Diagnostics to Assess Toxicokinetic-Toxicodynamic Models

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Xia Xu*+ and Philip Dixon
• Companies: Merck Research Laboratories and Iowa State Univ
• Keywords: toxicokinetics ; survival analysis ; diagnostics ; proportional hazard ; Hyalella azteca

Abstract

In ecotoxicology studies, toxicokinetic-toxicodynamic (TKTD) models are increasingly being used to relate toxicant concentration to survival. These have a toxicokinetic component that specifies a model for toxicant uptake and elimination and a toxicodynamic component that specifies a model for the relationship between internal body concentration of toxicant and the hazard rate. Often, the toxicodynamic model is a proportional hazards model. We develop diagnostic methods to assess the appropriateness of the toxicokinetic and hazard models. A log-cumulative hazard plot is used to assess visually the proportional hazard assumption. This can be further evaluated by an approximate test based on a linear regression. If the proportional hazard assumption is valid, a plot of toxicant concentration against the average of log cumulative hazard for each concentration assesses the kinetic model. The use of these diagnostic tools is illustrated by fitting and evaluating a TKTD model for Hyalella azteca survival during and after exposure to copper sulfate and sodium pentachlorophenol.