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atish_azad ☆ 2008-10-01 16:18 (6466 d 14:51 ago) Posting: # 2461 Views: 8,599 |
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Dear Hs and all, For evaluating Dose Proportionality if I get 95%CI for the slope and if it does not contain Zero can I conclude Dose Proportionality, under assumption that standard deviation of response is proportional to the dose. Kindly guide me how can I conclude Dose Proportionality. Regards, Atish |
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martin ★★ Austria, 2008-10-01 20:24 (6466 d 10:45 ago) @ atish_azad Posting: # 2463 Views: 7,556 |
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dear atish ! note that there is a difference between dose-proportionality and dose-linearity. the existence of dose-proportionality implies also dose-linearity but not vice versa. when you would like to show dose-proportionality you have to ensure that a dose of zero leads to an AUC of zero (you have no intrinsic level of the substance investigated = baseline value of zero) this is identical to an intercept of zero when you plot AUC (y-scale) versus dose on the (x-scale). A simple regression analysis may be misleading when you have an saturable absorption or saturable metabolism at high doses investigated. for this reason, I suggest to check simply your baseline levels. the following paper gives a nice introduction on this topic: Hummel at al (2008). Exploratory assessment of dose proportionality: review of current approaches and proposal for a practical criterion. Pharmaceutical statistics, early view. a more complicated topic is the statistical identification (with a given type I error) of a dose range where dose-proportionality holds. this problem can be formulated as a sequence of hypothesis testing problems similar as in dose-finding studies as on the assumption of dose-proportionaliy AUC/dose = µ (i.e. constant for all doses investigated). hope this helps martin |
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atish_azad ☆ 2008-10-02 20:19 (6465 d 10:51 ago) @ martin Posting: # 2467 Views: 7,351 |
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Dear Martin, Thank you for a quick response. I will go through the article. Regards, Atish |
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martin ★★ Austria, 2008-10-03 11:24 (6464 d 19:45 ago) @ atish_azad Posting: # 2470 Views: 7,339 |
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dear atish ! you may find also pages 128-129 of Cawello et al. (2003). Parameters for Compartment-free Pharamcokinetics. Shaker Verlag, Aachen of interest. on assumption of dose-proportionality the following conditions hold 1) a dose of zero leads to an AUC of zero 2) the ratio of AUC/dose is constant for all doses (irrespective of equally or non-equally spaced doses) a plot the ratio of AUC/dose on the y-axis and dose on the x-axis should therefore be a straight line parallel to the x-axis. - in the case that the ratio of AUC/dose increases at higher doses you may have an saturable metabolism at higher doses - in the case that the ratio of AUC/dose decreases at higher doses you may have an saturable absorption at higher doses hope this helps martin |
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ElMaestro ★★★ Denmark, 2008-10-10 00:37 (6458 d 06:32 ago) @ martin Posting: # 2500 Views: 7,323 |
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Hi, That's all very good, but theory and practice often differ quite a bit. Typically it is the wish of a generic company to argue for linearity, but data for doing so are not produced by the generic company. In stead values are looked up in the literature (googling stuff is still cheaper than doing a clinical study). And that does more often than not gives 'something' which is difficult to handle. Perhaps, if you are really lucky, you find 4 or 5 data points for AUC as function of dose. So let me therefore ask: Given 4 or 5 points of AUC as function of Cmax, what criteria would you evaluate in order to argue for or against linearity? R squared in my opinion is rather useless here. Agreed you get a 'free' point (0,0) - that in fact is the only point that will be known with certainty for exogenous molecules. But still you are not really in the comfort zone, are you?! EM. |
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martin ★★ Austria, 2008-10-10 11:58 (6457 d 19:12 ago) @ ElMaestro Posting: # 2504 Views: 7,219 |
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Dear Elmaestro ! I am definitely not proposing R squared to assess dose-proportionality. you can assess the relation between dose and AUC/Cmax using the power-law model. the power-law model allows you to estimate a “proportionality parameter” along with a confidence interval (CI). based on these results you can assess dose-proportionality (testing for difference / testing for equivalence). calculation details can be found in the mentioned paper of Hummel et al. (2008). the width of the CI for the proportionality parameter clearly depend on the sample size used as with every statistical method. however, this CI gives you an estimate for the size of a potential disproportional behavior which can be used to assess the effect in terms of clinical relevance AND in term of statistical significance. note that Hummel et al (2008) suggest a rather wide acceptance range to accept dose-proportionality which may be motivated for the reasons you pointed out. best regards Martin |
Ing. Helmut Schütz