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A Three‐State Multiplicative Model for Rodent Tumorigenicity Experiments

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  • Jane C. Lindsey
  • Louise M. Ryan

Abstract

A three‐state illness–death model provides a useful way to represent data from rodent tumorigenicity experiments. Some of the earliest proposals use fully parametric models based on, for example, Weibull distributional assumptions. Recently, nonparametric versions of this model have been proposed, but these generally require large data sets with frequent interim sacrifices to yield stable estimates. As a compromise between these extremes, others have considered semiparametric models. In this paper, we develop a model that assumes a multiplicative relationship between death rates with and without tumour and a piecewise exponential model for the base‐line transition rates. The model can be fitted with information from a single sacrifice. An EM algorithm provides a useful way to fit the model, since the likelihood corresponds to that from a standard piecewise exponential survival model when time to tumour onset is known. We discuss the relationship between the piecewise exponential model and other recent proposals and illustrate the method with data from two carcinogenicity studies.

Suggested Citation

  • Jane C. Lindsey & Louise M. Ryan, 1993. "A Three‐State Multiplicative Model for Rodent Tumorigenicity Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(2), pages 283-300, June.
    • Handle: RePEc:bla:jorssc:v:42:y:1993:i:2:p:283-300
    DOI: 10.2307/2986233
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    Cited by:

    1. Ming‐Hui Chen & Joseph G. Ibrahim, 2001. "Maximum Likelihood Methods for Cure Rate Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 57(1), pages 43-52, March.
    2. Jonathan L. French & Joseph G. Ibrahim, 2002. "Bayesian Methods for a Three–State Model for Rodent Carcinogenicity Studies," Biometrics, The International Biometric Society, vol. 58(4), pages 906-916, December.
    3. Pierre Joly & Daniel Commenges, 1999. "A Penalized Likelihood Approach for a Progressive Three-State Model with Censored and Truncated Data: Application to AIDS," Biometrics, The International Biometric Society, vol. 55(3), pages 887-890, September.
    4. David B. Dunson & Gregg E. Dinse, 2002. "Bayesian Models for Multivariate Current Status Data with Informative Censoring," Biometrics, The International Biometric Society, vol. 58(1), pages 79-88, March.
    5. Man-Ho Ling & Narayanaswamy Balakrishnan & Chenxi Yu & Hon Yiu So, 2021. "Inference for One-Shot Devices with Dependent k -Out-of- M Structured Components under Gamma Frailty," Mathematics, MDPI, vol. 9(23), pages 1-24, November.
    6. Zhu, Xiaojun & Balakrishnan, N., 2022. "One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications," Reliability Engineering and System Safety, Elsevier, vol. 221(C).

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