PharmPK Discussion - Numerical optimization for 2-compartment model

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• On 28 Jun 2006 at 16:46:31, Greg Tarpinian (sasprog474474.-a-.yahoo.com) sent the message
`The following message was posted to: PharmPKAll,I have been trying to use the nls( ) function in Splus to fit a 2-compartmentmodel to some oral dosing plasma PK data.  The nls( ) function allowsforsimple nonlinear least squares and weighted least squares.  I haveobtainedreasonable starting values using the "Method of Residuals" asdescribed inGibaldi & Perrier -- subject-specific plots appear to be very reasonableapproximations to the actual plasma concentrations.When I use nls( ) to try to refine these initial estimates, theestimatedgradient always turns out to be singular.  The algorithm stops in anugly way.My questions:    (1) What kind of algorithm should I be using to optimize a 2-compartment        model?  Nelder-Mead? Levenberg-Marquardt? Steepest Descent?    (2) If I want to obtain a weighted least squares estimate, whatkind of        weighting function would be typical to use?  I have seen somepeople        use ActualConc = EstimatedConc(1 + error) where error ~ N(0,1).....Any help would be greatly appreciated.Kind regards,     Greg[No experience with nls() but have you defined all the de equationsof the model. The algorithm and weighting shouldn't cause yourproblem if you have good estimates. Nelder-Mead is mathematicallymore robust on tough models - db]`
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• On 30 Jun 2006 at 10:38:19, "Walt Woltosz" (walt.-a-.simulations-plus.com) sent the message
`The following message was posted to: PharmPKGreg,Fitting PK to oral doses is not generally straightforward.The likelihood of different absorption rates in different regions of theintestinal tract is high (Ka is NOT a constant, even when thepermeabilityin all regions is nearly equal). Complications due to solubility,dissolution, precipitation, first pass extraction, etc., can alsoconfoundthe analysis. You can fit models that give pretty pictures, but indoing so,you may be covering up important phenomena to make the simulation gothroughthe data points in an artificial way. The value of such an incorrectmodelis questionable.There are, of course, those "easy" drugs where bioavailability iscomplete,permeability and solubility are high, ionization is not important,and soon, and for such drugs you can get away with simpler approaches. Buttheyare the exception, not the rule.Best regards,WaltWalt WoltoszChairman & CEOSimulations Plus, Inc. (AMEX: SLP)42505 10th Street WestLancaster, CA  93534-7059U.S.A.http://www.simulations-plus.comPhone: (661) 723-7723FAX:   (661) 723-5524E-mail: walt.-a-.simulations-plus.com`
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• On 1 Jul 2006 at 09:00:17, "Ma Guangli" (guanglima.-at-.gmail.com) sent the message
`Dear Greg,     Hi,     I am sorry that I have no nls() experience.     1) L-M algorithm is best choice in derivative methods such asGauss-Newton, steepest descent...Anyway, you should get more datapoints for derivative methods. Otherwise, the program should alert'singular'.     Nelder-Mead is robust. You can use N-M to estimate the initialvalues. Then input the initial values into L-M algorithm for moreexact results.     2)  If you want to obtain weighted least square estimates usingnls(), the choices are 1/C, 1/C*C, 1/(some function). They aretypical. Some weighted functions are changed during interations .They are diffcult to implement for nls().Best regardsMa Guangli`
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• On 2 Jul 2006 at 20:21:57, "Pravin Jadhav" (pravinj.at.gmail.com) sent the message
`Hello,There are several things you might need to check, if you think youhave reasonable initial estimates and a model. Take a look at thefollowing posting by Douglas Bates on the very same issue.http://www.biostat.wustl.edu/archives/html/s-news/1999-07/msg00201.htmlAlso, if you are using a self-starting function in Splus- make surethe data setup is appropriate.Hope it helps.Pravin`
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