Parameter Uncertainty and Covariate effects

Dear All, In order to account for uncertainty in estimated parameters when running a simulation, a natural approach would be running multiple simulations for different parameter vectors which are drawn from the (theoretical, asymptotic) distribution of the estimator (i.e. normal with mean THETA and covariance according to the NONMEMs $COR output for the THETAs). This approach may in some cases (particularly, when there are a lot of covariate effects estimated) lead to very broad parameter distributions, even assigning some quite high probability of unphysiological values if one didn’t have good quality data, strong priors or a very careful parametrization of the model (e.g. transforming/bounding parameters, which requires/introduces prior knowledge as well). Another problem connected with parameter uncertainty on covariate effects is the following. Say we model TVCL = THETA(1) SEX_EFF = THETA(2) CL = TVCL * SEX_EFF**SEX, (Eq. 1) where male is coded as SEX=0, female as SEX=1. In this case, when using the above mentioned technique to account for parameter uncertainty, the female population will have a more variable (uncertain) PK, not just different one. If we phrase the problem differently, using CL = TVCL * SEX_EFF**(1-SEX) , (Eq. 2) The conclusion would be the other way around (i.e. male PK is more uncertain). One approach to deal with the second problem could be this: In order to remove this (usually unjustified) assumption (the female population having a less certain PK compared to the male), one could try to model the same covariate effect as follows: TVCL = THETA(1) SQRT_SEX_EFF = THETA(2) CL = TVCL * SQRT_SEX_EFF**SEX / SQRT_SEX_EFF**(1-SEX) In this case TVCL would already include “half” of the effect (on the log scale; the “new” TVCL would be TVCL*SQRT(SEX_EFF) in terms of the parameters used in Eq.1). With this approach, both sub-populations, male and female get “some part” of the uncertainty effect. Of course it would be even nicer to let the data decide which sub-population gets how much uncertainty exactly instead of evenly splitting it. How do you deal with uncertainty in the estimates of covariate effects when it comes to simulations/predictions? Kind Regards, ________________________________________________________________________________________________________________________ SVEN STODTMANN, PHD Pharmacometrician AbbVie Deutschland GmbH & Co KG Clinical Pharmacology and Pharmacometrics Knollstrasse 50 67065 Ludwigshafen am Rhein, Germany OFFICE +49 621-589-1940 EMAIL [email protected] abbvie.com ________________________________________________________________________________________________________________________ ________________________________ Sitz der Gesellschaft: Wiesbaden - Registergericht: AG Wiesbaden HRA 9790 Persönlich haftende Gesellschafterin: AbbVie Komplementär GmbH Sitz der persönlich haftenden Gesellschafterin: Wiesbaden - Registergericht: AG Wiesbaden HRB 26371 Geschäftsführer: Dr. Patrick Horber, Thomas Scheidmeir, Dr. Stefan Simianer, William J. Chase Vorsitzende des Aufsichtsrats: Dr. Azita Saleki-Gerhardt This communication may contain information that is proprietary, confidential, or exempt from disclosure. If you are not the intended recipient, please note that any other dissemination, distribution, use or copying of this communication is strictly prohibited. Anyone who receives this message in error should notify the sender immediately by telephone or by return e-mail and delete it from his or her computer. Diese Kommunikation kann Informationen enthalten, die geheim, vertraulich oder hinsichtlich der Offenlegung beschränkt sind. Wenn Sie nicht der beabsichtigte Empfänger sind, nehmen Sie bitte zur Kenntnis, dass jede Weitergabe, Verteilung, Verwendung oder Vervielfältigung dieser. Kommunikation strikt untersagt ist. Jeder, der diese Nachricht fehlerhaft erhält, sollte den Sender unverzüglich telefonisch oder durch Rücksendung der E-Mail benachrichtigen und diese von seinem oder ihrem Computer löschen.

Dear Sven If you don't assume the covariance between THETA(1) and THETA(2) to be zero but use the estimated covariance value, you do let the data speak. A problem in this respect is that publications never give such values even if it of course is possible. With online access to model code and output (as with the DDMoRe repository (repository.ddmore.eu)) it will be more likely to find the information. Best regards, Mats Skickat från min iPhone > 11 jan 2016 kl. 14:28 skrev Stodtmann, Sven <[email protected]>: > > Dear All, > > In order to account for uncertainty in estimated parameters when running a > simulation, a natural approach would be running multiple simulations for > different parameter vectors which are drawn from the (theoretical, > asymptotic) distribution of the estimator (i.e. normal with mean THETA and > covariance according to the NONMEMs $COR output for the THETAs). > This approach may in some cases (particularly, when there are a lot of > covariate effects estimated) lead to very broad parameter distributions, even > assigning some quite high probability of unphysiological values if one didn’t > have good quality data, strong priors or a very careful parametrization of > the model (e.g. transforming/bounding parameters, which requires/introduces > prior knowledge as well). > > Another problem connected with parameter uncertainty on covariate effects is > the following. Say we model > TVCL = THETA(1) > SEX_EFF = THETA(2) > CL = TVCL * SEX_EFF**SEX, (Eq. > 1) > where male is coded as SEX=0, female as SEX=1. > In this case, when using the above mentioned technique to account for > parameter uncertainty, the female population will have a more variable > (uncertain) PK, not just different one. If we phrase the problem differently, > using > CL = TVCL * SEX_EFF**(1-SEX) , (Eq. 2) > The conclusion would be the other way around (i.e. male PK is more uncertain). > > One approach to deal with the second problem could be this: > In order to remove this (usually unjustified) assumption (the female > population having a less certain PK compared to the male), one could try to > model the same covariate effect as follows: > TVCL = THETA(1) > SQRT_SEX_EFF = THETA(2) > CL = TVCL * SQRT_SEX_EFF**SEX / SQRT_SEX_EFF**(1-SEX) > In this case TVCL would already include “half” of the effect (on the log > scale; the “new” TVCL would be TVCL*SQRT(SEX_EFF) in terms of the parameters > used in Eq.1). > With this approach, both sub-populations, male and female get “some part” of > the uncertainty effect. > Of course it would be even nicer to let the data decide which sub-population > gets how much uncertainty exactly instead of evenly splitting it. > > How do you deal with uncertainty in the estimates of covariate effects when > it comes to simulations/predictions? > > Kind Regards, > ________________________________________________________________________________________________________________________ > SVEN STODTMANN, PHD > Pharmacometrician > > AbbVie Deutschland GmbH & Co KG > Clinical Pharmacology and Pharmacometrics > Knollstrasse 50 > 67065 Ludwigshafen am Rhein, Germany > OFFICE +49 621-589-1940 > EMAIL [email protected] > > abbvie.com > ________________________________________________________________________________________________________________________ > > ________________________________ > > Sitz der Gesellschaft: Wiesbaden - Registergericht: AG Wiesbaden HRA 9790 > Persönlich haftende Gesellschafterin: AbbVie Komplementär GmbH > Sitz der persönlich haftenden Gesellschafterin: Wiesbaden - Registergericht: > AG Wiesbaden HRB 26371 > Geschäftsführer: Dr. Patrick Horber, Thomas Scheidmeir, Dr. Stefan Simianer, > William J. Chase > Vorsitzende des Aufsichtsrats: Dr. Azita Saleki-Gerhardt > > This communication may contain information that is proprietary, confidential, > or exempt from disclosure. If you are not the intended recipient, please note > that any other dissemination, distribution, use or copying of this > communication is strictly prohibited. Anyone who receives this message in > error should notify the sender immediately by telephone or by return e-mail > and delete it from his or her computer. > > Diese Kommunikation kann Informationen enthalten, die geheim, vertraulich > oder hinsichtlich der Offenlegung beschränkt sind. Wenn Sie nicht der > beabsichtigte Empfänger sind, nehmen Sie bitte zur Kenntnis, dass jede > Weitergabe, Verteilung, Verwendung oder Vervielfältigung dieser. > Kommunikation strikt untersagt ist. Jeder, der diese Nachricht fehlerhaft > erhält, sollte den Sender unverzüglich telefonisch oder durch Rücksendung der > E-Mail benachrichtigen und diese von seinem oder ihrem Computer löschen.

Hi Sven, As Mats said, you need to account for correlation between parameters. Using uncorrelated parameters, you will have all the issues discussed below (high variability on the second population). For model building, you could do the following to minimize that correlation and have the variance of your terms more reasonable (likely approximately proportional to the percent of subjects in your data set who are men and women): TVCL = THETA(1)*(1-SEX) + THETA(2)*SEX That would give separate estimates of THETA(1) and THETA(2) for each sex that would be logically uncorrelated. If you have a specific desire to estimate the ratio of clearance, there are several potential ways to estimate it from separate parameters. The best is probably bootstrapping the results and using the empirical distribution from the bootstrap. Taking the ratio of two normally distributed variables unfortunately gives a Cauchy distributed parameter which has no mean or standard deviation (though many people just take the ratio and move on-- it's not far from accurate). Thanks, Bill