An extension of the EM algorithm and its applications in risk estimation
for quantitative responses from non-homogeneous populations

In many biological experiments with laboratory animals, it is frequently
observed that some animals in the same experimental group are more
susceptible to a dose of a chemical than others. To account for this
non-homogeneity in the population, a mixture of two or more distributions
is often proposed to describe the dose-response relationship. To assess
the risk of an adverse effect at a given low human exposure level, when
the response of interest is quantitative in nature, the likelihood
approach leads to a set of nonlinear equations subject to a risk
constraint. An extension of the EM algorithm is proposed and a procedure
based on the Newton-Raphson technique is utilized to evaluate the
equations. An example in toxicology is given to provide further
illustration.