SV: Ambiguous independence of independent variable.

Hi Matts, I agree on your conclusions and think the issue of missing data is a very similar problem. There the missing completely at random and missing at random would match your examples a and b. For missing data there exists litterature and also perhaps a better understanding among statistician. Rubins book I think is a good referece with results showing good properties of maximum likelihood. Bw Magnus ________________________________ Frn: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> fr Matts Kgedal <mattskagedal_at_gmail.com> Skickat: den 30 september 2015 20:33:16 Till: nmusers_at_globomaxnm.com mne: [NMusers] Ambiguous independence of independent variable. 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> ________________________________ Confidentiality Notice: This message is private and may contain confidential and proprietary information. If you have received this message in error, please notify us and remove it from your system and note that you must not copy, distribute or take any action in reliance on it. Any unauthorized use or disclosure of the contents of this message is not permitted and may be unlawful.

Hi Matts, I agree on your conclusions and think the issue of missing data is a very similar problem. There the missing completely at random and missing at random would match your examples a and b. For missing data there exists litterature and also perhaps a better understanding among statistician. Rubins book I think is a good referece with results showing good properties of maximum likelihood. Bw Magnus ________________________________ Från: [email protected] <[email protected]> för Matts Kågedal <[email protected]> Skickat: den 30 september 2015 20:33:16 Till: [email protected] Ämne: [NMusers] Ambiguous independence of independent variable. 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> ________________________________ Confidentiality Notice: This message is private and may contain confidential and proprietary information. If you have received this message in error, please notify us and remove it from your system and note that you must not copy, distribute or take any action in reliance on it. Any unauthorized use or disclosure of the contents of this message is not permitted and may be unlawful.