Dose linearity

After the administration of a drug, its concentration in plasma rises, reaches a peak, and then declines gradually to the starting level, due to the processes of distribution and elimination (p. 46). Plasma concentration at a given point in time depends on the dose administered. Many drugs exhibit a linear relationship between plasma concentration and dose within the therapeutic range (dose-linear kinetics (A) note different scales on ordinate). However, the same does not apply to drugs whose elimination processes are already sufficiently activated at therapeutic plasma levels so as to preclude further proportional increases in the rate of elimination when the concentration is increased further. Under these conditions, a smaller proportion of the dose administered is eliminated per unit of time. 

The time course of the effect and of the concentration in plasma are not identical, because the concentration-effect relationships obeys a hyperbolic function (B cf. also p. 54). This means that the time course of the effect exhibits dose dependence also in the presence of dose-linear kinetics (C). 

The default approach for non-threshold carcinogens is to assume low-dose linearity. This default approach applies when the information on the mode of action is supportive of linearity or the mode of action is not sufficiently understood. 

Models can predict low-dose linearity provided only that the response increases smoothly with dose. However, it is difficult to prove or disprove low-dose linearity experimentally even in bioassays involving extremely large numbers of animals. Often, linear extrapolation is criticized as being too conservative. 

This model assumes that any dosage effect has the same mechanism as that which causes the background incidence. Low-dose linearity follows directly from this additive assumption, provided that any fraction of the background effect is additive no matter how small. A best fit curve is fitted to the data obtained from a long-term rodent cancer bioassay using computer programs. The estimates of the parameters in the polynomial are called Maximum Likelihood Estimates (MLE), based upon the statistical procedure used for fitting the curve, and can be considered as best fit estimates. Provided the fit of the model is satisfactory, the estimates of these parameters are used to extrapolate to low-dose exposures. 

Edwards DMF, Pillizzoni C, Breuel HP, et al. Pharmacokinetics of reboxetine in healthy volunteers. Single oral doses, linearity and plasma protein binding. Biopharm Drug Dispos 1995 16 443-460. 

In light of uncertainty about mechanisms and human dose-response, the assumption of low-dose linearity continues to be a reasonable one. The large and growing burden of cancer in the United States (now at 500,000 deaths per year) vividly demonstrates the need for prevention. Prevention means not only addressing those cancer risks already established as "major" contributors to the disease burden (such as smoking). . . but also reducing current involuntary exposures to identified industrial carcinogens. 

Weyhenmeyer R, Mascher H, Birkmayer J. Study on dose-linearity of the pharmacokinetics of silibinin diastereomers using a new stereospecilic assay. Int J Clin Pharmacol Ther Toxicol 1992 30 134-138. 

The residue depletion profiles of closantel in cattle and swine are almost similar. Highest concentrations of closantel are seen in kidney, whereas the depletion of closantel from all edible tissues is very slow over the first 28 days of withdrawal. Within animal species, the parenteral and the oral routes of adminis-fration yield comparable residue concentrations provided that the oral dose is twice the parenteral dose. A dose linearity is also observed for residue concentrations in tissues doubling the dose for a particular route of administration doubles the residue level. 

Mueller, E.A. et al. (1994a) Improved dose linearity of cyclosporine pharmacokinetics from a microemulsion formulation.Pharm. Res., 11 301-304. 

Mollmann, H., P. Rhodewald, J. Barth, M. Verho, and H. Derendorf. 1989. Pharmacokinetics and dose linearity testing of methylprednisolone phosphdteopharm. Drug Disposl0 453-464. 

Response to a unit dose. Under an assumption of low-dose linearity, the response per unit dose is independent of dose, and the response to a unit dose is often given. Typical units of dose include ppm or ppb (parts per billion) in food or water, mg (kg d)-1 by ingestion, or ppm or jg m in air. 

Although some investigators have claimed that models lacking low-dose linearity are not appropriate for substances that cause... 

The current proprietary cyclosporin formulation, Sandimmun Neoral, is a microemulsion formulation. Although the formulation details of the Neoral formulation are not generally available, the relative bioavailabilities of the Neoral formulation and the initial Sandimmun formulation have been reported. In a dose linearity study, the relative bioavailability of the Neoral formulation compared with the Sandimmun formulation varied from 1.74 at a 200-mg dose to 2.39 at an 800-mg dose, illustrating the usefulness of the microemulsion formulation and suggesting an approximate twofold increase in bioavailability from the microemulsion formulation [74], Further studies showed that the absorption of cyclosporin from the Neoral formulation was significantly less variable [75] and less dependent on bile flow [76] than oral Sandimmun and that its absorption was unaffected by food [77], In terms of its apparent lack of reliance on bile for absorption, it is not known whether cyclosporin is absorbed from the formulation directly or just requires much lower bile salt concentrations to facilitate absorption. 

In particular, high-dose data usually cannot identify a threshold. A threshold is a dose or exposure below which there is no effect. It is often assumed that there is no threshold for an end point, like a gene mutation, that may involve one molecule of the toxicant and one target molecule in such a case, the dose-response relationship would be linear at low doses. If the observed relationship is linear over the dose range studied and if the fitted line is extrapolated to no effect (or the background frequency of effects) at zero dose, linear kinetics with no threshold are likely. But data are usually not clear. Even such a large carcinogenesis study as the EDqi study conducted by... 

The first tolerability studies in early clinical development always provide pharmacokinetic (PK) data over a considerable dose range. Especially the explorative first-in-man study with escalating single doses, or an explorative proof of principle study with escalating multiple doses provides a valuable basis for an exploratory assessment of dose linearity/ proportionality of drugs in humans. In addition such an assessment can directly help within the same study to optimize the dose selection and dose progression. Already in this early phase of the development, these data are going to support exposure-response relationships, and thus a potential submission (US FDA 2003, ICH E4 1994). 

Information on dose linearity/proportionality in humans is required during later development, if the dosage form is to be modified (EU CPMP1999), and especially if several strengths are in use (EU CPMP 2001). 

The design of an exploratory assessment of dose linearity/proportionality during the conduct of a first-in-man study for candidate drug (XYZ1234) is presented below. For the purposes of simplicity, the description is limited to the collection, handling, and interpretation of pharmacokinetic data although clearly safety parameters are in the main focus. 

As mentioned earlier, this type of supportive study provides explorative data related to dose linear-... 

If a pivotal investigation of dose linearity/proportion-ality becomes necessary, a dedicated study has to be conducted. It will typically be a study where the subjects get at least three different doses in a randomized, intra-individual crossover. The dose steps should cover the clinical recommended dose range, and - if possible - should also include the maximum tolerated dose they should ideally increase in a geometric progression. 

As described, the assessment of the dose linear-ity/proportionality is hampered in this case by the fact that for the lower doses the profile is not complete assessable, that obviously at the highest dose the resorption is limited, and that the used suboptimal formulation generates a lot of variability. Nevertheless, the example shows that even in this case predictions to support dose escalation were possible, and were even very helpful in that specific study. 

The information originating from preceding studies is needed for the proper design of a food interaction study safety and tolerance data has to be considered as well as the PK results including a food screen. The terminal half-life of the drug or its active metabolite(s) will provide the basis for the washout periods. Single dose linearity/proportionality will help to define the dose. Safety and tolerance data will justify the dose. The PK comparison in a food screen (FIM study, see below) will influence the sample size. 

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