Re: Ambiguous independence of independent variable.

Dear Matts, Your question with respect to adaptive study designs is very interesting and relevant. You wrote: > PK measured at day 1 and day 10. Patients with high AUC on day 1 dose reduce before day 10. *example 1:* If naively analyzing the relation between dose and PK on day 10 it will appear that the PK is not dose proportional, when it actually is. This results when the supposedly independent variable (dose) is not independent of the DV. (In this example it will falsely appear that low dose will result in low clearance.) If you mean with ‘naively analyzing the relation between dose and PK’ to perform a correlation analysis between the dose and drug concentration (e.g. AUC), this indeed will result in the false conclusion that AUC is not related to dose, since all patients will have approximately the same AUC because the dose was adjusted to get the same AUC. This indeed would be a nice example of poor science, since the independent variable dose is dependent on the dependent variable (AUC). On the other hand, if the data are analysed using a population pharmacokinetic model using the data on day 1 and/or day 10, one would conclude that there is inter-individual variability in clearance, and mean and inter-individual variability can be obtained from an appropriate population analysis. Even the data on day 1 are not required. However, it should be realized that this study design does not allow to prove dose-linearity. But if dose-linearity has been proven in earlier studies, I don’t see how this study design with proper analysis could lead to biased estimates of PK parameters. If this view is correct, your remaining questions seem not relevant anymore. I would appreciate any comment to my perhaps naive comments. best regards, Johannes H. Proost Matts Kågedal schreef op 30-9-2015 om 20:33: > Hi nonmem users! > > I have troubles explaining to statisticians (and perhaps to myself) why it can be OK to model data where the dose is adjusted based on the dependent variable, and wonder if I could get some help. > > This is a very relevant issue when planing for adaptive designs where the dose is being adjusted based on the endpoint of interested or a correlated endpoint. It then becomes important to have a good understanding of the potential impact and ideally some convincing references for any skeptical colleagues. Also in many cases doses are modified based on safety (e.g. in oncology), and understanding how this can impact the analysis is important. Statisticians can become very suspicious (which is their job) when there is any ambiguity in the independence of the independent variable. > > *A PK study example for illustration of the problem:* > > PK measured at day 1 and day 10. Patients with high AUC on day 1 dose reduce before day 10. > > *example 1:* If naively analyzing the relation between dose and PK on day 10 it will appear that the PK is not dose proportional, when it actually is. This results when the supposedly independent variable (dose) is not independent of the DV. (In this example it will falsely appear that low dose will result in low clearance.) > > *example 2: *If analyzed longitudinally using all data and a pop PK model, this problem goes away, since the model will be informed also by day 1 PK and the PK-parameters will be unbiased. > > *example 3:* If however no PK-measurements were taken on day one but dose reduction could still occur based AEs, we would get a biased dose proportionality assessment if AEs are correlated with exposure. (pop-PK analysis would not help). > > The above is a PK-example for illustration, but the question may probably be more relevant when modeling safety and efficacy data. > > Thinking along the same lines as for informative vs non-informative censoring, the parameters of a longitudinal model based on data with dose modifications will be _unbiased_ if: a) the dose modifications are completely uncorrelated to the dependent variable (DV). (We could call this non-informative dose modification or dose modification completely at random) b) if the dose modification is based on an _*observed*_ value of the DV where this observation is included in the analysis (We could call this non-informative dose modification or dose modification at random) (corresponds to example 2 above). > > - The parameters will be _biased_ if: > > c) the dose modification is based on an unobserved value of the DV (Could call this informative dose modification or modified not at random). (corresponds to example 3 above) > > In case C, the model would need to include a function that estimates the probability of dose reduction based on the endpoint of interest. E.g. for example 3, one would need to estimate the probability of dose reduction as a function of exposure. > > Coming back to my original question, is there any literature that could help understanding this issue? (Ideally in a language that can be understood also by the less statistically oriented pharmacometrician, I find statistical literature hard to read sometimes). > > Are there further/better arguments for why example 2 will result in unbiased parameter estimates (in addition to explanation b). Any arguments against? > > Are there any examples in the literature showing when failure to account for "informative dose adjustments" results in biased parameter estimates? > > Best regards, > Matts > > -- > > Matts Kagedal > Pharmacometrician, Genentech > Mobile: +1(650) 255 2534 <tel:%2B1%28650%29%20255%202534>