#### Abstract

The statistical analysis of dose-response experiments typically models observed responses as a function of an applied dosage series. The estimated "dose-response curve" is used in predicting future responses, however, it is also commonly rewritten in an inverted form where dose is expressed as a function of the response. This modified "calibration curve" is useful in cases where observed responses are available, but their associated dosages are unknown. Traditional statistical techniques for the estimation of unknown doses from the dose-response curve are problematic, involving approximate solutions and methods. Alternatively, this type of inverse calibration problem naturally falls into the framework of Bayesian analysis. That is, one wishes to estimate the probability of an unknown dose value at an observed value of the response given the underlying relationship between the dose and response. This paper examines some potential Bayesian solutions to the calibration problem under various assumptive conditions. The required methodology in each case will be outlined for a dichotomous response variable and a logistic dose-response function. Empirical results will be demonstrated using data from an organic pesticide dose-response trial.

#### Keywords

Binomial Response, Logistic Function, Bayesian Estimation

#### Creative Commons License

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BAYESIAN ANALYSIS OF DOSE-RESPONSE CALIBRATION CURVES

The statistical analysis of dose-response experiments typically models observed responses as a function of an applied dosage series. The estimated "dose-response curve" is used in predicting future responses, however, it is also commonly rewritten in an inverted form where dose is expressed as a function of the response. This modified "calibration curve" is useful in cases where observed responses are available, but their associated dosages are unknown. Traditional statistical techniques for the estimation of unknown doses from the dose-response curve are problematic, involving approximate solutions and methods. Alternatively, this type of inverse calibration problem naturally falls into the framework of Bayesian analysis. That is, one wishes to estimate the probability of an unknown dose value at an observed value of the response given the underlying relationship between the dose and response. This paper examines some potential Bayesian solutions to the calibration problem under various assumptive conditions. The required methodology in each case will be outlined for a dichotomous response variable and a logistic dose-response function. Empirical results will be demonstrated using data from an organic pesticide dose-response trial.