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From |
Maarten buis <[email protected]> |

To |
[email protected] |

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

Date |
Thu, 25 Oct 2007 12:30:14 +0100 (BST) |

--- Rosy Reynolds <[email protected]> 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. > In general, how could I calculate an estimate and confidence interval > for the x required to achieve any given value of y? The general formula for a ED_{100*a} = ln(a/(1-a))/b2 + b3. You can use -nlcom- to calculate ED for any a, with its confidence interval. However, you should be aware that the estimated ED's can be way outside your observed range of x, in other words you can end up with an extrapolation. In the example below I estimated different EDs and also, just for fun, created a graph of ED_{100*a} against a. In this graph I added a rug for the values of x, and two horizontal lines representing the minimum and maximum observed value of x, to show when these estimated EDs are based on sparse data and when they are actually extrapolations. I created the rug by putting a minor tick on the inside of the y-axis for each unique value of x. The unique values of x are stored in r(levels) after -levelsof(x)-, and the minor ticks were placed using the -ymticks()- option. Tricks I used to store the lower and upper bounds of the confidence interval are discussed in: http://home.fsw.vu.nl/m.buis/wp/pvalue.html *---------------------- begin example -------------------- /*Create some data*/ set more off set seed 1234 drop _all set obs 500 gen x = invnorm(uniform()) gen y = 2 + 4 /(1 + exp(-.5*(x - 1))) + .5*invnorm(uniform()) /*Estimate the model*/ nl log4: y x estimates store log4 /*Calculating ED90*/ local lodds = ln(.9/(1-.9)) nlcom `lodds'/[b2]_b[_cons] + [b3]_b[_cons] /*graphing EDs*/ gen a = .05*_n in 1/19 gen ed = . gen lb = . gen ub = . local j = 1 forvalues i = 0.05(0.05)1 { di `i' estimates restore log4 local lodds = ln(`i'/(1-`i')) nlcom `lodds'/[b2]_b[_cons] + [b3]_b[_cons], post replace ed = _b[_nl_1] in `j' replace lb = _b[_nl_1] - invnormal(.975)*_se[_nl_1] in `j' replace ub = _b[_nl_1] + invnormal(.975)*_se[_nl_1] in `j++' } sum x local min = r(min) local max = r(max) levelsof x twoway rarea lb ub a || /* */ line ed a, /* */ clpattern(solid) /* */ ytitle(ED_100*a) /* */ legend(order( 1 "ci" 2 "ED"))/* */ ymticks(`r(levels)', /* */ tpos(inside) /* */ tlength(*2)) /* */ yline(`min' `max', lpattern(dot)) *----------------------- end example --------------------- (For more on how to use examples I sent to the Statalist, see http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html ) Hope this helps, Maarten ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- ___________________________________________________________ Want ideas for reducing your carbon footprint? Visit Yahoo! For Good http://uk.promotions.yahoo.com/forgood/environment.html * * 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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**References**:**st: reverse prediction - confidence interval for x at given y in nonlinear model***From:*"Rosy Reynolds" <[email protected]>

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