# [R] Fieller's Conf Limits and EC50's

From: Stephen B. Cox <stephen.cox_at_ttu.edu>
Date: Thu 14 Jul 2005 - 02:42:52 EST

Folks

I have modified an existing function to calculate 'ec/ld/lc' 50 values and their associated Fieller's confidence limits. It is based on EC50.calc (writtien by John Bailer) - but also borrows from the dose.p (MASS) function. My goal was to make the original EC50.calc function flexible with respect to 1) probability at which to calculate the expected dose, and 2) the link function. I would appreciate comments about the validity of doing so! In particular - I want to make sure that the confidence limit calculations are still valid when changing the link function.

ec.calc<-function(obj,conf.level=.95,p=.5) {

# calculates confidence interval based upon Fieller's thm.
# modified version of EC50.calc found in P&B Fig 7.22
# now allows other link functions, using the calculations
# found in dose.p (MASS)
# SBC 19 May 05

call <- match.call()

```         coef = coef(obj)
vcov = summary.glm(obj)\$cov.unscaled
b0<-coef
b1<-coef
var.b0<-vcov[1,1]
var.b1<-vcov[2,2]
cov.b0.b1<-vcov[1,2]
alpha<-1-conf.level
zalpha.2 <- -qnorm(alpha/2)
gamma <- zalpha.2^2 * var.b1 / (b1^2)
eta = family(obj)\$linkfun(p)  #based on calcs in V&R's dose.p

EC50 <- (eta-b0)/b1

const1 <- (gamma/(1-gamma))*(EC50 + cov.b0.b1/var.b1)

const2a <- var.b0 + 2*cov.b0.b1*EC50 + var.b1*EC50^2 -
gamma*(var.b0 - cov.b0.b1^2/var.b1)

const2 <- zalpha.2/( (1-gamma)*abs(b1) )*sqrt(const2a)

LCL <- EC50 + const1 - const2
UCL <- EC50 + const1 + const2

conf.pts <- c(LCL,EC50,UCL)
names(conf.pts) <- c("Lower","EC50","Upper")

return(conf.pts,conf.level,call=call)
```
}

Thanks

Stephen Cox

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