Title: Polynomial (ordinary differential equation) Model Search
Author: Mangiarotti S., Coudret R., Drapeau L.
Description: PoMoS-package aims to determine from a set of N time
series the optimal polynomial structure of a model built on
first-order ordinary differential equations. The core of the
package is based on the poMoS function: an evolutionary
algorithm combined with a least square fitting. Optimality is
estimated with AIC (Akaike, 1974) or AIC-like criterions.
Although efficient in its selection, the identification of the
optimal structure cannot be guaranteed. Therefore, both
selected and rejected models are reconsidered after optimal
solutions are obtained from the evolutionary algorithm for
another analysis. This analysis is based on a statistical

Title: Posterior Predictive (PoP) Design for Phase I Clinical Trials
Description: The primary goal of phase I clinical trials is to find the maximum tolerated dose (MTD). To reach this objective, we introduce a new design for phase I clinical trials, the posterior predictive (PoP) design. The PoP design is an innovative model-assisted design that is easy to implement in a manner similar to the traditional 3+3 design, as its decision rules can be pre-tabulated prior to the onset of trial, but is of more flexibility of selecting diverse target toxicity rates and cohort sizes. The PoP design has desirable properties, such as coherence and consistency. Moreover, the PoP design provides better performance than the BOIN and Keyboard design with respect to high average probabilities of choosing the MTD and slightly lower risk of treating patients at subtherapeutic or overly toxic doses. Reference: Brunk, H., Barlow, R. E., Bartholomew, D. J. & Bremner, J. M (1972, ISBN-13: 978-0471049708).

Description: The primary goal of phase I clinical trials is to find the maximum tolerated dose (MTD). To reach this objective, we introduce a new design for phase I clinical trials, the posterior predictive (PoP) design. The PoP design is an innovative model-assisted design that is as simply as the conventional algorithmic designs as its decision rules can be pre-tabulated prior to the onset of trial, but is of more flexibility of selecting diverse target toxicity rates and cohort sizes. The PoP design has desirable properties, such as coherence and consistency. Moreover, the PoP design provides better empirical performance than the BOIN and Keyboard design with respect to high average probabilities of choosing the MTD and slightly lower risk of treating patients at subtherapeutic or overly toxic doses.