Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

A truncation in the Aryl Hydrocarbon Receptor of the CRL:WI(Han) rat does not affect the developmental toxicity of TCDD

The Aryl Hydrocarbon Receptor (AhR) is required for the toxicity of TCDD, and so the AhR of CRL:WI and CRL:WI(Han) rats was characterised. Western blot showed AhR proteins of ~110 and ~97 kDa in individual rats from both strains. The AhR cDNA from a CRL:WI(Han) rat with the ~110kDa protein revealed a sequence that was identical to that of the CRL:WI and SD rat. However, cloning of the AhR from a rat with the ~97kDa protein revealed a point mutation, and five variants encoding two C-terminally truncated variants of the AhR protein, arising from a point mutation in the intron/exon junction and consequent differential splicing. These C-terminally truncated variants were expressed and shown to give rise to a protein of ~97kDa; the recombinant AhR bound TCDD with an affinity that was not statistically different from the full-length protein. A single-nucleotide polymorphism (SNP) assay was developed, and showed that both alleles were represented in a Hardy-Weinberg equilibrium in samples of CRL:WI and CRL:WI(Han) populations; both alleles are abundant. Rats from two studies of TCDD developmental toxicity were genotyped, and the association with toxicity investigated using statistical analysis. There was no plausible evidence that the AhR allele had a significant effect on the toxic endpoints examined. These data show that the two AhR alleles are common in two strains of Wistar rat, and that the AhR alleles had no effect on TCDD-induced developmental toxicity in two independent studies.