Effect of an effluent on the growth of mysid shrimp

Juvenile mysid shrimp (Mysidopsis bahia) were exposed to up to 32% effluent in a 7-day survival and growth test. The average weight per treatment replicate of surviving organisms was measured.

Usage

data(M.bahia)

Format

A data frame with 40 observations on the following 2 variables.

conc: a numeric vector of effluent concentrations (%)
dryweight: a numeric vector of average dry weights (mg)

Details

The data are analysed in Bruce and Versteeg (1992) using a log-normal dose-response model (using the logarithm with base 10).

At 32% there was complete mortality, and this justifies using a model where a lower asymptote of 0 is assumed.

Source

Bruce, R. D. and Versteeg, D. J. (1992) A statistical procedure for modeling continuous toxicity data, Environ. Toxicol. Chem., 11, 1485–1494.

Examples

library(drc)

M.bahia.m1 <- drm(dryweight~conc, data=M.bahia, fct=LN.3())

## Variation increasing
plot(fitted(M.bahia.m1), residuals(M.bahia.m1))


## Using transform-both-sides approach
M.bahia.m2 <- boxcox(M.bahia.m1, method = "anova")

summary(M.bahia.m2)  # logarithm transformation
#> 
#> Model fitted: Log-normal with lower limit at 0 (3 parms)
#> 
#> Parameter estimates:
#> 
#>                Estimate Std. Error t-value   p-value    
#> b:(Intercept) -0.444809   0.056065 -7.9338 1.679e-09 ***
#> d:(Intercept)  0.671979   0.043185 15.5603 < 2.2e-16 ***
#> e:(Intercept)  3.905716   0.883294  4.4218 8.278e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.2271316 (37 degrees of freedom)
#> 
#> Non-normality/heterogeneity adjustment through Box-Cox transformation
#> 
#> Estimated lambda: -0.182 
#> Confidence interval for lambda: [-0.697, 0.371] 
#> 

## Variation roughly constant, but still not a great fit
plot(fitted(M.bahia.m2), residuals(M.bahia.m2))


## Visual comparison of fits
plot(M.bahia.m1, type="all", broken=TRUE)
plot(M.bahia.m2, add=TRUE, type="none", broken=TRUE, lty=2)


ED(M.bahia.m2, c(10,20,50), ci="fls")
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:10  0.21900    0.11667
#> e:20  0.58881    0.24576
#> e:50  3.90572    0.88329

## A better fit
M.bahia.m3 <- boxcox(update(M.bahia.m1, fct = LN.4()), method = "anova")
#plot(fitted(M.bahia.m3), residuals(M.bahia.m3))
plot(M.bahia.m3, add=TRUE, type="none", broken=TRUE, lty=3, col=2)

ED(M.bahia.m3, c(10,20,50), ci="fls")
#> 
#> Estimated effective doses
#> 
#>      Estimate Std. Error
#> e:10  0.95677    0.18697
#> e:20  1.17193    0.19303
#> e:50  1.72756    0.19818