Modelling grouped survival times in toxicological studies using generalized additive models

A method for combining a proportional-hazards survival time model with a bioassay model where the log-hazard function is modelled as a linear or smoothing spline function of log-concentration combined with a smoothing spline function of time is described. The combined model is fitted to mortality numbers, resulting from survival times that are grouped due to a common set of observation times, using Generalized Additive Models (GAMs). The GAM fits mortalities as conditional binomials using an approximation to the log of the integral of the hazard function and is implemented using freely-available, general software for fitting GAMs. Extensions of the GAM are described to allow random effects to be fitted and to allow for time-varying concentrations by replacing time with a calibrated cumulative exposure variable with calibration parameter estimated using profile likelihood. The models are demonstrated using data from a studies of a marine and a, previously published, freshwater taxa. The marine study involved two replicate bioassays of the effect of zinc exposure on survival of an Antarctic amphipod, Orchomenella pinguides. The other example modelled survival of the daphnid, Daphnia magna, exposed to potassium dichromate and was fitted by both the GAM and the process-based DEBtox model. The GAM fitted with a cubic regression spline in time gave a 61 % improvement in fit to the daphnid data compared to DEBtox due to a non-monotonic hazard function. A simulation study using each of these hazard functions as operating models demonstrated that the GAM is overall more accurate in recovering lethal concentration values across the range of forms of the underlying hazard function compared to DEBtox and standard multiple endpoint probit analyses.

Nature of crystalline particle assembly in ring shaped colloidal stains from concentrated dispersions

The drying of colloidal droplet suspensions is important in many realms of practical application and has sustained the interest of researchers over two decades. The arrangements of polystyrene and silica beads, both of diameter 1 μm, 10% by volume of solid deposited on normal glass (hydrophilic), and silicone (hydrophobic) surfaces evaporated from a suspension volume of 3 μL, were investigated. Doughnut shape depositions were found, imputing the influence of strong central circulation flows that resulted in three general regions. In the central region which had strong particle build-up, the top most layers of particle arrangement was confirmed to be disordered using power spectrum and radial distribution function analysis. On closer examination, this appeared more like frustrated attempts to crystallize into larger grains rather than beads arranging in a disordered fashion throughout the piling process. With an adapted micro-bulldozing operation to progressively remove layers of particles from the heap, we found that the later efforts to crystallize through lateral capillary inter-particle forces were liable to be undone once the particles contacted the disorganized particles underneath, which were formed out of the jamming of fast particles arriving at the surface. © 2014 Elsevier B.V.