A comparison of methods for treatment selection in seamless phase II/III clinical trials incorporating information on short-term endpoints

In an adaptive seamless phase II/III clinical trial interim analysis data are used for treatment selection, enabling resources to be focussed on comparison of more effective treatment(s) with a control. In this paper we compare two methods recently proposed to enable use of short-term endpoint data for decision-making at the interim analysis. The comparison focusses on the power and the probability of correctly identifying the most promising treatment. We show that the choice of method depends on how well short-term data predict the best treatment, which may be measured by the correlation between treatment effects on short-term and long-term endpoints

Jupiter's polar ionospheric flows: measured intensity and velocity variations poleward of the main auroral oval

Recent analysis of high-resolution spectra of Doppler-shifted H3+ emission from the auroral/polar regions of Jupiter revealed a complex wind system, with a persistent auroral electrojet and strong anti-sunward flows in a region of lesser intensity centred around the magnetic pole [ Stallard et al., 2001 ]. This region, which we have called the Dark Polar Region (DPR), is re-investigated, transforming the observed line-of-sight velocities into a frame of reference fixed with respect to the magnetic pole. The DPR is shown to include a region essentially stagnant in this frame of reference (the f-DPR). We identify it as a region coupled to open magnetotail field lines. There is also a transition region in which the ion velocity returns to corotation (the r-DPR)

Multiply connected wandering domains of entire functions

The dynamical behaviour of a transcendental entire function in any periodic component of the Fatou set is well understood. Here we study the dynamical behaviour of a transcendental entire function $f$ in any multiply connected wandering domain $U$ of $f$. By introducing a certain positive harmonic function $h$ in $U$, related to harmonic measure, we are able to give the first detailed description of this dynamical behaviour. Using this new technique, we show that, for sufficiently large $n$, the image domains $U_n=f^n(U)$ contain large annuli, $C_n$, and that the union of these annuli acts as an absorbing set for the iterates of $f$ in $U$. Moreover, $f$ behaves like a monomial within each of these annuli and the orbits of points in $U$ settle in the long term at particular `levels' within the annuli, determined by the function $h$. We also discuss the proximity of $\partial U_n$ and $\partial C_n$ for large $n$, and the connectivity properties of the components of $U_n \setminus \bar{C_n}$. These properties are deduced from new results about the behaviour of an entire function which omits certain values in an annulus

Estimating age-status-specific demographic rates that are consistent with the projected summary measures in family households projection

This paper proposes procedures for estimating age-status-specific demographic rates to ensure that the projected summary measures of marriage/union formation and dissolution and marital and non-marital fertility in the future years are achieved consistently. The procedures proposed in this paper can be applied in both macro and micro models for family household or actuarial/welfare projections and simulations that need the time-varying age-status-specific demographic rates as input.family demography

Dynamics of meromorphic functions with direct or logarithmic singularities

We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Julia set contains continua. This intersection has an unbounded component if and only if the function has no Baker wandering domains. We also give estimates of the Hausdorff dimension and the upper box dimension of the Julia set of a meromorphic function with a logarithmic singularity over infinity. The above theorems are deduced from more general results concerning functions which have "direct or logarithmic tracts", but which need not be meromorphic in the plane. These results are obtained by using a generalization of Wiman-Valiron theory. The method is also applied to complex differential equations.Comment: 29 pages, 2 figures; v2: some overall revision, with comments and references added; to appear in Proc. London Math. So

Estimating time-varying sex-age-specific o/e rates of marital status transitions in family household projection or simulation

This article presents a procedure for estimating time-varying sex-age-specific occurrence/exposure (o/e) rates of marital status transitions to ensure that the projected life course propensities of marriage/union formation and dissolution are achieved consistently in the one-sex family status life table model. Procedures for estimating time-varying sex-age-specific marital status transition o/e rates that are consistent with the two-sex constraints and projected summary measures of marriage/union formation and dissolution in the future years in the two-sex family household projection model is proposed. The procedures proposed in this article are practically useful and can be applied in both macro and micro models for family household projections or simulations that need time-varying sex-age-specific o/e rates of marital status transitions.family, household, marriage, projections, simulation

Estimating time-varying sex-age-specific o/e rates of marital status transitions in family household projection or simulation

This article presents a procedure for estimating time-varying sex-age-specific occurrence/exposure (o/e) rates of marital status transitions to ensure that the projected life course propensities of marriage/union formation and dissolution are achieved consistently in the one-sex family status life table model. Procedures for estimating time-varying sex-age-specific marital status transition o/e rates that are consistent with the two-sex constraints and projected summary measures of marriage/union formation and dissolution in the future years in the two-sex family household projection model is proposed. The procedures proposed in this article are practically useful and can be applied in both macro and micro models for family household projections or simulations that need time-varying sex-age-specific o/e rates of marital status transitions.