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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

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

Subject |
Re: st: nl -choice between alternative parametrisations of sigmoid models |

Date |
Sat, 27 Oct 2007 00:18:22 -0700 |

Rosy Reynolds wrote (excerpted): In the other set, b2 is negative, the sign of b1 is reversed, and b0 becomes the outcome at infinitely high dose instead of at the lowest doses. The lowest-dose outcome is now given by b0+b1. With our data, -nl- naturally produces the set of coefficients with negative b2. -------------------------------------------------------------------------------- I wonder if your dose-response curve is descending (e.g., growth rate of a bacterium in presence of increasing concentrations of an antibiotic drug to which it's susceptible). If that's the case, then it explains why -nllog4.ado- sets up initial values that lead to what you've been seeing. If it's the case, then you can reparameterize your model to accommodate that the response is inhibitory in nature. Take a look at: www.boomer.org/pkin/PK01/PK2001138.html . Scroll down about halfway, where Nick Holford posts a reply. The pertinent text includes, "The inhibitory sigmoid Emax model simply has a negative value for Emax but can also be written like this (the inhibitory fractional sigmoid Emax model): E = E0*(1 - Emax * C^Hill / (EC50^Hill + C^Hill)) where Emax is now a (non-negative) fraction between 0 and 1. If Emax=1 then the response will be 0 at infinite C i.e. the drug produces complete inhibition of the response." On the otherhand, if your dose-response curve is ascending with homoscedastic errors as in the example do-files that you've posted, and if you set up your initial values with Emax >> Emin, Hill >=1 and any reasonable estimate for log ED50, then I can't imagine why -nl- would wander off toward negative values for Hill coefficients with any dataset where it's going to attain convergence with nonmissing coefficient standard errors. About the only other thought that occurs (other than imposing nonlinear constraints, as others have already suggested) would be to automatically calculate initial values: summarize response, meanonly local Emax = r(max) local E0 = r(min) summarize log_dose, meanonly local log_ED50 = r(mean) nl log4: . . . , initial(b0 `E0' b1 `Emax' b2 1 b3 `log_ED50') If your dose-response is descending (inhibitory) and you're using Nick Holford's suggestion to parameterize as an inhibitory fraction sigmoid Emax model, then you'd set E0 to be r(max), and set Emax to be 1 - r(min) / r(max). If the middle dose is always the same in your designed experiments, then there's no need to go through the motions of -summarize log_dose- each replicate to get an initial value. Likewise, if you some prior knowledge that the Hill coefficient should be in the neighborhood of, say, 3, then that will be a better fixed initial value than 1. You might be able to accommodate zero doses by modifying the four-parameter logistic model in the manner that Daniel Waxman suggests, i.e., set up an indicator variable for zero-valued doses, create a modified logarithmically transformed dose variable that has nonmissing value (pick one arbitrarily) for observations at zero dose, and fit: nl (response = {Emin} * dose_is_zero_dummy + /// {Emax} * (1 - dose_is_zero_dummy) / (1 + /// exp({Hill} * ({ED50} - log_dose))), initial(. . .) I'm not sure that that would be my first choice over just using the conventional parameterization of the sigmoid Emax model, but it might be worth a try if you insist upon the four-parameter logistic. In your reply to Austin Nichols, you indicated a reluctance to choose starting values. With nonlinear regression, you're liable to encounter a few occasions where you'll need to choose starting values manually. 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/

**Follow-Ups**:**Re: st: nl -choice between alternative parametrisations of sigmoid models***From:*"Rosy Reynolds" <rr@dandr.demon.co.uk>

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