Application of multistate modeling to clinical data analysis.

Multistate models have been used for decades to analyze the economics of expensive and long-lasting treatments. More recently they also served to address questions in clinical drug development. It seems timely to introduce the broader pharmacometrics community to the technical aspects and the problem-solving capabilities of these models. A minimal model is introduced that can answer questions of interest to drug developers, regulatory agencies, and patients (with their carers and payers). A clinical study is simulated where 1000 patients are randomly allocated (1:1) to placebo and active treatment. After a recruitment phase, deaths are counted, and an administrative data cutoff occurs 858 days after the first patient is randomized. The minimal model has one initial state, two transient states, and two absorbing states. Fully parameterized semi-Markov processes govern the unidirectional transitions between states. Simulations explore the influence of parameter uncertainty and sample size on the validity of statistical inferences. The questions of interest to stakeholders are addressed predominantly with graphic displays. All programming codes are made available. Both drug developers and regulators are invited to re-evaluate the methods currently in use to assess the benefits and risks of new treatments.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect.

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

Solvent fluctuations around solvophobic, solvophilic, and patchy nanostructures and the accompanying solvent mediated interactions.

Using classical density functional theory(DFT), we calculate the density profile ρ(𝐫) and local compressibility χ(𝐫) of a simple liquidsolvent in which a pair of blocks with (microscopic) rectangular cross section are immersed. We consider blocks that are solvophobic, solvophilic and also ones that have both solvophobic and solvophilic patches. Large values of χ(𝐫) correspond to regions in space where the liquid density is fluctuating most strongly. We seek to elucidate how enhanced density fluctuations correlate with the solvent mediated force between the blocks, as the distance between the blocks and the chemical potential of the liquid reservoir vary. For sufficiently solvophobic blocks, at small block separations and small deviations from bulk gas-liquid coexistence, we observe a strongly attractive (near constant) force, stemming from capillary evaporation to form a low density gas-like intrusion between the blocks. The accompanying χ(𝐫) exhibits a structure which reflects the incipient gas-liquid interfaces that develop. We argue that our model system provides a means to understanding the basic physics of solvent mediated interactions between nanostructures, and between objects such as proteins in water that possess hydrophobic and hydrophilic patches.

Two-dimensional colloidal fluids exhibiting pattern formation.

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase diagram using Monte Carlo computer simulations and also with density functional theory (DFT). The DFT predictions for the structures formed are in good agreement with the results from the simulations, which occur in the portion of the phase diagram where the theory predicts the uniform fluid to be linearly unstable. However, the mean-field DFT does not correctly describe the transitions between the different morphologies, which the simulations show to be analogous to micelle formation. We determine how the heat capacity varies as the model parameters are changed. There are peaks in the heat capacity at state points where the morphology changes occur. We also map the lattice model onto a continuum DFT that facilitates a simplification of the stability analysis of the uniform fluid.