Polina Kurbatova

Experimental designs for small randomised clinical trials: An algorithm for choice

BackgroundSmall clinical trials are necessary when there are difficulties in recruiting enough patients for conventional frequentist statistical analyses to provide an appropriate answer. These trials are often necessary for the study of rare diseases as well as specific study populations e.g. children. It has been estimated that there are between 6,000 and 8,000 rare diseases that cover a broad range of diseases and patients. In the European Union these diseases affect up to 30 million people, with about 50% of those affected being children. Therapies for treating these rare diseases need their efficacy and safety evaluated but due to the small number of potential trial participants, a standard randomised controlled trial is often not feasible. There are a number of alternative trial designs to the usual parallel group design, each of which offers specific advantages, but they also have specific limitations. Thus the choice of the most appropriate design is not simple.MethodsPubMed was searched to identify publications about the characteristics of different trial designs that can be used in randomised, comparative small clinical trials. In addition, the contents tables from 11 journals were hand-searched. An algorithm was developed using decision nodes based on the characteristics of the identified trial designs.ResultsWe identified 75 publications that reported the characteristics of 12 randomised, comparative trial designs that can be used in for the evaluation of therapies in orphan diseases. The main characteristics and the advantages and limitations of these designs were summarised and used to develop an algorithm that may be used to help select an appropriate design for a given clinical situation. We used examples from publications of given disease-treatment-outcome situations, in which the investigators had used a particular trial design, to illustrate the use of the algorithm for the identification of possible alternative designs.ConclusionsThe algorithm that we propose could be a useful tool for the choice of an appropriate trial design in the development of orphan drugs for a given disease-treatment-outcome situation.

Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage

The production and regulation of red blood cells, erythropoiesis, occurs in the bone marrow where erythroid cells proliferate and differentiate within particular structures, called erythroblastic islands. A typical structure of these islands consists of a macrophage (white cell) surrounded by immature erythroid cells (progenitors), with more mature cells on the periphery of the island, ready to leave the bone marrow and enter the bloodstream. A hybrid model, coupling a continuous model (ordinary differential equations) describing intracellular regulation through competition of two key proteins, to a discrete spatial model describing cell-cell interactions, with growth factor diffusion in the medium described by a continuous model (partial differential equations), is proposed to investigate the role of the central macrophage in normal erythropoiesis. Intracellular competition of the two proteins leads the erythroid cell to either proliferation, differentiation, or death by apoptosis. This approach allows considering spatial aspects of erythropoiesis, involved for instance in the occurrence of cellular interactions or the access to external factors, as well as dynamics of intracellular and extracellular scales of this complex cellular process, accounting for stochasticity in cell cycle durations and orientation of the mitotic spindle. The analysis of the model shows a strong effect of the central macrophage on the stability of an erythroblastic island, when assuming the macrophage releases pro-survival cytokines. Even though it is not clear whether or not erythroblastic island stability must be required, investigation of the model concludes that stability improves responsiveness of the model, hence stressing out the potential relevance of the central macrophage in normal erythropoiesis.

Hybrid Model of Erythropoiesis and Leukemia Treatment with Cytosine Arabinoside

A hybrid model of cell population dynamics, where cells are discrete elements whose dynamics depend on continuous intracellular and extracellular processes, is developed to simulate the evolution of immature red blood cells in the bone marrow. Cell differentiation, self-renewal or apoptosis are determined by an intracellular network, based on two proteins, Erk and Fas, and described by ordinary differential equations, and by local extracellular regulation performed by Fas- ligand, a protein produced by mature cells whose concentration evolution is represented by a partial differential equation. The model is used to study normal and leukemic red blood cell production (erythropoiesis), and treatment of leukemia. Normal cells are assumed to have a circadian rhythm that influences their cell cycle progression, whereas leukemic cells, are assumed to escape circadian rhythms. We consider a treatment based on periodic administration of Ara-C, an anti-cancer agent targeting cells in DNA synthesis. A detailed pharmacodynamic/pharmacokinetic model of Ara-C is proposed and used to simulate the treatment. Influence of the period of the treatment and the day delivery time on the outcome of the treatment is investigated and stress the relevance of considering chronotherapeutic treatments to treat leukemia.

Hybrid Model of Erythropoiesis

A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.

A methodological framework for drug development in rare diseases.

IntroductionDeveloping orphan drugs is challenging because of their severity and the requisite for effective drugs. The small number of patients does not allow conducting adequately powered randomized controlled trials (RCTs). There is a need to develop high quality, ethically investigated, and appropriately authorized medicines, without subjecting patients to unnecessary trials.Aims and ObjectivesThe main aim is to develop generalizable framework for choosing the best-performing drug/endpoint/design combinations in orphan drug development using an in silico modeling and trial simulation approach. The two main objectives were (i) to provide a global strategy for each disease to identify the most relevant drugs to be evaluated in specific patients during phase III RCTs, (ii) and select the best design for each drug to be used in future RCTs.Methodological approachIn silico phase III RCT simulation will be used to find the optimal trial design and was carried out in two steps: (i) statistical analysis of available clinical databases and (ii) integrative modeling that combines mathematical models for diseases with pharmacokinetic-pharmacodynamics models for the selected drug candidates.ConclusionThere is a need to speed up the process of orphan drug development, develop new methods for translational research and personalized medicine, and contribute to European Medicines Agency guidelines. The approach presented here offers many perspectives in clinical trial conception.

Multi-Agent Systems and Blood Cell Formation

The objective of this chapter is to give an insight of the mathematical modellng of hematopoiesis using multi-agent systems. Several questions may arise then: what is hematopoiesis and why is it interesting to study this problem from a mathematical point of view? Has the multi-agent system approach been the only attempt done until now? What does it bring more than other techniques? What were the results obtained? What is there left to do?

Model of mucociliary clearance in cystic fibrosis lungs

Mucus clearance is a primary innate defense mechanism in the human airways. Cystic fibrosis (CF) is a genetic disease caused by mutations in the gene encoding the cystic fibrosis transmembrane conductance regulator (CFTR) protein. CF is characterized by dehydration of airway surface liquid and impaired mucociliary clearance. As a result, microorganisms are not efficiently removed from the airways, and patients experience chronic pulmonary infections and inflammation. We propose a new physiologically based mathematical model of muco-ciliary transport consisting of the two major components of the mucociliary clearance system: (i) periciliary liquid layer (PCL) and (ii) mucus layer. We study mucus clearance under normal conditions and in CF patients. Restoring impaired clearance of airway secretions in one of the major goals of therapy in patients with CF. We consider the action of the aerosolized and inhaled medication dornase alfa, which reduces the viscosity of cystic fibrosis mucus, by selectively cleaving the long DNA strands it contains. The results of the model simulations stress the potential relevance of the location of the drug deposition in the central or peripheral airways. Mucus clearance was increased in case the drug was primarily deposited peripherally, i.e. in the small airways.

An in silico approach helped to identify the best experimental design, population, and outcome for future randomized clinical trials.

OBJECTIVES The main objective of our work was to compare different randomized clinical trial (RCT) experimental designs in terms of power, accuracy of the estimation of treatment effect, and number of patients receiving active treatment using in silico simulations. STUDY DESIGN AND SETTING A virtual population of patients was simulated and randomized in potential clinical trials. Treatment effect was modeled using a dose-effect relation for quantitative or qualitative outcomes. Different experimental designs were considered, and performances between designs were compared. One thousand clinical trials were simulated for each design based on an example of modeled disease. RESULTS According to simulation results, the number of patients needed to reach 80% power was 50 for crossover, 60 for parallel or randomized withdrawal, 65 for drop the loser (DL), and 70 for early escape or play the winner (PW). For a given sample size, each design had its own advantage: low duration (parallel, early escape), high statistical power and precision (crossover), and higher number of patients receiving the active treatment (PW and DL). CONCLUSION Our approach can help to identify the best experimental design, population, and outcome for future RCTs. This may be particularly useful for drug development in rare diseases, theragnostic approaches, or personalized medicine.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.