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From |
"Joseph Coveney" <[email protected]> |

To |
"Statalist" <[email protected]> |

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

Date |
Fri, 26 Oct 2007 01:15:05 -0700 |

Rosy Reynolds wrote: Sigmoid models are customary in pharmacodynamics (dose-response studies). According to custom, I am using a 4-parameter logistic (sigmoid Emax) model. This is very easily done with -nl- as Stata has this model already built in. The model is y= b0 + b1/(1 + exp(-b2*(x-b3))) + error and the coefficients can be interpreted as b0 = baseline outcome b1 = Emax i.e. largest change from baseline b2 = Hill or slope coefficient b3 = ED50 i.e. value of x (dose) required to produce half-maximal effect, that is x required for y=b0 + b1 / 2 As the ED50 is a parameter of the model, -nl- reports it with a standard error and confidence interval. What I would like to do is obtain estimates with standard errors and confidence intervals for other similar measures e.g. the ED90, the dose required for 90% of maximal effect. [redacted] -------------------------------------------------------------------------------- Maarten gave a solid, well documented answer, as usual. Just a comment and a follow-on question. First the comment. If I'm not mistaken, the four-parameter logistic model Rosy used is for the *logarithm* of dose and *logarithm* of ED50, and not the dose and ED50, per se (cf. Maarten's y-axis values). So, Rosy will need to remember to logarithmically transform drug doses before fitting the model, and to back-transform the log-ED50 (log-ED90) values and their confidence limits afterward. I believe that this parameterization is sometimes advocated in order to guarantee strictly positive values when lower confidence limits for ED50 (ED10, etc.) are back-transformed, that is, in order to assure that you won't end up with a value of, say, -10 mg of drug as a lower confidence limit for a poorly estimated ED10. Perhaps the parameterization is numerically stabler, too, in some sense, but you cannot use it if you wanted to include results from a placebo treatment group in a clinical study or a vehicle-control condition in a laboratory setting. As to the question: given that the generally accepted four-parameter (so-called, sigmoid Emax) model for a dose-response curve is E = Emin + Emax * Dose^Hill / (Dose^Hill + ED50^Hill) (E is response, Emin is response at zero dose, Emax is asymptotic response at infinite dose, Dose is untransformed dose, Hill is the coefficient of receptor cooperativity, ED50 is dose yielding a response that is Emin + half of Emax), does the -nl log4:- four-parameter logistic model give rise to biased estimates of ED50 (ED10, ED90, etc.) and confidence intervals in the original measurement scale with nonasymptotic sample sizes? That is, should a pharmacologist ever use -nl log4:- in lieu of the model shown just above? Joseph Coveney * * 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/

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