bmad calculation

[t-anton]

Why doesn't "bmad" calculation use "constant=1" within R's "mad" function?

For example, instead of

e1 <- bquote(dat[ , bmad := mad(resp[cndx %in% 1:2 & wllt == "t"], na.rm = TRUE)])

why not

e1 <- bquote(dat[ , bmad := mad(resp[cndx %in% 1:2 & wllt == "t"], constant = 1, na.rm = TRUE)]) ?

I think that the default value should be used for larger samples. In the "bmad" calculation, we only consider 2 responses for the two lowest concentrations.

Below I show the difference between default mad function and with constant=1:

mad(c(6,7,7,8,12,14,15,16,16,19,22,24,26,26,29,46))
[1] 11.8608

mad(c(6,7,7,8,12,14,15,16,16,19,22,24,26,26,29,46),constant=1)
[1] 8

[sedavid01]

The N used for the BMAD calculation is actually fairly large, as we are typically using the replicates in the lowest two concentrations from all chemicals tested within an endpoint. That is, calculating one BMAD for an endpoint to be used across all chemicals rather than a BMAD for each chemical within an endpoint). Thus, the sample size N is not just N = 2 but is much larger - though it should be noted N varies by assay endpoint based on experimental design. In some cases we use all DMSO (or vehicle control) wells for the assay endpoint, but again this is much greater than N=2 on an endpoint basis.

Additionally, the default constant = 1.4826 the expected value of MAD estimated by R is equal to the standard deviation (sigma) when the responses are normally distributed or it converges to sigma when the sample size (N) is large.