Assessing drug effect from distributional data: A population approach with application to Duchenne Muscular Dystrophy treatment.

BACKGROUND AND OBJECTIVE: In Duchenne Muscular Dystrophy (DMD) treatment, muscle fiber size can be considered as an indicator of muscle health and function. In particular, the statistical distribution of fibers cross-sectional areas (CSAs) has been used as quantitative efficacy endpoint. For each patient, assessment of treatment effect relies on the comparison of pre- and post-treatment biopsies. Since biopsies provide "distributional data", i.e. empirical distributions of fibers CSA, the comparison must be carried out between the empirical pre- and post-treatment distributions. METHODS: Here, distributional fiber CSA data are analyzed by means of a hierarchical statistical model based on the population approach, considering both the single patient and the population level. RESULTS: The proposed method was used to assess the histological clinical effects of Givinostat, a compound under study for DMD treatment. At the single patient level, a two-component Gaussian mixture adequately represents pre- and post-treatment distributions of log-transformed CSAs; drug effect is described via a dose-dependent multiplicative increase of muscle fiber size. The single patient model was also validated via muscle composition data. At the patient population level, typical model parameters and inter-patient variabilities were obtained. CONCLUSIONS: The proposed methodological approach completely characterizes fiber CSA distributions and quantifies drug effect on muscle fiber size, both at the single patient and at the patient population level. This approach might be applied also in other contexts, where outcomes measured in terms of distributional data are to be assessed.

The GHRH + arginine stimulated pituitary GH secretion in children and adults with Prader-Willi syndrome shows age- and BMI-dependent and genotype-related differences.

OBJECTIVE: The quantitative and qualitative aspects of the pituitary response in children and adults with Prader-Willi syndrome (PWS) are compared in order to verify the possible age-dependent and genotype-related differences in terms of GH secretion. DESIGN: 29 young subjects (21 males and 8 females) and 65 adults (24 males and 41 females) with PWS were studied. All subjects underwent a standard GH Releasing Hormone (GHRH 1-29, 1 µg/kg as i.v. bolus at 0 minutes)+arginine (0.5 g/kg) test. Peak GH values, standard GH area under the curve (AUC), AUC of the instantaneous secretion rate (ISR), and secretion response analysis (i.e. half-secretion time) were evaluated. A regression analysis was performed to investigate which are the patient characteristics that affect the amplitude and shape of the GH secretion response. RESULTS: Peak GH values and AUCGH were significantly higher in PWS children than in PWS adults, these differences being also significant both in PWS DEL15 (only peak GH value) and PWS UPD15. Moreover, PWS children showed significantly lower half secretion time than PWS adults, this delayed response being present both in PWS DEL15 and PWS UPD15. Significant negative correlations between AUCGH and BMISDS were observed in the two groups (adults and children), as well as in adults and children DEL15, but not in adults and children PWS UPD15. A regression analysis performed on the whole dataset showed that for PWS DEL15 the statistically significant variable explaining GH responsiveness was BMISDS (p<0.0001), while for UPD15 no statistically significant covariate was found. Conversely, when the delay of the secretion response was considered, the regression model yielding the best performances was the one with only age as a regressor (p<0.001). CONCLUSIONS: The quantitative and qualitative analyses of GH responsiveness to GHRH+arginine highlight relevant differences between PWS children and PWS adults and genotype-related traits. The negative influence of BMISDS on GH secretion reinforces the need for an early start of life-long weight management in PWS subjects.

A minimal model of tumor growth inhibition in combination regimens under the hypothesis of no interaction between drugs.

One important issue in the preclinical development of an anticancer drug is the assessment of the compound under investigation when administered in combination with other drugs. Several experiments are routinely conducted in xenograft mice to evaluate if drugs interact or not. Experimental data are generally qualitatively analyzed on empirical basis. The ability of deriving from single drug experiments a reference response to the joint administrations, assuming no interaction, and comparing it to real responses would be key to recognize synergic and antagonist compounds. Therefore, in this paper, the minimal model of tumor growth inhibition (TGI), previously developed for a single drug, is reformulated to account for the effects of noninteracting drugs and simulate, under this hypothesis, combination regimens. The model is derived from a minimal set of basic assumptions that include and extend those formulated at cellular level for the single drug administration. The tumor growth dynamics is well approximated by the deterministic evolution of its expected value that is obtained through the solution of an ordinary and several partial differential equations. Under suitable assumptions on the cell death process, the model reduces to a lumped parameter model that represents the extension of the very popular Simeoni TGI model to the combined administration of noninteracting drugs.

Joint modeling of efficacy, dropout, and tolerability in flexible-dose trials: a case study in depression.

Many difficulties may arise during the modeling of the time course of Hamilton Rating Scale for Depression (HAM D)scores in clinical trials for the evaluation of antidepressant drugs: (i) flexible designs, used to increase the chance of selecting more efficacious doses, (ii) dropout events, and (iii) adverse effects related to the experimental compound.It is crucial to take into account all these factors when designing an appropriate model of the HAM D time course and to obtain a realistic description of the dropout process. In this work, we propose an integrated approach to the modeling of a double-blind, flexible-dose, placebo-controlled, phase II depression trial that comprises response,tolerability, and dropout. We investigate three different dropout mechanisms in terms of informativeness. Goodness of fit is quantitatively assessed with respect to response (HAM D score) and dropout data. We show that dropout is a complex phenomenon that may be influenced by HAM D evolution, dose changes, and occurrence of drug-related adverse effects.

Modular closed-loop control of diabetes.

Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called "artificial pancreas," modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic components, starting with subsystems for assured patient safety and followed by higher layer components that serve to modify the patient's basal rate in real time. In this paper, we introduce a three-layer modular architecture for the control of diabetes, consisting in a sensor/pump interface module (IM), a continuous safety module (CSM), and a real-time control module (RTCM), which separates the functions of insulin recommendation (postmeal insulin for mitigating hyperglycemia) and safety (prevention of hypoglycemia). In addition, we provide details of instances of all three layers of the architecture: the APS© serving as the IM, the safety supervision module (SSM) serving as the CSM, and the range correction module (RCM) serving as the RTCM. We evaluate the performance of the integrated system via in silico preclinical trials, demonstrating 1) the ability of the SSM to reduce the incidence of hypoglycemia under nonideal operating conditions and 2) the ability of the RCM to reduce glycemic variability.

A new neural network approach for short-term glucose prediction using continuous glucose monitoring time-series and meal information.

In the last decade, improvements in diabetes daily management have become possible thanks to the development of minimally-invasive portable sensors which allow continuous glucose monitoring (CGM) for several days. In particular, hypo and hyperglycemia can be promptly detected when glucose exceeds the normal range thresholds, and even avoided through the use of on-line glucose prediction algorithms. Several algorithms with prediction horizon (PH) of 15-30-45 min have been proposed in the literature, e.g. including AR/ARMA time-series modeling and neural networks. Most of them are fed by CGM signals only. The purpose of this work is to develop a new short-term glucose prediction algorithm based on a neural network that, in addition to past CGM readings, also exploits information on carbohydrates intakes quantitatively described through a physiological model. Results on simulated data quantitatively show that the new method outperforms other published algorithms. Qualitative preliminary results on a real diabetic subject confirm the potentialities of the new approach.

Testing additivity of anticancer agents in pre-clinical studies: a PK/PD modelling approach.

In clinical oncology, combination regimens may result in a synergistic, additive or antagonistic interaction (i.e. the effect of the combination is greater, similar or smaller than the sum of the effects of the individual compounds). For this reason, during the drug development process, in vivo pre-clinical studies are performed to assess the interaction of anticancer agents given in combination. Starting from a widely used single compound PK/PD model, a new additivity model able to predict the tumour growth inhibition in xenografted mice after the administration of compounds in combination was developed, under the assumption of a pharmacodynamic null interaction. By comparing the predicted curves with actual tumour weight data, possible departures from additivity can be immediately ascertained by visual inspection; a statistical procedure based on a chi(2) test has also been developed for this aim. The advantages of the proposed approach in comparison to other modelling methodologies are discussed and its application to four combination studies is presented.

Predicting the active doses in humans from animal studies: a novel approach in oncology.

The success rate of clinical drug development is significantly lower in oncology than in other therapeutic areas. Predicting the activity of new compounds in humans from preclinical data could substantially reduce the number of failures. A novel approach for predicting the expected active doses in humans from the first animal studies is presented here. The method relies upon a PK/PD model of tumour growth inhibition in xenografts, which provides parameters describing the potency of the tested compounds. Anticancer drugs, currently used in the clinic, were evaluated in xenograft models and their potency parameters were estimated. A good correlation was obtained between these parameters and the exposures sustained at the therapeutically relevant dosing regimens. Based on the corresponding regression equation and the potency parameters estimated in the first preclinical studies, the therapeutically active concentrations of new compounds can be estimated. An early knowledge of level of exposure or doses to be reached in humans will improve the risk evaluation and decision making processes in anticancer drug development.

A mathematical model to study the effects of drugs administration on tumor growth dynamics.

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.

Nonparametric AUC estimation in population studies with incomplete sampling: a Bayesian approach.

The estimation of the AUC in a population without frequent and/or fixed individual samplings is of interest because the number of plasma samples can often be limited due to technical, ethical and cost reasons. Non-linear mixed effect models can provide both population and individual estimates of AUC based on sparse sampling protocols; however, appropriate structural models for the description of the pharmacokinetics are required. Nonparametric solutions have also been proposed to estimate the population AUC and the associated error when particular sampling protocols are adopted. However, they do not estimate the individual AUCs and lack flexibility. Also a semiparametric method has been proposed for addressing the problem of sparse sampling in reasonably well designed studies. In this work, we propose and evaluate a nonparametric Bayesian scheme for AUC estimation in population studies with arbitrary sampling protocols. In the stochastic model representing the whole population, the individual plasma concentration curves and the "mean" population curve are described by random walk processes, allowing the application of the method to the reconstruction of any kind of "regular" curves. Population and individual AUC estimation are performed by numerically computing the posterior expectation through a Markov chain Monte Carlo algorithm.

Regularization networks: fast weight calculation via Kalman filtering.

Regularization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. Their main drawback back is that the computation of the weights scales as O(n(3)) where n is the number of data. In this paper, we show that for a class of monodimensional problems, the complexity can be reduced to O(n) by a suitable algorithm based on spectral factorization and Kalman filtering. Moreover, the procedure applies also to smoothing splines.

Stimulated secretion of pituitary hormones in normal humans: a novel direct assessment from blood concentrations.

Gland responsiveness is usually assessed by administering suitable secretagogues and measuring the resulting hormone concentration in blood after the specific stimulus. Such response-to-stimulus tests are routinely conducted for the clinical diagnosis of pathologies involving the pituitary hormones growth hormone, prolactin, luteinizing hormone, follicle stimulating hormone, adrenocorticotropic hormone, and thyrotropin hormone. However, the current evaluation approaches, based on the maximum peak value or the (normalized) area under the curve, are inadequate under several respects. A more physiologically based index of responsiveness is the amount of released hormone. This is not directly accessible but is typically estimated by (computationally expensive) deconvolution analysis. The present work derives a simple formula yielding the amount of released hormone as a linear combination of blood concentrations through proper weights depending on hormone kinetics and sampling protocol. The weights are derived and reported for all six pituitary hormones and the more common sampling protocols. A validation study involving 174 test experiments has been carried out. The use of the formula shows excellent agreement with the cumulative secretion estimates obtained through deconvolution analysis.

Bayesian analysis of blood glucose time series from diabetes home monitoring.

This paper describes the application of a novel Bayesian estimation technique to extract the structural components, i.e., trend and daily patterns, from blood glucose level time series coming from home monitoring of insulin dependent diabetes mellitus patients. The problem is formulated through a set of stochastic equations, and is solved in a Bayesian framework by using a Markov chain Monte Carlo technique. The potential of the method is illustrated by analyzing data coming from the home monitoring of a 14-year old male patient.

Abnormal LH pulsatility in women with hyperprolactinaemic amenorrhoea normalizes after bromocriptine treatment: deconvolution-based assessment.

OBJECTIVE: The present study examines the LH secretory process in hyperprolactinaemic women before, during and after bromocriptine therapy, using restrictive clinical selection criteria as well as improved methodological tools. PATIENTS AND DESIGN: Six women (aged 20-40 years) with microprolactinomas (mean +/- SE prolactin, PRL: 2478 +/- 427 mU/l, range: 1370-3800 mU/l) and four age- and sex-matched healthy controls were admitted to the study. After an overnight fast, all patients and controls had blood samples withdrawn at 10 minute intervals for 6 h (during saline infusion) from 0800 h to 1400 h to determine serum LH and PRL concentrations. After baseline evaluation, patients were treated with bromocriptine, which was started at a daily dose of 1.25 mg for 7 days; the dose was then increased to 2.5 mg daily for the next 7 days and subsequently to 2.5 mg twice daily. PRL levels were evaluated at weekly intervals after the beginning of bromocriptine therapy for the duration of the study. The 6 h pulsatility study was repeated on four patients during treatment at a time when PRL levels were decreased, although not normalized (PRL range: 450-1350 mU/l) and, on four patients, with the attainment of normal serum PRL levels (PRL < 450 mU/l) in the early follicular phase of the menstrual cycle (days 2-5). The LH instantaneous secretion rate was reconstructed by a nonparametric deconvolution method. In addition to pulse analysis made using the program DETECT, the evaluation of the secretion rate yielded the pulse frequency as well as the pulse amplitude distribution. RESULTS: Each time series was submitted to deconvolution analysis using a nonparametric method in order to estimate the instantaneous secretion rate (ISR). Hyperprolactinaemic patients had very few high-amplitude LH pulses above 0.2 IU/(l minutes) before treatment (average frequency: 0.83 +/- 0.40 pulses/6 h) and at the intermediate evaluation (0.25 +/- 0.25 pulses/6 h). In both cases, the pulse frequency was significantly lower than in controls (P < 0.05 and P < 0.01, respectively). When PRL was normalized, the number of high-amplitude LH pulses (4.25 +/- 1.03 pulses/6 h), became statistically different from the pulse number before (P < 0.01) and during (P < 0.01) therapy; in particular the pulse frequency after therapy rose to a level not statistically different from that in controls. CONCLUSION: The present study shows the presence of reduced LH pulsatility in hyperprolactinaemic women that recovers completely to within the physiological distribution when PRL levels are normalized by bromocriptine therapy.

LH and FSH secretory responses to GnRH in normal individuals: a non-parametric deconvolution approach.

OBJECTIVE: To reconstruct the instantaneous secretion rate (ISR) of LH and FSH after GnRH administration in normal volunteers using non-parametric deconvolution, and to derive a direct integration formula to evaluate the amount of LH and FSH secreted during the first 60 min after the stimulus. DESIGN AND METHODS: First, the deconvolution method was validated in vivo by reconstructing doses ranging from 7.5 IU to 75 IU injected in three healthy adult volunteers whose endogenous LH had previously been downregulated by pretreating them, 3-4 weeks earlier, with 3.75 mg GnRH agonist i.m. Then, 40 healthy adult male volunteers were tested with a single 100 microg GnRH bolus, administered at 0 min. LH and FSH concentrations were determined at -30, 0, 15, 30, 45, 60, 90, and 120 min. RESULTS AND CONCLUSIONS: The validation study, conducted over a 10-fold range of doses, demonstrated that non-parametric deconvolution provided a reasonably accurate estimate of the amount of hormone entering the circulation. Applying deconvolution to the LH and FSH responses to GnRH, the ISRs of both hormones were shown to have a similar pattern, with a clearly delimited pulse after the GnRH bolus. In conjunction with earlier analyses of estimates of GHRH-stimulated GH secretion, we conclude that secretagogues evoke discrete LH, FSH, and GH secretory bursts of about 60 min total duration, despite markedly unequal (glyco-)protein hormone half-lives (18-500 min). With respect to the assessment of total hormone release during the first 60 min after the stimulus, the integration formula provided a reliable approximation of the result obtained by deconvolution, and had a negligible dependence on the samples at times 90 and 120 min.

Mining biomedical time series by combining structural analysis and temporal abstractions.

This paper describes the combination of Structural Time Series analysis and Temporal Abstractions for the interpretation of data coming from home monitoring of diabetic patients. Blood Glucose data are analyzed by a novel Bayesian technique for time series analysis. The results obtained are post-processed using Temporal Abstractions in order to extract knowledge that can be exploited "at the point of use" from physicians. The proposed data analysis procedure can be viewed as a Knowledge Discovery in Data Base process that is applied to time-varying data. The work here described is part of a Web-based telemedicine system for the management of Insulin Dependent Diabetes Mellitus patients, called T-IDDM.

Non-parametric deconvolution provides an objective assessment of GH responsiveness to GH-releasing stimuli in normal subjects.

OBJECTIVE: Deconvolution analysis has been proposed as an effective method for analysing the physiology of GH secretion. In the literature, it has been applied to spontaneous secretion data characterized by long and uniform sampling paradigms. In the present study we investigated the applicability of non-parametric deconvolution to the analysis of response-to-stimuli (RTS) data characterized by infrequent and non-uniform sampling. PATIENTS: Thirty-six healthy adult male volunteers (age range 24-37 years) were randomly subdivided into two groups (group I, n = 30; group II, n = 6). DESIGN: Subjects of group I were tested with a single 1 microgram/kg body weight GH-releasing hormone (GHRH) bolus, administered at 0 minutes. Subjects of group II were tested, in random order, with a 4- or 5-day interval, with (1) two consecutive 1 microgram/kg body weight GHRH boluses at 0 and 120 minutes and (2) two consecutive 1 microgram/kg body weight hexarelin boluses, administered at 0 and 120 minutes. MEASUREMENTS: GH levels were determined at 0, 15, 30, 45, 60, 90 and 120 minutes (group I) and -30, 0, 15, 30, 45, 60, 120, 135, 150, 165, 180 and 240 minutes (group II). A numerically efficient regularization-based non-parametric deconvolution algorithm incorporating non-negativity constraints was used to estimate the time profile of the instantaneous secretion rate (ISR). Confidence limits allowing for both measurement error and kinetic model uncertainty were computed using a Monte-Carlo procedure. In order to validate the deconvolution method, a simulated benchmark problem was set up. RESULTS: The analysis of the benchmark problem showed that the proposed method is capable of providing an accurate reconstruction of the ISR (as measured by the root mean square (RMS) error). Moreover, it appeared that reliable confidence limits cannot be obtained unless the kinetic model uncertainty is taken into account. The analysis of the data showed a clear rise in the ISR subsequent to the first bolus (either GHRH or hexarelin), with most of the response occurring within 60 minutes of the stimulus. In group I, it was also seen that discarding the samples collected at times 90 and 120 minutes only marginally affected the estimate of the cumulated ISR over 0-60 minutes (the variation was always less than 3%). The analysis of GH responsiveness to repeated stimuli (group II) showed that the amount of hormone secreted after the second bolus was clearly reduced in comparison with the elicited by the first stimulus, most of the response occurring within 60 minutes of the injection. The amount of GH secreted after the second stimulus ranged from 13 to 36% (GHRH 17-36%; hexarelin 13-36%) of the overall amount of hormone secreted after time 0 minutes. CONCLUSIONS: Even with relatively few samples, non-parametric deconvolution of response-to-stimulus data is capable of providing a reliable, smooth and non-negative estimate of the GH instantaneous secretion rate that offers a realistic representation of the GH secretory dynamics. The non-parametric approach compares favourably with respect to discrete deconvolution methods, that yield discontinuous instantaneous secretion rates profiles, and parametric methods that would require more stringent assumptions on the shape of the instantaneous secretion rate. When assessing confidence limits it is essential to take into account both measurement error and kinetic model uncertainty. Using deconvolution in normal subjects, the estimated instantaneous secretion rate between 0 and 60 minutes is scarcely affected by samples taken after time 60 minutes. Since most of the secretory response takes place during this time interval, there is motivation for investigating the use of shorter sampling protocols in conjunction with deconvolution analysis. Although pulse detection and the assessment of the shape of spontaneous pulses have not been investigated, it could be interesting to apply non-parametric deconvolution to spontaneous sec

Adaptive controllers for intelligent monitoring.

The project we describe here is aimed at assisting out-patients affected by Insulin Dependent Diabetes Mellitus. Our approach exploits the usual scheme of diabetic patients management, based on (i) a periodic evaluation of patients' metabolic control performed by the physician, and (ii) patient-tailored tables for self-adjustments of insulin dosages. Following this scheme we have defined a system built on a two-level architecture. The High Level Module exploits both medical knowledge and clinical information in order to assess an insulin protocol, defined in terms of insulin timing, type, and total amount. The High Level Module exchanges information with the Low Level Module in order to define the control actions to be taken at the low level, as well as to periodically evaluate protocol adequacy on the basis of patient data. The goal of the Low Level Module, whose characteristics can be adaptively modified by the High Level Module, is to suggest the next insulin dosage, depending on the actual blood glucose measurement and a certain pre-defined insulin delivery protocol. The Level Control Module is based on an adaptive controller, consisting of a Fuzzy Set Controller and an ARX (Autoregressive eXogenous input) Model. The scheme here presented may be conveniently viewed in a telemedicine context, in which the low level controller is implemented on a portable device communicating to the high level controller, implemented on a remote computer. A preliminary assessment has been performed, analyzing a data set of 60 patients provided by the American Association of Artificial Intelligence, Artificial Intelligence in Medicine Subgroup, and the implementation of the system is currently in progress.

WENDEC: a deconvolution program for processing hormone time-series.

The estimation of the glandular secretory rate from time-series of hormone concentration in plasma can be formulated as a deconvolution problem. In particular, the paper addresses the analysis of frequently sampled data collected in order to study spontaneous pulsatile secretion. Standard deconvolution methods do not allow for the non-negativity constraint and the presence of high-frequency components in the secretory rate. In order to overcome the intrinsic ill-conditioning of the problem, the maximum entropy method is used to obtain a probabilistic representation of the prior knowledge concerning the unknown secretory signal, thus leading to a White Exponential Noise (WEN) model. The deconvolution problem is then posed within a Bayesian framework and solved by means of Maximum-A-Posteriori estimation. The program that implements the algorithm handles non-negativity constraints, provides confidence intervals, and is computationally and memory efficient.

Deconvolution of infrequently sampled data for the estimation of growth hormone secretion.

In this paper, the deconvolution of infrequently and nonuniformly sampled data is addressed. A nonparametric technique is worked out that provides a smooth estimate of the unknown input signal and takes into account nonnegativity constraints. In spite of the size of the problem, efficient algorithms for solving the constrained optimization problem and computing confidence intervals are proposed. The new technique is used to estimate growth hormone (GH) secretion after repeated GH-releasing hormone (GHRH) administration from samples of blood concentration.