A filtered polynomial approach to density estimation

In this paper, a little known computational approach to density estimation based on filtered polynomial approximation is investigated. It is accompanied by the first online available density estimation computer program based on a filtered polynomial approach. The approximation yields the unknown distribution and density as the product of a monotonic increasing polynomial and a filter. The filter may be considered as a target distribution which gets fixed prior to the estimation. The filtered polynomial approach then provides coefficient estimates for (close) algebraic approximations to (a) the unknown density function and (b) the unknown cumulative distribution function as well as (c) a transformation (e.g., normalization) from the unknown data distribution to the filter. This approach provides a high degree of smoothness in its estimates for univariate as well as for multivariate settings. The nice properties as the high degree of smoothness and the ability to select from different target distributions are suited especially in MCMC simulations. Two applications in Sects. 1 and 7 will show the advantages of the filtered polynomial approach over the commonly used kernel estimation metho

Integrating Phase 2 into Phase 3 based on an Intermediate Endpoint While Accounting for a Cure Proportion -- with an Application to the Design of a Clinical Trial in Acute Myeloid Leukemia

For a trial with primary endpoint overall survival for a molecule with curative potential, statistical methods that rely on the proportional hazards assumption may underestimate the power and the time to final analysis. We show how a cure proportion model can be used to get the necessary number of events and appropriate timing via simulation. If Phase 1 results for the new drug are exceptional and/or the medical need in the target population is high, a Phase 3 trial might be initiated after Phase 1. Building in a futility interim analysis into such a pivotal trial may mitigate the uncertainty of moving directly to Phase 3. However, if cure is possible, overall survival might not be mature enough at the interim to support a futility decision. We propose to base this decision on an intermediate endpoint that is sufficiently associated with survival. Planning for such an interim can be interpreted as making a randomized Phase 2 trial a part of the pivotal trial: if stopped at the interim, the trial data would be analyzed and a decision on a subsequent Phase 3 trial would be made. If the trial continues at the interim then the Phase 3 trial is already underway. To select a futility boundary, a mechanistic simulation model that connects the intermediate endpoint and survival is proposed. We illustrate how this approach was used to design a pivotal randomized trial in acute myeloid leukemia, discuss historical data that informed the simulation model, and operational challenges when implementing it.Comment: 23 pages, 3 figures, 3 tables. All code is available on github: https://github.com/numbersman77/integratePhase2.gi

Extinction times in multitype Markov branching processes

In this paper, a distributional approximation to the time to extinction in a subcritical continuous-time Markov branching process is derived. A limit theorem for this distribution is established and the error in the approximation is quantified. The accuracy of the approximation is illustrated in an epidemiological example. Since Markov branching processes serve as approximations to nonlinear epidemic processes in the initial and final stages, our results can also be used to describe the time to extinction for such processes

A mechanistic individual-based two-host interaction model for the transmission of a parasitic disease

A mechanistic individual-based model for the infection dynamics of the parasite Echinococcus granulosus in a two host transmission system is proposed. The model describes the individual densities of the parasites in the two host populations. The architecture consists of two sub-processes for the acquisition and severity of infection in the host populations and a superimposed infection contact scheme between the hosts. The parasite dynamics within the host population are modeled using a compound mixed Poisson process for the sheep and a shot-noise process for the dogs. All model parameters are estimated based on available data. The fitted model is then used for simulations of the transmission dynamics between the two hosts to investigate environmental factors and evaluate intervention programs

PROFILES - WP3: Stakeholders involvement and interaction. PROFILES Curricular Study on Science Education : Interim Report on the third round of the UL, Slovenia working group

The outcomes of this study will serve the development of innovative learning environments (WP4) and the preparation of continuous teacher training courses (WP5) “aiding the implementation and dissemination of PROFILES ideas, intentions and objectives to facilitate the uptake of innovative science teaching and the enhancement of scientific literacy” (PROFILES Consortium, 2010, p. 20). Promoting scientific literacy is only possible if the complexity of the scientific literacy construct is taken account of in content, method and conception. Therefore, the empirically identified aspects of desirable science education from round 1 were in the second part of round 2 considered in relation to content, method and conception

A filtered polynomial approach to density estimation

Density estimation, Empirical transformation, Filtered polynomial, MCMC simulation, Multivariate settings, C63,