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sensible approximations to reality. For example, if the data showed an increasing effect ofdose on mortality and only models that allowed for a decreasing effect of dose onmortality are fit, AIC will still rank these silly models and give the relative ranking ofthese silly models. Consequently, the fit of the model should also be ascertained by theanalyst (this usually is done via residual plots and other methods).The models in the model set should be specified in advance and the temptation to “datadredge” should be avoided. “Data dredging” would involve looking at the data andadding models that fit this particular dataset well, but have no a priori biologicalrationale. The danger is that the added models based on inspection of the data may be agood fit for this particular set of data, but minor changes in the data set would lead you tochoose a different model to add. In reality, some model specification is driven by apreliminary look at the data, e.g. is hormesis present, and as along as the general class ofmodels added is very general, this should be acceptable.Because BMDs are typically computed as a function of the model parameters, there issome ambiguity in how the BMDs should be averaged. For example, should the BMD beaveraged on the log-scale and then the averages are anti-logged, or should the averagingtake place directly on the anti-log scale. There is no biological definitive answer (forexample, concentration of sulphates are measured on mg/L scale, but pH are measured ona logarithmic scale). The two approaches can lead to slightly different answers becausethe log() function is a non-linear transform, but the two methods should lead to similarresults. As many models used in this project fit models where sulphates are measured onthe log() scale, the model averaging will take place on the log-scale with a final anti-log()taken at the end of the process. This will lead to asymmetric confidence intervals on theanti-log scale. For example, from Table 4, the estimated BMD on the log-scale is 4.84(SE 0.51). This gives 95% confidence intervals on the log-scale of (3.85, 5.84) whichlead to 95% confidence intervals on the antilog scale of e 3.85 = 47,e 5.84 = 342( ) .Wheeler and Bailer (2007) discuss an alternate way to use model averaging where thedose-response curves are model averaged and the model-averaged curve is used to findthe BMD, rather than model averaging the BMDs directly. This approach has not beenapplied in this report.In some cases, a model may fit the observed data reasonably well, but is unable toprovide an estimate of the BMD. This usually happens for one of two reasons. First, themodel should (in theory) provide an estimate of the BMD, but sparsity in the data leads toa model fit where the BMD not longer exists. For example, the mortality in the observeddose range in the study is relatively constant but because of natural variability, theobserved mortality declines with dose (e.g. 2/10 die at dose 100, 1/10 die at dose 200, and0/2 die at dose 300). A fitted Probit model would lead to a model where the mortalitydeclines as function of dose and would never reach 50% mortality (the LC50) and so noestimate of the BMD is available.Second, the model may fit the observed data well, but cannot be extrapolated outside theobserved range of the data. This is most common with isotonic models where the