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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: reverse prediction - confidence interval for x at given y in nonlinear model |

Date |
Fri, 26 Oct 2007 19:21:58 +0100 |

We have been at cross purposes. Your log(0) as 0 is, I see, only a trick that keeps the zeros in the frame _so long as you also have a dummy for 0_. My point is that it does not help in problems in which there is no dummy for 0. Suppose your doses are 0 0.1 0.2 0.3 0.4 0.5 in whatever units are being used. Neither Stata nor the mathematics knows about the units. Then the recipe cond(dose == 0, 0, log(dose)) is not even monotonic in dose. 0 is treated as if were larger than any other positive value in the data! Also if any dose is 1, this recipe treats 0 and 1 as equivalent. Nick n.j.cox@durham.ac.uk -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Daniel Waxman Sent: 26 October 2007 19:07 To: statalist@hsphsun2.harvard.edu Subject: RE: st: reverse prediction - confidence interval for x at given y in nonlinear model Regarding Nicks comment on replacing log(0) with zero: It may not be pretty, but it does work! If zdose=0 when dose=0, 1 otherwise and ldose=log(dose) for the condition dose!=0, zero otherwise then you are fitting the model: xb =b [zdoseXldose]*zdose*ldose + b[zdose]*zdose + b[cons] so when dose=0 the first two terms drop out and the coefficient for the constant represents dose=0. In all other cases, all 3 terms remain. It might be more palatable if you replace all the zeroes in the preceding discussion with a *very small number* For the record, this gives exactly the same result as using the catzero option with Patrick Royston's -mfp- routine. See . help mfp Dan -----Original Message----- From: "Nick Cox" <n.j.cox@durham.ac.uk> Subj: RE: st: reverse prediction - confidence interval for x at given y in nonlinear model Date: Fri Oct 26, 2007 9:15 am Size: 1K To: <statalist@hsphsun2.harvard.edu> The idea of a dummy for zero dose is interesting but doesn't seem to map on the kind of model being discussed here. More importantly, that does nothing to solve the major issue, which is thinking up a good alternative to log(0). Replacing log(0) by 0 is equivalent to replacing 0 by 1 in whatever units are being used. How sensible that is will depend partly on the range of the data. If the rest of the data were 0.1 to 0.5 it would be crazy! The problem in general is that mapping 0 to a very small number creates a very large negative logarithm. Although I guess that there must be other solutions, one is to do a sensitivity analysis of varying choices of c in log(x + c), or cond(x == 0, c, log(x)). Nick n.j.cox@durham.ac.uk Daniel Waxman Regarging the treatment of zeroes in log(dose): Since zero likely reflects a qualitatively different situation than small values of dose you are better off treating it as such. Here is a trick to get stata to do what you want: gen ldose = log(dose) gen zdose = 1 - (dose == 0) replace ldose = 0 if dose == 0 logit outcome ldose zdose ... Thus ldose is a term which represents log dose for positive values, and falls out for doses of zero. zdose is a dummy which is zero for doses of zero and one otherwise. If you look at the model as: logit outcome ldose*zdose zdose and look at what happens as dose (untransformed) becomes infinitesimal, you can see how this works. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ --- message truncated --- * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: reverse prediction - confidence interval for x at given y in nonlinear model***From:*"Daniel Waxman" <dan@amplecat.com>

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