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Comparing Methods for Determining Power Priors Based on Different Congruence Measures

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Abstract

Experiments are routinely conducted to evaluate the toxicity of water effluents or chemicals. In a Ceriodaphnia dubia reproduction test, organisms are exposed to varying concentration levels of the toxicant or other adverse treatment and the number of young produced after a given experiment period are recorded. To analyze the test outcomes, mean reproduction is modeled as a function of the concentration, and the estimated concentrations associated with specified levels of adverse effect often are used in risk management. While aquatic toxicity analyses often focus on outcomes from the current test, laboratories commonly have a history of conducting such tests using the same species, following a similar experimental protocol. So it seems reasonable to assume that the same underlying biological process generates the historical and current tests. In the present study, we propose using a calibrated power prior approach to incorporate historical control outcomes as prior input, and compare the behavior of the method when different congruence measures are used to determine the amount of historical input that will be incorporated. Simulation results show that three of the congruence measures can improve precision and reduce bias of the potency estimates.Supplementary material to this paper is provided online.

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References

  • Bailer AJ, Oris JT (1993) Modeling reproductive toxicity in Ceriodaphnia tests. Environ Toxicol Chem 12:787–791

    Article  Google Scholar 

  • Bailer AJ, Oris JT (1997) Estimating inhibition concentrations for different response scales using generalized linear models. Environ Toxicol Chem 16:1554–1559

    Article  Google Scholar 

  • Bailer AJ, Hughes MR, Denton DL, Oris JT (2000) An empirical comparison of effective concentration estimators for evaluating aquatic toxicity test responses. Environ Toxicol Chem 19:141–150

    Article  Google Scholar 

  • Bliss C (1934) The method of probits. Science 79(2037):38–39

    Article  Google Scholar 

  • Chen M, Ibrahim JG, Shao Q (2000) Power prior distributions for generalized linear models. J Stat Plan Inference 84:121–137

    Article  MathSciNet  MATH  Google Scholar 

  • Crump K (1984) A new method for determining allowable daily intakes. Fundam Appl Toxicol 4:854–871

    Article  Google Scholar 

  • Duan Y, Ye K, Smith EP (2006) Evaluating water quality using power priors to incorporate historical information. Environmetrics 17:95–106

    Article  MathSciNet  Google Scholar 

  • Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472

    Article  MATH  Google Scholar 

  • Hobbs BP, Carlin BP, Mandrekar SJ, Sargent DJ (2011) Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics 67(3):1047–1056

    Article  MathSciNet  MATH  Google Scholar 

  • Ibrahim JG, Chen MH (2000) Power prior distributions for regression models. Stat Sci 15:46–60

    MathSciNet  Google Scholar 

  • Kolmogorov A (1933) Sulla determinazione empirica di una legge di distribuzione. G Ist Ital Attuari 4:83–91

    MATH  Google Scholar 

  • Neuenschwander B, Capkun-Niggli G, Branson M, Spiegelhalter D (2010) Summarizing historical information on controls in clinical trials. Clin Trial 7:5–18

    Article  Google Scholar 

  • Norberg-King T (1993) A linear interpolation method for sublethal toxicity: the inhibition concentration (ICp) approach. National Effluent Toxicity Assessment Center Technical Report 03-93. U.S. Environmental Protection Agency, Duluth, MN

  • Pan H, Yuan Y, Xia J (2016) A calibrated power prior approach to borrow information from historical data with application to biosimilar clinical trials. J R Stat Soc Ser C (Appl Stat) 66:979–996

    Article  MathSciNet  Google Scholar 

  • R Core Team (2021) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

  • Smirnov N (1948) Table for estimating the goodness of fit of empirical distributions. Ann Math Stat 19(2):279–281

    Article  MathSciNet  MATH  Google Scholar 

  • Stan Development Team (2023) RStan: the R interface to Stan. R package version 2.21.8. https://mc-stan.org/

  • Weber CI, Peltier WH, Norberg-King TJ, Horning WB, Kessler FA, Menkedick JR, Neiheisel TW, Lewis PA, Kemm K, Pickering QH, Robinson EL, Lazorchack JM, Wymer LJ, Freyberg RW (1989) Short-term methods for estimating the chronic toxicity of effluents and receiving waters to freshwater organisms, 2nd edn. EPA/600/4-89/001A, U.S. Environmental Protection Agency, Cincinnati

    Google Scholar 

  • Ye K, Han Z, Duan Y, Bai T (2022) Normalized power prior Bayesian analysis. JSPI 216(8):29–50

    MathSciNet  MATH  Google Scholar 

  • Zhang J, Bailer AJ (2023) Impact of organism allocations on potency estimates from C. dubia reproduction tests. Environ Toxicol Chem (in press)

  • Zhang J, Bailer AJ, Oris JT (2012) Bayesian approach to estimating reproductive inhibition potency in aquatic toxicity testing. Environ Toxicol Chem 31(8):916–927

    Article  Google Scholar 

  • Zhang J, Kong Y, Bailer AJ, Zhu Z, Smucker BJ (2022) Incorporating historical data when determining sample size requirements for aquatic toxicity experiments. J Agric Biol Environ Stat 27:544–561

    Article  MathSciNet  MATH  Google Scholar 

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Zhang, J., Helling, A. & Bailer, A.J. Comparing Methods for Determining Power Priors Based on Different Congruence Measures. JABES (2023). https://doi.org/10.1007/s13253-023-00579-6

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