Effect of placebo or drug to the baseline value

Dear NM users, Many PK-PD articles reported the effect of placebo or drug to the baseline value to be 1. Additive: Baseline- Placebo effect - Drug effect 2. Proportiona: Baseline*(1- Placebo effect)*(1-Drug effect) However, I have not come across any literature with combined approach of additive and proportional treatment effect e.g (Baseline- Placebo effect)*(1-Drug effect) Based on the initial dose-response relationship analysis using longitudinal data, combined additive placebo effect and proportional drug effect (Baseline- Placebo effect)*(1-Drug effect) resulted in lowest OFV, good parameter estimates and better Goodness of fit plots compared to the above 2 approaches. I would like to seek your opinion on combined approach in PKPD modeling. Thanking you, Best Regards, Venkatesh Pilla Reddy PhD Fellow, Dept. of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands Email: [email protected]

Hi Venkatesh, I think it is reasonable to postulate models with combined additive and proportional effects as long as they are supported by the data. You may wish to generate some graphical diagnostics to support your structural model choice in addition to the OFV (especially since these different structural forms are not hierarchical). For example, to illustrate that Baseline and Placebo responses are additive where Y=B - P, you could plot change from baseline (i.e. D=Y - B versus B for the placebo group and show that there is no trend across subjects. If there is a trend such that the delta increases with baseline then perhaps a multiplicative relationship exists. If Baseline and Placebo effects are multiplicative where Y = B*(1-P) then a plot of Y/B (or P=1-Y/B) versus B should show no trend. You could do a similar graphical diagnostic for drug effect but it's much harder to evaluate if you don't have crossover data where the same patient receives both placebo and active drug treatments. Assuming you do have crossover data and for each subject you have a baseline response for placebo (Bpbo) and active treatment (Btrt) and post-baseline responses for placebo (Ypbo) and active treatment (Ytrt), then for your combined additive and proportional model you have Ypbo = (Bbpo - P) and Ytrt = (Btrt - P)*(1-D). We can solve for P in the first equation to obtain P = Bpbo - Ypbo. Now substitute for P in the second equation and solve for D and you get D = [(Ypbo - Bpbo) - (Ytrt - Btrt)]/[(Ypbo - Bpbo) + Btrt] and if you plot this versus baseline (for Bpbo or Btrt) it should not show a trend across subjects. You can contrast this with a similar approach for the fully additive model where Y = B - P - D and show that D=(Ypbo - Bpbo) - (Ytrt - Btrt) for the additive model. Thus, if a plot of (Ypbo - Bpbo) - (Ytrt - Btrt) versus baseline (for Bpbo or Btrt) shows a trend and a plot of [(Ypbo - Bpbo) - (Ytrt - Btrt)]/[(Ypbo - Bpbo) + Btrt] versus baseline does not, then I think you have a graphical diagnostic to illustrate/support your choice of using the combined additive and proportional model. If you have longitudinal data you may want to generate such a plot by time point and if you have more than one active dose level you may want to generate such plots for each dose. I hope this helps. Kind regards, Ken Kenneth G. Kowalski President & CEO A2PG - Ann Arbor Pharmacometrics Group, Inc. 110 E. Miller Ave., Garden Suite Ann Arbor, MI 48104 Work: 734-274-8255 Cell: 248-207-5082 Fax: 734-913-0230 [email protected]