Modelling grouped survival times in toxicological studies using generalized additive models

Candy,SG, Sfiligoj,BJ, King,CK and Mondon,JA 2014, Modelling grouped survival times in toxicological studies using generalized additive models, Environmental and Ecological Statistics, vol. 22, no. 3, pp. 465-491, doi: 10.1007/s10651-014-0306-3.

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Title Modelling grouped survival times in toxicological studies using generalized additive models
Author(s) Candy,SG
Mondon,JAORCID iD for Mondon,JA
Journal name Environmental and Ecological Statistics
Volume number 22
Issue number 3
Start page 465
End page 491
Total pages 27
Publisher Springer
Place of publication New York, NY
Publication date 2014-12-14
ISSN 1352-8505
Keyword(s) Dose–response model
Generalized Additive Model
Grouped survival times
Time–response model
Summary 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.
Language eng
DOI 10.1007/s10651-014-0306-3
Field of Research 050204 Environmental Impact Assessment
Socio Economic Objective 970105 Expanding Knowledge in the Environmental Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2014, Springer
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