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Dose proportionality: a critical element in drug development and patient therapy

In pharmacokinetics, the term dose proportionality is commonly used. If a drug product exhibits dose proportionality, there will be a proportional increase in the amount of drug reaching the systemic circulation, usually expressed in the exposure such as AUC or Cmax, when the dose is increased. Exposure analysis of three or more doses is typically used to assess dose proportionality.

Why is Dose Proportionality useful and important? 

Early in the pre-clinical development process, we evaluate dose proportionality in animal species. Thereafter, if the drug advances to clinical trials, one of the first assessments in humans is to evaluate dose proportionality.

In general, there are three possible outcomes of dose proportionality:

  1. Exposure is dose proportional (double the dose, double the amount in circulation)
  2. Exposure is less than dose proportional (double the dose, less than double the amount in circulation)
  3. Exposure is greater than dose proportional (double the dose, more than double the amount in circulation

Dose-response studies in terms of Pharmacokinetics (PK) 

The pharmacokinetics or PK parameters AUC and Cmax are often to characterize the dose-response curve with respect to efficacy. Dose proportionality is perhaps the most desirable dose-response relationship between dose level and PK responses, such as area under the curve concentration-time curve (AUC) due to its clear interpretation. For example, we will expect to see a doubled AUC if we double the dose under the assumption of dose proportionality.

One can predict the concentration for a given dose with dose proportionality and can predict the drug level at different dose levels, which is the significant information during the early drug development. Predicting whether a drug level falls within the therapeutic range, especially when the window is narrow, is critical information for drug development and potential patient treatment. The main determinant of dose proportionality is drug clearance. Understanding dose proportionality can also aid in the management of potential safety concerns or toxicity if the drug is not proportionally eliminated, regardless of whether the drug can be built up or not.

The use case of Dose Proportionality in Clinical Studies 

There are points to consider when conducting clinical trials as part of the clinical research development program. Dose proportionality clinical trials with detailed precision dosing/clinic conduct, as well as data analyses, are essential for achieving the study’s objectives. BioPharma Services Inc., a global leader in clinical research and phase 1 clinical trials, with extensive experience in such clinical study, can assist you to reach your goal. Our scientists in the pharmacokinetics and pharmacometrics department will assist your drug development by providing scientific phase 1 clinical trial design, with professional staff that carry out the clinical trial with precision and GCP regulation.

There are a number of different approaches to the assessment of dose proportionality, but most of these are directed toward hypothesis testing. An empirical model relating the log of the pharmacokinetic parameter linearly to the log of the dose (the “power model”) provides a readily interpreted measure of the degree of non-proportionality. 

Various methods for assessment of dose proportionality have been proposed in literature. Gough, et al. concluded that dose proportionality assessment is a problem of estimation rather than hypothesis testing. Both estimation of a treatment difference and comparison of the corresponding confidence interval (CI) to an equivalence region have been applied in numerous studies. 

Typically, log-transformed, dose normalized AUC values are evaluated by ANOVA and ratios of geometric means and their corresponding 90% CI’s are reported. Dose proportionality is concluded if the CI for the difference between two treatments lies entirely within the range defined for bioequivalence testing. Treating dose as a continuous, rather than a categorical variable, requires a mathematical model. 

Smith et al. proposed that to establish dose proportionality, the 90% CI for the ratio of dose normalized means should lie within pre-specified limits. In the case of applying the power model, this equates to comparing the 90% CI around the slope, b.

Power-law Model Expression


Power-law Model sampled from actual study completed by BioPharma Services.

When a Sponsor Pharma company comes to BioPharma Services to conduct a dose proportionality study, we evaluate the analysis options depending on the study objectives. Many times, the BioPharma Services Statistician Team recommends the use of the Power Model as the statistical methodology to determine whether the doses are proportional. 

Power model is a simple regression analysis of log of the pharmacokinetic parameter and log of the dose. We recommend the use of the Power Model and reporting both the point estimate and its confidence interval of the slope.

After the logarithmic transformation, the power-law model can be expressed as: 

logarithmic transformation

Why Choose BioPharma Services for a Dose Proportionality study?

The information gained from the dose proportionality study can help predict the drug level at the dose of interest, and also help monitor the patient level during the therapy. Dose proportionality is a critical part of the new drug product development and required by the FDA and other major regulatory agencies. BioPharma Services can help on your journal from generating of scientific design, conduct of the clinical portion with subject dosing and safety management, carrying out the statistical data analyses and completion of the clinical study report. As a preferred clinical research partner, BioPharma Services can assist you in all critical steps for your success of clinical development with dose proportionality study. 

Find out why BioPharma might be the right partner for you! Learn more about BioPharma Services and the wide array of services we provide.

BioPharma Services, Inc., a Think Research Corporation and clinical trial services company, is a full-service Contract Clinical Research Organization (CRO) based in Toronto, Canada, specializing in Phase 1 clinical trials 1/2a and Bioequivalence clinical trials for international pharmaceutical companies worldwide. BioPharma has clinical facilities both in the USA and Canada with access to healthy volunteers and special populations.

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