Prospective power calculations for the Four Lab study of a multigenerational reproductive/developmental toxicity rodent bioassay using a complex mixture of disinfection by-products in the low-response region

Int J Environ Res Public Health. 2011 Oct;8(10):4082-101. doi: 10.3390/ijerph8104082. Epub 2011 Oct 24.


In complex mixture toxicology, there is growing emphasis on testing environmentally representative doses that improve the relevance of results for health risk assessment, but are typically much lower than those used in traditional toxicology studies. Traditional experimental designs with typical sample sizes may have insufficient statistical power to detect effects caused by environmentally relevant doses. Proper study design, with adequate statistical power, is critical to ensuring that experimental results are useful for environmental health risk assessment. Studies with environmentally realistic complex mixtures have practical constraints on sample concentration factor and sample volume as well as the number of animals that can be accommodated. This article describes methodology for calculation of statistical power for non-independent observations for a multigenerational rodent reproductive/developmental bioassay. The use of the methodology is illustrated using the U.S. EPA's Four Lab study in which rodents were exposed to chlorinated water concentrates containing complex mixtures of drinking water disinfection by-products. Possible experimental designs included two single-block designs and a two-block design. Considering the possible study designs and constraints, a design of two blocks of 100 females with a 40:60 ratio of control:treated animals and a significance level of 0.05 yielded maximum prospective power (~90%) to detect pup weight decreases, while providing the most power to detect increased prenatal loss.

Keywords: Four Lab Study; chemical mixtures; disinfection by-products (DBP); drinking water; experimental design; low dose; low response; power calculations.

Publication types

  • Evaluation Study

MeSH terms

  • Animals
  • Biological Assay / methods*
  • Complex Mixtures / analysis
  • Complex Mixtures / chemistry
  • Complex Mixtures / toxicity
  • Disinfectants / analysis
  • Disinfectants / chemistry
  • Disinfectants / toxicity*
  • Drinking Water / analysis
  • Female
  • Halogenation
  • Male
  • Models, Statistical*
  • Rats*
  • Risk Assessment
  • Toxicity Tests / methods*
  • United States
  • United States Environmental Protection Agency
  • Water Pollutants, Chemical / analysis
  • Water Pollutants, Chemical / chemistry
  • Water Pollutants, Chemical / toxicity*
  • Water Purification


  • Complex Mixtures
  • Disinfectants
  • Drinking Water
  • Water Pollutants, Chemical