[R-sig-eco] Fitting a Weibull with a 0 dose

[Dixon, Philip M [STAT]]

Katie,

I second Ben's suggestion to use functions in the drc library, not nls().  Not only do those functions model binomial or overdispersed binomial data, but they provide estimates and confidence intervals for the EC50 and any other EC, e.g. EC10.

However, neither handles x=0 very well.  The problem is the way the Weibull function is coded.  Instead of x^power, both use exp(power*log(x) ...).  The first is defined for x=0, the second is not.  

A work around is to use a small positive value for x, e.g. 0.01, as you suggest.  If there is some background level of x, so experimental dose = 0  is really exposure to a small background concentration, that background concentration is an easily justified replacement for 0.  If not, I rerun the analysis with different choices of small positive value.  If the low dose asymptote is well determined by the data, you should get similar parameter values and estimated ECx's for any small positive value.  This is a robustness check to make sure that an arbitrary choice doesn't affect the results.

Best wishes,
Philip