumor potency of a new candidate drug based only on biomarker response is discussed.

Continuous-time Markov modelling of flexible-dose depression trials.

The aim of this paper is to provide a systematic methodology for modelling longitudinal data to be used in contexts of limited or even absent knowledge of the physiological mechanism underlying the disease time course. Adopting a system-theoretic paradigm, a population response model is developed where the clinical endpoint is described as a function of the patient's health state. In particular, a continuous-time stochastic approach is proposed where the clinical score and its time-derivative summarize the patient's health state affected by a random term accounting for exogenous unpredictable factors. The proposed approach is validated on experimental data from the placebo and drug arms of a Phase II depression trial. Since some subjects in the trial may undergo changes in their treatment dose due to the flexible dosing scheme, dose escalations are modelled as instantaneous perturbations on the state. In its simplest form--an integrated Wiener process--was able to correctly capture the individual responses in both treatment arms. However, a better description of inter-individual variability was obtained by means of a stable Markovian model. Parameter estimation has been carried out according to the empirical Bayes method.

Population model of longitudinal FEV1 data in asthmatics: meta-analysis and predictability of placebo response.

Asthma is an obstructive lung disease where the mechanism of disease progression is not fully understood hence motivating the use of empirical models to describe the evolution of the patient's health state. With reference to placebo response, measured in terms of FEV1 (Forced Expiratory Volume in 1 s), a range of empirical models taken from the literature were compared at a single trial level. In particular, eleven GSK trials lasting 12 weeks in mild-to-moderate asthma were used for the modelling of longitudinal placebo responses. Then, the chosen exponential model was used to carry out an individual participant data meta-analysis on eleven trials. A covariate analysis was also performed to find relevant covariates in asthma to be accounted for in the meta-analysis model. Age, gender, and height were found statistically significant (e.g. the taller the patients the higher the FEV1, the older the patients the lower the FEV1, and females have lower FEV1). By truncating each trial at week 4, the predictive properties of the meta-analysis model were also investigated, showing its ability to predict long-term FEV1 response from truncated trials. Summarizing, the study suggests that: (i) the exponential model effectively describes the placebo response; (ii) the meta-analysis approach may prove helpful to simulate new trials as well as to reduce trial duration in view of its predictive properties; (iii) the inclusion of available covariates within the meta-analysis model provides a reduction of the inter-individual variability.

Deconvolution-based assessment of pituitary GH secretion stimulated with GHRH+arginine in Prader-Willi adults and obese controls.

OBJECTIVE: The assessment of GH deficiency in adult patients with Prader-Willi syndrome (PWS) has been previously assessed through the evaluation of quantitative parameters, such as the peak value of GH response to exogenous stimuli. A comprehensive description of the pattern of secretory response obtainable by deconvolution analysis is still lacking. The aim of our study was to characterize the time evolution of responses of PWS subjects compared with obese controls. DESIGN AND SUBJECTS: GH responsiveness was measured following the combined administration of GHRH+arginine to 65 PWS adults (24 males, 41 females) aged 18-41·2 years, and 17 age-, gender- and body mass index-matched obese controls. PWS subjects were analysed considering the stratification on different genotypes. MEASUREMENTS: GH response to GHRH+arginine was analysed in terms of peak values, standard area under the curves (AUCs), AUCs due to the stimulus, AUCs of the Instantaneous Secretion Rate signal and Secretion Response Analysis. RESULTS: In terms of both peak values and AUC, GH responses were statistically different between PWS UPD15 and PWS DEL15 subjects as well as between PWS UPD15 and obese controls. PWS subjects showed a lower and a more delayed GH response compared with obese controls. Moreover, PWS UPD15 subjects had the most delayed GH response. CONCLUSIONS: Our findings demonstrate that impaired GH secretion in PWS subjects compared with obese controls regards not only amplitude parameters such as peak value and AUC, but also the shape of the secretory response, which is more delayed, especially for UPD15 subjects.

Modeling of human tumor xenografts and dose rationale in oncology.

Xenograft models are commonly used in oncology drug development. Although there are discussions about their ability to generate meaningful data for the translation from animal to humans, it appears that better data quality and better design of the preclinical experiments, together with appropriate data analysis approaches could make these data more informative for clinical development. An approach based on mathematical modeling is necessary to derive experiment-independent parameters which can be linked with clinically relevant endpoints. Moreover, the inclusion of biomarkers as predictors of efficacy is a key step towards a more general mechanism-based strategy.

A PCA approach to population analysis: with application to a Phase II depression trial.

For psychiatric diseases, established mechanistic models are lacking and alternative empirical mathematical structures are usually explored by a trial-and-error procedure. To address this problem, one of the most promising approaches is an automated model-free technique that extracts the model structure directly from the statistical properties of the data. In this paper, a linear-in-parameter modelling approach is developed based on principal component analysis (PCA). The model complexity, i.e. the number of components entering the PCA-based model, is selected by either cross-validation or Mallows' Cp criterion. This new approach has been validated on both simulated and clinical data taken from a Phase II depression trial. Simulated datasets are generated through three parametric models: Weibull, Inverse Bateman and Weibull-and-Linear. In particular, concerning simulated datasets, it is found that the PCA approach compares very favourably with some of the popular parametric models used for analyzing data collected during psychiatric trials. Furthermore, the proposed method performs well on the experimental data. This approach can be useful whenever a mechanistic modelling procedure cannot be pursued. Moreover, it could support subsequent semi-mechanistic model building.

Correction of Italian under-reporting in the first COVID-19 wave via age-specific deconvolution of hospital admissions.

When the COVID-19 pandemic first emerged in early 2020, healthcare and bureaucratic systems worldwide were caught off guard and largely unprepared to deal with the scale and severity of the outbreak. In Italy, this led to a severe underreporting of infections during the first wave of the spread. The lack of accurate data is critical as it hampers the retrospective assessment of nonpharmacological interventions, the comparison with the following waves, and the estimation and validation of epidemiological models. In particular, during the first wave, reported cases of new infections were strikingly low if compared with their effects in terms of deaths, hospitalizations and intensive care admissions. In this paper, we observe that the hospital admissions during the second wave were very well explained by the convolution of the reported daily infections with an exponential kernel. By formulating the estimation of the actual infections during the first wave as an inverse problem, its solution by a regularization approach is proposed and validated. In this way, it was possible to compute corrected time series of daily infections for each age class. The new estimates are consistent with the serological survey published in June 2020 by the National Institute of Statistics (ISTAT) and can be used to speculate on the total number of infections occurring in Italy during 2020, which appears to be about double the number officially recorded.

Early detection of variants of concern via funnel plots of regional reproduction numbers.

Early detection of the emergence of a new variant of concern (VoC) is essential to develop strategies that contain epidemic outbreaks. For example, knowing in which region a VoC starts spreading enables prompt actions to circumscribe the geographical area where the new variant can spread, by containing it locally. This paper presents 'funnel plots' as a statistical process control method that, unlike tools whose purpose is to identify rises of the reproduction number ([Formula: see text]), detects when a regional [Formula: see text] departs from the national average and thus represents an anomaly. The name of the method refers to the funnel-like shape of the scatter plot that the data take on. Control limits with prescribed false alarm rate are derived from the observation that regional [Formula: see text]'s are normally distributed with variance inversely proportional to the number of infectious cases. The method is validated on public COVID-19 data demonstrating its efficacy in the early detection of SARS-CoV-2 variants in India, South Africa, England, and Italy, as well as of a malfunctioning episode of the diagnostic infrastructure in England, during which the Immensa lab in Wolverhampton gave 43,000 incorrect negative tests relative to South West and West Midlands territories.

Modelling of the outcome of non-inferiority trials by integration of historical data.

The approval and differentiation of new compounds in clinical development often demands non-inferiority trials, in which the test drug is compared against a reference treatment. However, non-inferiority trials impose major operational burden with serious ethical and scientific implications for the development of new medicines. Traditional approaches make limited use of historical information on placebo and neglect inter-trial variability, relying on the constancy assumption that the control-to-placebo effect size is maintained across trials. We propose a model-based approach that overcomes such limitations and may be used as a tool to explore differentiation during clinical development. Parameter distributions are introduced which reflect the heterogeneity of trials. The method is illustrated using data from impetigo trials. Based on simulation scenarios, this Bayesian technique yields a definitive, consistent increase in the statistical power over two accepted statistical methods, allowing lower sample size requirements for the assessment of non-inferiority.

Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy.

Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)1, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model2, which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs ([Formula: see text] = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs ([Formula: see text] = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open-close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses.

In Vitro-In Vivo Correlation (IVIVC) Population Modeling for the In Silico Bioequivalence of a Long-Acting Release Formulation of Progesterone.

Health authorities carefully evaluate any change in the batch manufacturing process of a drug before and after regulatory approval. In the absence of an adequate in vitro-in vivo correlation (Level A IVIVC), an in vivo bioequivalence (BE) study is frequently required, increasing the cost and time of drug development. This study focused on developing a Level A IVIVC for progesterone vaginal rings (PVRs), a dosage form designed for the continuous delivery in vivo. The pharmacokinetics (PK) of four batches of rings charged with 125, 375, 750 and 1500 mg of progesterone and characterized by different in vitro release rates were evaluated in two clinical studies. In vivo serum concentrations and in vitro release profiles were used to develop a population IVIVC progesterone ring (P-ring) model through a direct differential-equation-based method and a nonlinear-mixed-effect approach. The in vivo release, Rvivo(t), was predicted from the in vitro profile through a nonlinear relationship. Rvivo(t) was used as the input of a compartmental PK model describing the in vivo serum concentration dynamics of progesterone. The proposed IVIVC P-ring model was able to correctly predict the in vivo concentration-time profiles of progesterone starting from the in vitro PVR release profiles. Its internal and external predictability was carefully evaluated considering the FDA acceptance criteria for IVIVC assessment of extended-release oral drugs. Obtained results justified the use of the in vitro release testing in lieu of clinical studies for the BE assessment of any new PVRs batches. Finally, the possible use of the developed population IVIVC model as a simulator of virtual BE trials was explored through a case study.

Insulin Pulse Characteristics and Insulin Action in Non-diabetic Humans.

OBJECTIVE: Pulsatile insulin secretion is impaired in diseases such as type 2 diabetes that are characterized by insulin resistance. This has led to the suggestion that changes in insulin pulsatility directly impair insulin signaling. We sought to examine the effects of pulse characteristics on insulin action in humans, hypothesizing that a decrease in pulse amplitude or frequency is associated with impaired hepatic insulin action. METHODS: We studied 29 nondiabetic subjects on two occasions. On 1 occasion, hepatic and peripheral insulin action was measured using a euglycemic clamp. The deuterated water method was used to estimate the contribution of gluconeogenesis to endogenous glucose production. On a separate study day, we utilized nonparametric stochastic deconvolution of frequently sampled peripheral C-peptide concentrations during fasting to reconstruct portal insulin secretion. In addition to measuring basal and pulsatile insulin secretion, we used approximate entropy to measure orderliness and Fourier transform to measure the average, and the dispersion of, insulin pulse frequencies. RESULTS: In univariate analysis, basal insulin secretion (R2 = 0.16) and insulin pulse amplitude (R2 = 0.09) correlated weakly with insulin-induced suppression of gluconeogenesis. However, after adjustment for age, sex, and weight, these associations were no longer significant. The other pulse characteristics also did not correlate with the ability of insulin to suppress endogenous glucose production (and gluconeogenesis) or to stimulate glucose disappearance. CONCLUSIONS: Overall, our data demonstrate that insulin pulse characteristics, considered independently of other factors, do not correlate with measures of hepatic and peripheral insulin sensitivity in nondiabetic humans.

Multinomial logistic estimation of Markov-chain models for modeling sleep architecture in primary insomnia patients.

Hypnotic drug development calls for a better understanding of sleep physiology in order to improve and differentiate novel medicines for the treatment of sleep disorders. On this basis, a proper evaluation of polysomnographic data collected in clinical trials conducted to explore clinical efficacy of novel hypnotic compounds should include the assessment of sleep architecture and its drug-induced changes. This work presents a non-linear mixed-effect Markov-chain model based on multinomial logistic functions which characterize the time course of transition probabilities between sleep stages in insomniac patients treated with placebo. Polysomnography measurements were obtained from patients during one night treatment. A population approach was used to describe the time course of sleep stages (awake stage, stage 1, stage 2, slow-wave sleep and REM sleep) using a Markov-chain model. The relationship between time and individual transition probabilities between sleep stages was modelled through piecewise linear multinomial logistic functions. The identification of the model produced a good adherence of mean post-hoc estimates to the observed transition frequencies. Parameters were generally well estimated in terms of CV, shrinkage and distribution of empirical Bayes estimates around the typical values. The posterior predictive check analysis showed good consistency between model-predicted and observed sleep parameters. In conclusion, the Markov-chain model based on multinomial logistic functions provided an accurate description of the time course of sleep stages together with an assessment of the probabilities of transition between different stages.

On the agreement between bibliometrics and peer review: Evidence from the Italian research assessment exercises.

This paper analyzes the concordance between bibliometrics and peer review. It draws evidence from the data of two experiments of the Italian governmental agency for research evaluation. The experiments were performed by the agency for validating the adoption in the Italian research assessment exercises of a dual system of evaluation, where some outputs were evaluated by bibliometrics and others by peer review. The two experiments were based on stratified random samples of journal articles. Each article was scored by bibliometrics and by peer review. The degree of concordance between the two evaluations is then computed. The correct setting of the experiments is defined by developing the design-based estimation of the Cohen's kappa coefficient and some testing procedures for assessing the homogeneity of missing proportions between strata. The results of both experiments show that for each research areas of science, technology, engineering and mathematics the degree of agreement between bibliometrics and peer review is-at most-weak at an individual article level. Thus, the outcome of the experiments does not validate the use of the dual system of evaluation in the Italian research assessments. More in general, the very weak concordance indicates that metrics should not replace peer review at the level of individual article. Hence, the use of the dual system in a research assessment might worsen the quality of information compared to the adoption of peer review only or bibliometrics only.

Diabetes-associated genetic variation in TCF7L2 alters pulsatile insulin secretion in humans.

BACKGROUNDMetabolic disorders such as type 2 diabetes have been associated with a decrease in insulin pulse frequency and amplitude. We hypothesized that the T allele at rs7903146 in TCF7L2, previously associated with ß cell dysfunction, would be associated with changes in these insulin pulse characteristics.METHODSTwenty-nine nondiabetic subjects (age 46 ± 2, BMI 28 ± 1 kg/m2) participated in this study. Of these, 16 were homozygous for the C allele at rs7903146 and 13 were homozygous for the T allele. Deconvolution of peripheral C-peptide concentrations allowed the reconstruction of portal insulin secretion over time. These data were used for subsequent analyses. Pulse orderliness was assessed by approximate entropy (ApEn), and the dispersion of insulin pulses was measured by a frequency dispersion index (FDI) after a Fast Fourier Transform (FFT) of individual insulin secretion rates.RESULTSDuring fasting conditions, the CC genotype group exhibited decreased pulse disorderliness compared with the TT genotype group (1.10 ± 0.03 vs. 1.19 ± 0.04, P = 0.03). FDI decreased in response to hyperglycemia in the CC genotype group, perhaps reflecting less entrainment of insulin secretion during fasting.CONCLUSIONDiabetes-associated variation in TCF7L2 is associated with decreased orderliness and pulse dispersion, unchanged by hyperglycemia. Quantification of ApEn and FDI could represent novel markers of ß cell health.FUNDINGThis work was funded by US NIH (DK78646, DK116231), University of Padova research grant CPDA145405, and Mayo Clinic General Clinical Research Center (UL1 TR000135).