Skip to main content
Log in

A bayesian predictive approach to sequential search for an optimal dose: Parametric and nonparametric models

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

This paper looks at a new approach to the problem of finding the maximal tolerated dose (or optimal dose, Eichhorn and Zacks, 1973) of certain drugs which in addition to their therapeutic effects have secondary harmful effects.

The problem is investigated in a sequential setting from a Bayesian predictive approach. Search procedures are proposed for parametric and nonparametric models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aitchinson, J. andDunsmore, I. R. (1975),Statistical prediction analysis, Cambridge: Cambridge University Press.

    Google Scholar 

  • Antoniak, C. (1974), «Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems».Annals of Statistics, 2, 1152–1174.

    MATH  MathSciNet  Google Scholar 

  • Berger, J. O. andBerry, D. A. (1988), «The relevance of stopping rules in Statistical inference», with discussion. In:Statistical Decision Theory and Related Topics IV (S. S. Gupta and J. O. Berger eds.), Springer-Verlag, N. Y., Vol. 1, 29–72.

    Google Scholar 

  • Blackwell, D. (1973), «Discreteness of Ferguson selections».Annals of Statistics, 1, 356–358.

    MATH  MathSciNet  Google Scholar 

  • Cifarelli, D. M., Muliere, P. andScarsini, M. (1981), «Il modello lineare nell'approccio Bayesiano non parametrico».Quaderni dell'Istituto Matematico G. Castelnuovo n. 15, Università di Roma.

  • Cifarelli, D. M. andRegazzini, E. (1978), «Problemi statistici non parametrici in condizioni di scambiabilità parziale. Impiego di medie associative».Quaderni dell'Istituto di Matematica Finanziaria, Università di Torino.

  • Diaconis, P. andFreedman, D. A. (1986), «On the consistency of Bayes estimates».Annals of Statistics, 14, 1–26.

    MATH  MathSciNet  Google Scholar 

  • Eichhorn, B. H. andZacks, S. (1973), «Sequential search of an optimal dosage. I».Journal of the American Statistical Association, 68, 594–598.

    Article  MathSciNet  Google Scholar 

  • Eichhorn, B. H. (1974), «Sequential search of an optimal dosage for cases of linear dosage-toxicity regression».Communications in Statistics, 3, 263–271.

    Article  MathSciNet  Google Scholar 

  • Eichhorn, B. H. andZacks, S. (1981), «Bayes sequential search of an optimal dosage: linear regression with both parameters unknown».Communications in Statistics —Theory and Methods A10, 931–953.

    MathSciNet  Google Scholar 

  • Ferguson, T. S. (1973), «A Bayesian analysis of some nonparametric problems».Annals of Statistics, 1, 209–230.

    MATH  MathSciNet  Google Scholar 

  • Korwar, R. M. andHollander, M. (1973), «Contributions to the theory of Dirichlet processes».Annals of Probability, 1, 705–711.

    MATH  MathSciNet  Google Scholar 

  • Muliere, P. andPetrone, S. (1992), «La ricerca sequenziale di una dose ottimale: impostazione bayesiana previsiva».Atti della XXXVI Riunione scientifica SIS, Pescara, 203–210.

  • Muliere, P. andScarsini, M. (1983), «Impostazione Bayesiana di un problema di analisi della varianza a due criteri».Giornale degli Economisti e Annali di Economia, 519–526.

  • O'Quigley, J., Pepe, M. andFisher, L. (1990), «Continual Reassessment Method: A practical design for phase 1 clinical trials in cancer».Biometrics, 46, 33–48.

    Article  MATH  MathSciNet  Google Scholar 

  • Robinson, J. A. (1978), «Sequential choice of an optimal dose: A prediction interval approach».Biometrika, 65, 75–78.

    Article  MATH  Google Scholar 

  • Shih, W. J. (1989), «Prediction approaches to sequentially searching for an optimal dose»,Biometrics, 45, 623–628.

    Article  MATH  Google Scholar 

  • Shiryayev, A. N. (1978),Optimal stopping rules. Springer-Verlag, N.Y.

    MATH  Google Scholar 

  • Tierney, L. (1991),Lisp-Stat, Wiley, N.Y.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muliere, P., Petrone, S. A bayesian predictive approach to sequential search for an optimal dose: Parametric and nonparametric models. J. It. Statist. Soc. 2, 349–364 (1993). https://doi.org/10.1007/BF02589069

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02589069

Keywords

Navigation