Summary - People.stat.sfu.ca - Simon Fraser University

More documents

Recommendations

Info

In some cases, model averaged estimates have very large standard errors. For example,the model averaged LC10 for EC-Fathead Minnows mortality at hardness 250 is 3200mg/L with a SE=16000! In this case, the observed mortality in the best fitting model atthe highest dose was very small, based on only a few organisms, and the extrapolation isnot very reliable.Conversely, the observed standard errors may appear to be very small (e.g. estimate ofLC10 for EC-Fathead Minnows mortality at hardness 100 is 1400 (SE 7). In this case, thebest fitting model is the 4-parameter logistic hormesis model (see fit below)The observed data has such a steep decline from increasing in doses up to 1000, then to 0in higher doses that the curve fit must be very sharp.Interpretation of the results then follows a two-step process. First, examine the modelselection tables (Table 2) to examine the support for models with a common dose-
esponse curve across all hardness levels vs. models with a separate dose-response curveby hardness level. The majority of these tables indicate that there is strong evidence thatthe dose-response curve varies by hardness. Next consider the model averaged estimatedLCxx/ICxx values for each hardness level. Even if there is strong support for an effect ofhardness, the effect of hardness may be small enough that a common LCxx/ICxx valueacross the hardness levels may be appropriate. This is not contradictory as the modelselection in Table 2 is comparing the models over the entire-dose response curve, whilethe estimates in Table 4 are for specific points on the dose-response curve.6. Discussion As outlined by Wheeler and Bailer (2005), model averaging provides a way toincorporate model uncertainty into the risk assessment process. Simply selecting thesingle “best” model may give a false sense of precision (i.e. single model reportedstandard errors typically underreport the true uncertainty in the BMD).Model averaging is not a panacea. Estimates of BMDs within the observed range of thedoses in a study will typically be very similar across a wide range of models as all of themodels must come “close” to the observed data. However, extrapolations that are faroutside the observed dose ranges of the data will typically be very sensitive to the choiceof models.It would be possible to extend the above modeling approach by incorporating both theeffects of hardness and sulphate upon the observed responses and deriving a single doseresponsecurve that incorporates both hardness and sulphate levels. The advantage of thismore complex approach is that a (model averaged) prediction equation for the BMD canbe established as a function of any hardness rather than relying on the observedhardnesses in the study. Unfortunately, in most cases, only a few levels of hardness werestudies and so the models for the effect of hardness must be very simple (e.g. linear) andextrapolations outside the observed ranges of hardness will be unwise.ReferencesAnderson, D. (2008) Model Based Inference in the Life Sciences: A Primer on Evidence.Springer: New York.Bailer AJ, Wheeler M, Dankovick D, Noble R, Bena J (2005) Incorporating uncertaintyand variability in the assessment of occupational hazards. Int J Risk Assess Manage5:344–357.Bailer, Noble, and Wheeler (2005) Model uncertainty and risk estimation for
Page 1 and 2: An assessment of the effect of hard
Page 3 and 4: 2. Studies used. There are two gr
Page 5 and 6: number of free parameters in the mo
Page 7 and 8: isotonicity constraint can be appli
Page 9 and 10: fewer mortalities occurred at highe
Page 11 and 12: Survival10.90.80.70.60.50.40.30.20.
Page 13 and 14: is inconsequential relative to the
Page 18 and 19: The function fit isA(1+ E • X)Y =
Page 22 and 23: experimental studies of quantal res
Page 24 and 25: Figure 1b. The Probit, Separate, CN
Page 26: Figure 1d. The Probit, Common LC50,
Page 29 and 30: Figure 1g. The Probit, Common, CNR,
Page 31 and 32: Figure 2b. The Probit, SeparateMono
Page 33 and 34: Table 1. Summary of sampling protoc
Page 35 and 36: Table 2-EC-CH-mortality. Summary of
Page 37 and 38: Table 2-EC-FH-weight. Summary of AI
Page 39 and 40: Table 2-EC-HY-weight. Summary of AI
Page 42 and 43: Table EC-MY-mortality. Summary of A
Page 44 and 45: Table 2-NA-AL-cell. Summary of AIC
Page 46 and 47: Table 2-NA-DA-repro. Summary of mod
Page 48 and 49: Table 2-NA-FH-weight. Summary of AI
Page 51: Table 2-NA-TA-weight. Summary of mo
Page 54 and 55: Table 3. Summary of model averaged
Page 56 and 57: Table 3. Summary of model averaged

Summary - People.stat.sfu.ca - Simon Fraser University

Create successful ePaper yourself

Delete template?

Save as template?