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Modelling grouped survival times in toxicological studies using generalized additive models
journal contribution
posted on 2014-12-14, 00:00 authored by S G Candy, Bianca Sfiligoj, C K King, Julie MondonJulie MondonA 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.
History
Journal
Environmental and Ecological StatisticsPagination
1 - 27Publisher
SpringerLocation
New York, NYPublisher DOI
ISSN
1352-8505Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2014, SpringerUsage metrics
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Dose–response modelGeneralized Additive ModelGrouped survival timesTime–response modelScience & TechnologyLife Sciences & BiomedicinePhysical SciencesEnvironmental SciencesMathematics, Interdisciplinary ApplicationsStatistics & ProbabilityEnvironmental Sciences & EcologyMathematicsDose-response modelTime-response modelMAXIMUM-LIKELIHOODLINEAR-MODELSBIOASSAYS
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