A Practical Approach, Second Edition=Ronald D. Ho.pdf

STATISTICAL ANALYSIS FOR DEVELOPMENTAL AND REPRODUCTIVE TOXICOLOGISTS 709B. ExampleWe use the hydroxyurea data to illustrate the procedure. The maximum likelihood estimates of theWeibull dose-response model are ˆ−2 , ˆ −11 α = 3. 46 × 10 β = 9. 88 × 10 , and ŵ = 4.24. The point estimatesand the 95% lower confidence limits of benchmark doses areBenchmark dose 1% 5% 10%MLE estimate 78.05 114.67 135.92Confidence limit 49.15 84.62 107.51Based on the result from the quasi-likelihood method in Table 17.4, the NOAEL is 100 ppm. Thisnumber is very close to the LED 10 of 107.51 ppm. Benchmark doses can be calculated with softwaresuch as TOX_RISK 32 and ToxTools. 33VI. DISCUSSIONStatistical analysis of developmental endpoints presents a number of important issues. Developmentalendpoints consist of both continuous and discrete outcomes. The analysis should accountfor the correlations induced by the clustering effects within litters. The litter-based ANOVAapproach is the simplest method for data analysis. Once the data are normalized, the ANOVA canbe applied directly as described. The ANOVA is also used in more complex experiments involvingcrossed (e.g., dose levels, replicates) and nested (e.g., litter effects) factors. The repeated measuresANOVA is used for the analysis of postnatal behavioral data. The ANOVA and conventional posthoc test procedures such as the Dunnett test and linear regression analysis are all available instandard statistical software packages.The parametric likelihood-based and quasi-likelihood (generalization estimating equations)approaches are two alternative methods. The mixed-effects model is a general parametric approachto modeling continuous outcomes. The parametric model for the binary outcomes from fetalresponses is described in terms of the sum of correlated binary variables resulting in a generalizedbinomial distribution. The distribution for the common developmental endpoints, such as the numberof malformations per litter, is often an overdispersed binomial, but the distribution of sex combinationscan be an underdispersed binomial. For count data, the negative binomial distribution hasbeen used to model overdispersed count data, such as results from an ovarian toxicity experiment.However, the parametric approach has disadvantages in that it does not allow for underdispersedvariations and its maximum likelihood estimates can be biased or numerically unstable. The quasilikelihoodapproach is a semiparametric approach. It can be applied to modeling both over- andundervariation data. The estimates derived are generally more stable than the parametric maximumlikelihood estimates. The quasi-likelihood approach does not provide inference on the dispersionparameter.In a typical reproductive and developmental study, various endpoints are collected in order toobtain the maximum information from the study. As described, the standard approach for riskassessment of a compound has been based on the analysis of each reproductive and developmentalendpoint separately. Statistical analysis often involves a large number of tests, both in terms ofmultiple comparisons among groups and multiple tests on many endpoints. Multiple testing procedures,e.g., Dunnett’s test, are commonly applied to group comparisons, rather than to the analysisof test endpoints. In a single experiment, statistical tests are performed on 10 to 20 reproductiveand developmental endpoints. Because of the conduct of a large number of statistical tests, thechance of false positive findings is considerably increased. For example, the overall false positiverate is about 0.40 ≈1−( 1− 005 . )10 for tests of 10 independent developmental and reproductiveendpoints, all at α = 0.05.© 2006 by Taylor & Francis Group, LLC