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The function fit isA(1+ E • X)Y =1+ exp(!C(X ! D))and the estimated values from the fit were A=104.42, C=-.004325, D=1279, andE=.0006324.CETIS estimates the IC50 as 1509.9 mg/L. The value of Y at this point is:A(1+ E • X)Y =1+ exp(!C(X ! D)) = 104.42(1+ .0006324 •1509.9)1+ exp(!(!.004325)(1509.9 !1279))= 55.06This is NOT 50% of the 104.42 (the value of mean biomass when dose = 0). Rather it is50% of the mean biomass at dose = 93. At does=93, the response isA(1+ E • X)Y =1+ exp(!C(X ! D)) = 104.42(1+ .0006324 • 93)1+ exp(!(!.004325)(93!1279))= 110.12For both the 3-parameter log-logistic and the 4-parameter logistic hormesis model, thebaseline values for this report were taken as the expected response at dose=0.Consequently, estimates of BMDs may differ in the report from those reported by CETIS.
5. Results. The model selection table for each species/response listed in Table 1 is presented in Table2. Plots of the models fit to the raw data are available in Schwarz (2011) and on the webat http://www.stat.sfu.ca/~cschwarz/Consulting/MOE/2011-Sulphates/EC-analyses andhttp://www.stat.sfu.ca/~cschwarz/Consulting/MOE/2011-Sulphates/NA-analyses. As alsoshown in the previous report (Schwarz, 2011), models with separate dose-response curvesfor each hardness level are given the majority of model weight in all but three cases. Intwo cases, the EC-Lemna frond numbers, EC-Lemna frond weight, there was substantialsupport for models where the dose-response curve was invariant across hardness levels.In these cases, natural variation in the data and a limited response to sulphate (i.e. theresponse was almost flat across the levels of sulphate) made it difficult to determine theeffect of hardness on the dose-response curve. In one case (Rainbow Trout mortality)support was almost evenly split between a model where the dose-response curve wasinvariant to hardness and where the dose-response curve was “protective” as hardnessincreased. In this case, extra-binomial variation (the random effect in the probit model)was detected which also made it difficult to distinguish the effect of hardness on the doseresponsecurve. This implies, that except in these latter cases, there is strong evidence thathardness appears to influence the dose-response curve against sulphate.A summary of the model averaged estimates of the LCxx/ICxx are presented in Table 3with complete details of the individual estimates from each model for each studyavailable on the web at http://www.stat.sfu.ca/~cschwarz/Consulting/MOE/Sulphate-2011/Reports/Appendix-2011-07-20. For example, Table 4 presents an extract of themodel averaging for the LC10 value for EC-Rainbow Trout at hardness 50. Both thecommon curve over all hardness levels and the separate curve with a monotonic(protective) effect of hardness have substantial support, with minor support for the othermodels. Estimates of the LC10 (on the log-scale) range from 4.73 (123 on the anti-logscale) to 5.22 (185 on the antilog scale). The weighted average LC10 is 4.84 (on the logscale) corresponding to 127 on the anti-log scale as reported in Table 3. The modelaverage SE incorporates the variability in the estimates among the models fit to the data.Because the two top models are “contradictory” (one has no effect of hardness while theother has a protective effect of hardness), the model averaged estimates of the LC10 atthe three hardness levels (127, 163, and 213 at hardness 50, 100, 250 respectively) are notthe same, but are closer together than the estimates from the Separate.Mono model alone(99, 181, and 257 for hardness 50, 100 and 250 respectively as extracted from theAppendix). The model averaged standard errors are larger than the standard errors forany model to account for this model uncertainty.In some cases, no estimates of the BMD are provided (e.g. estimates of LCxx values athardness levels 50 and 100 for the mortality studies of EC-Chinook eggs). Examinationof the actual data shows that observed mortality was so low, that no model was able toprovide sensible estimates of the LCxx values at lower hardness levels.
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 20 and 21: In some cases, model averaged estim
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

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