14,694 research outputs found
Elastic strips
Motivated by the problem of finding an explicit description of a developable
narrow Moebius strip of minimal bending energy, which was first formulated by
M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently
E.L. Starostin and G.H.M. van der Heijden found a numerical description for an
elastic Moebius strip, but did not give an integrable solution. We derive two
conservation laws, which describe the equilibrium equations of elastic strips.
In applying these laws we find two new classes of integrable elastic strips
which correspond to spherical elastic curves. We establish a connection between
Hopf tori and force--free strips, which are defined by one of the integrable
strips, we have found. We introduce the P--functional and relate it to elastic
strips.Comment: 21 pages, 2 figure
A multistate model for early decision making in oncology
The development of oncology drugs progresses through multiple phases, where
after each phase a decision is made about whether to move a molecule forward.
Early phase efficacy decisions are often made on the basis of single arm
studies based on RECIST tumor response as endpoint. This decision rules are
implicitly assuming some form of surrogacy between tumor response and long-term
endpoints like progression-free survival (PFS) or overall survival (OS). The
surrogacy is most often assessed as weak, but sufficient to allow a rapid
decision making as early phase studies lack the survival follow up and number
of patients to properly assess PFS or OS. With the emergence of therapies with
new mechanisms of action, for which the link between RECIST tumor response and
long-term endpoints is either not accessible yet because not enough data is
available to perform a meta-regression, or the link is weaker than with
classical chemotherapies, tumor response based rules may not be optimal. In
this paper, we explore the use of a multistate model for decision making based
on single-arm early phase trials. The multistate model allows to account for
more information than the simple RECIST response status, namely, the time to
get to response, the duration of response, the PFS time and time to death. We
propose to base the decision on efficacy on the OS hazard ratio (HR), predicted
from a multistate model based on early phase data with limited survival
follow-up, combined with historical control data. Using three case studies and
simulations, we illustrate the feasibility of the estimation of the OS HR using
a multistate model based on limited data from early phase studies. We argue
that, in the presence of limited follow up and small sample size, and on
assumptions within the multistate model, the OS prediction is acceptable and
may lead to better decisions for continuing the development of a drug
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