• Benchmark analysis;
  • Multistage model;
  • Simultaneous hyperbolic band;
  • Simultaneous three-segment band

Risk assessment studies where human, animal or ecological data are used to set safe low dose levels of a toxic agent are challenging as study information is limited to high dose levels of the agent. Simultaneous hyperbolic confidence bands for low-dose risk estimation with quantal data have been proposed in the literature. In this paper, a new method using three-segment confidence bands to construct simultaneous upper confidence limits on extra risks and simultaneous lower bounds on the benchmark dose for quantal data is proposed. The proposed method is illustrated with a real data application and simulation studies.