Consistency and asymptotic normality of the estimated effective doses in bioassay

Rabi Bhattacharya, Maiying Kong

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


In order to estimate the effective dose such as the 0.5 quantile ED50 in a bioassay problem various parametric and semiparametric models have been used in the literature. If the true dose-response curve deviates significantly from the model, the estimates will generally be inconsistent. One strategy is to analyze the data making only a minimal assumption on the model, namely, that the dose-response curve is non-decreasing. In the present paper we first define an empirical dose-response curve based on the estimated response probabilities by using the "pool-adjacent-violators" (PAV) algorithm, then estimate effective doses ED100 p for a large range of p by taking inverse of this empirical dose-response curve. The consistency and asymptotic distribution of these estimated effective doses are obtained. The asymptotic results can be extended to the estimated effective doses proposed by Glasbey [1987. Tolerance-distribution-free analyses of quantal dose-response data. Appl. Statist. 36 (3), 251-259] and Schmoyer [1984. Sigmoidally constrained maximum likelihood estimation in quantal bioassay. J. Amer. Statist. Assoc. 79, 448-453] under the additional assumption that the dose-response curve is symmetric or sigmoidal. We give some simulations on constructing confidence intervals using different methods.

Original languageEnglish (US)
Pages (from-to)643-658
Number of pages16
JournalJournal of Statistical Planning and Inference
Issue number3
StatePublished - Mar 1 2007


  • Confidence intervals
  • Dose-response curve
  • Logistic regression
  • Monotonic regression
  • Pool-adjacent-violators (PAV) algorithm

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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