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.

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.

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).

Citation gaming induced by bibliometric evaluation: A country-level comparative analysis.

It is several years since national research evaluation systems around the globe started making use of quantitative indicators to measure the performance of researchers. Nevertheless, the effects on these systems on the behavior of the evaluated researchers are still largely unknown. For investigating this topic, we propose a new inwardness indicator able to gauge the degree of scientific self-referentiality of a country. Inwardness is defined as the proportion of citations coming from the country over the total number of citations gathered by the country. A comparative analysis of the trends for the G10 countries in the years 2000-2016 reveals a net increase of the Italian inwardness. Italy became, both globally and for a large majority of the research fields, the country with the highest inwardness and the lowest rate of international collaborations. The change in the Italian trend occurs in the years following the introduction in 2011 of national regulations in which key passages of professional careers are governed by bibliometric indicators. A most likely explanation of the peculiar Italian trend is a generalized strategic use of citations in the Italian scientific community, both in the form of strategic author self-citations and of citation clubs. We argue that the Italian case offers crucial insights on the constitutive effects of evaluation systems. As such, it could become a paradigmatic case in the debate about the use of indicators in science-policy contexts.

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 .

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.

Model individualization for artificial pancreas.

BACKGROUND AND OBJECTIVE: The inter-subject variability characterizing the patients affected by type 1 diabetes mellitus makes automatic blood glucose control very challenging. Different patients have different insulin responses, and a control law based on a non-individualized model could be ineffective. The definition of an individualized control law in the context of artificial pancreas is currently an open research topic. In this work we consider two novel identification approaches that can be used for individualizing linear glucose-insulin models to a specific patient. METHODS: The first approach belongs to the class of black-box identification and is based on a novel kernel-based nonparametric approach, whereas the second is a gray-box identification technique which relies on a constrained optimization and requires to postulate a model structure as prior knowledge. The latter is derived from the linearization of the average nonlinear adult virtual patient of the UVA/Padova simulator. Model identification and validation are based on in silico data collected during simulations of clinical protocols designed to produce a sufficient signal excitation without compromising patient safety. The identified models are evaluated in terms of prediction performance by means of the coefficient of determination, fit, positive and negative max errors, and root mean square error. RESULTS: Both identification approaches were used to identify a linear individualized glucose-insulin model for each adult virtual patient of the UVA/Padova simulator. The resulting model simulation performance is significantly improved with respect to the performance achieved by a linear average model. CONCLUSIONS: The approaches proposed in this work have shown a good potential to identify glucose-insulin models for designing individualized control laws for artificial pancreas.

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.

Mathematical modeling of efficacy and safety for anticancer drugs clinical development.

INTRODUCTION: Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

Current mathematical models for cancer drug discovery.

INTRODUCTION: Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Histological effects of givinostat in boys with Duchenne muscular dystrophy.

Duchenne Muscular Dystrophy (DMD) is caused by mutations in the dystrophin gene leading to dystrophin deficiency, muscle fiber degeneration and progressive fibrotic replacement of muscles. Givinostat, a histone deacetylase (HDAC) inhibitor, significantly reduced fibrosis and promoted compensatory muscle regeneration in mdx mice. This study was conducted to evaluate whether the beneficial histological effects of Givinostat could be extended to DMD boys. Twenty ambulant DMD boys aged 7 to <11 years on stable corticosteroid treatment were enrolled in the study and treated for ≥12 months with Givinostat. A muscle biopsy was collected at the beginning and at the end of treatment to evaluate the amount of muscle and fibrotic tissue. Histological effects were the primary objectives of the study. Treatment with Givinostat significantly increased the fraction of muscle tissue in the biopsies and reduced the amount of fibrotic tissue. It also substantially reduced tissue necrosis and fatty replacement. Overall the drug was safe and tolerated. Improvement in functional tests was not observed in this study, but the sample size of the study was not sufficient to draw definitive conclusions. This study showed that treatment with Givinostat for more than 1 year significantly counteracted histological disease progression in ambulant DMD boys aged 7 to 10 years.

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.

Population pharmacokinetic model of ibrutinib, a Bruton tyrosine kinase inhibitor, in patients with B cell malignancies.

PURPOSE: Ibrutinib is an oral Bruton's tyrosine kinase inhibitor, recently approved for the treatment of mantle cell lymphoma (MCL) and chronic lymphocytic leukemia (CLL) patients with at least one prior therapy. We developed a population pharmacokinetic (PK) model for ibrutinib in patients. METHODS: Ibrutinib PK data (3,477 observations/245 patients) were available from the following clinical studies: (1) A phase I dose-escalation study in recurrent B cell malignancies (dose levels of 1.25-12.5 mg/kg/day and fixed dose of 560 mg/day); (2) a phase II study in MCL (fixed dose level of 560 mg/day); (3) a phase Ib/II dose-finding study in CLL (fixed dose levels of 420 and 840 mg/day). Different compartmental PK models were explored using nonlinear mixed effects modeling. RESULTS: A two-compartment PK model with sequential zero-first-order absorption and first-order elimination was able to characterize the PK of ibrutinib. The compound was rapidly absorbed, had a high oral plasma clearance (approximately 1,000 L/h) and a high apparent volume of distribution at steady state (approximately 10,000 L). PK parameters were not dependent on dose, study, or clinical indication. The fasting state was characterized by a 67 % relative bioavailability compared with the meal conditions used in the trials and administration after a high-fat meal. Body weight and coadministration of antacids marginally increased volume of distribution and duration of absorption, respectively. CONCLUSIONS: The proposed population PK model was able to describe the plasma concentration-time profiles of ibrutinib across various trials. The linear model indicated that the compound's PK was dose independent and time independent.

Population modelling of patient responses in antidepressant studies: a stochastic approach.

This paper addresses the problem of modelling longitudinal data describing patients' responses in clinical trials. In particular, a systematic approach relying on a system theoretic paradigm is proposed to deal with contexts where limited physiopathological knowledge is available on disease, drug response, and patients' characteristics. The model relies on the notion of patient's health state which summarizes the patient's condition. In order to cope with the limited number of clinical data usually available, the paper considers a very parsimonious realization where the two state variables are the clinical endpoint and its derivative. Within a population framework, the individual response is modelled as the sum of an individual shift and the average response of subjects belonging to the same study, both described as Markovian processes and identified by empirical Bayes techniques. The proposed approach is validated with experimental data from a Phase II, flexible-dose, depression trial. The dose changes due to the flexible-dose scheme are handled as perturbations on the state. The connection between inter-individual variability and model stability is evaluated showing that the introduction of stable poles helps to describe populations whose range of individual responses does not diverge with time. In this way, good individual fittings and visual predictive checks were obtained for the clinical data. The proposed analysis provides a systematic approach to semi-mechanistic modelling when a precise knowledge of the physiological mechanisms of the disease is incomplete or missing.