Reaction-diffusion waves of blood coagulation.

One of the main characteristics of blood coagulation is the speed of clot growth. In the current work we consider a mathematical model of the coagulation cascade and study existence, stability and speed of propagation of the reaction-diffusion waves of blood coagulation. We also develop a simplified one-equation model that reflects the main features of the thrombin wave propagation. For this equation we estimate the wave speed analytically. The resulting formulas provide a good approximation for the speed of wave propagation in a more complex model as well as for the experimental data.

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.

A methodological framework for drug development in rare diseases.

INTRODUCTION: Developing 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 OBJECTIVES: The 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 APPROACH: In 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. CONCLUSION: There 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.

Experimental designs for small randomised clinical trials: an algorithm for choice.

BACKGROUND: Small 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. METHODS: PubMed 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. RESULTS: We 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. CONCLUSIONS: The 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.