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A litter‐based approach to risk assessment in developmental toxicity studies via a power family of completely monotone functions
Author(s) -
Kuk Anthony Y. C.
Publication year - 2004
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1046/j.1467-9876.2003.05369.x
Subject(s) - pairwise comparison , mathematics , litter , joint probability distribution , monotone polygon , statistics , probability distribution , logistic regression , beta binomial distribution , class (philosophy) , negative binomial distribution , computer science , biology , poisson distribution , geometry , artificial intelligence , agronomy
Summary. A new class of distributions for exchangeable binary data is proposed that originates from modelling the joint success probabilities of all orders by a power family of completely monotone functions. The distribution proposed allows flexible modelling of the dose–response relationship for both the marginal response probability and the pairwise odds ratio and is especially well suited for a litter‐based approach to risk assessment. Specifically, the risk of at least one adverse response within a litter takes on a simple form under the distribution proposed and can be reduced further to a generalized linear model if a complementary log–log‐link function is used. Existing distributions such as the beta–binomial or folded logistic functions have a tendency to assign too much probability to zero, leading to an underestimation of the risk that at least one foetus is affected and an overestimation of the safe dose. The distribution proposed does not suffer from this problem. With the aid of symbolic differentiation, the distribution proposed can be fitted easily and quickly via the method of scoring. The usefulness of the class of distributions proposed and its superiority over existing distributions are demonstrated in a series of examples involving developmental toxicology and teratology data.