## A Generalized Multihit Dose-response Model for Low-dose Extrapolation |

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### Contents

A generalized MultiHit GMH | 17 |

Maximum Likelihood Estimation of | 27 |

Asymptotic Properties of Maximum | 48 |

Copyright | |

### Common terms and phrases

array at least Asymptotic Properties background response rate biological central limit theorem Chapter chi-squared distribution CM CM CM rH concave function consider consistent root control group data set density distribution with mean dose level dose-response curve estimate of VSD extreme value model Fletcher and Reeves FORMAT GMH dose-response model GMH model hence Hessian matrix IOUT large numbers law of large least of length likelihood equations likelihood function limit on VSD line segment joining linear log-likelihood function LOW-DOSE EXTRAPOLATION low-dose region lower confidence limit MAXFN maximum likelihood estimators MLE OF THETA Model with Background model without background MULTI-HIT DOSE RESPONSE Newton-Raphson method normal distribution number of animals one-hit model partial derivatives probit model Properties of MLE's random variables REAL array response at dose risk assessment Rolle's theorem Section Slutsky's theorem statistical subroutine sure convergent toxic effect toxic response variance-covariance matrix Virtually Safe