Patients’ Non-compliance with Drug Administration Times and Optimal Population Design in Pharmacokinetics.

Objectives: Optimal designs in population pharmacokinetics (PK) usually assume that drug administration times are fixed in the trial. However, the fact that patients take the drug later or earlier than specified by the experimenter shifts post-dose measurements to suboptimal times. The problem occurs when patients administer the drug unsupervised before coming to the clinic, as in certain Phase 2/3 trials.

In this setting, experimenter specifies how long before each clinical visit the patients should take the drug so as to maximise the precision of the population parameter estimates. Mathematically, the design problem is to find the optimal times to be specified, given the random error caused by patients’ non-compliance (cf. Pronzato, 2001). The problem is related to that described in Johnston et al. (2005). However, their study considers sampling windows rather than times, and additional clinical constraints (cf. also Green and Duffull, 2003).

The purpose of the presentation is to assess information loss arising from patients’ non-compliance with specified administration times. The assessment is made assuming realistic time compliance for a simulated D-optimally designed trial. To reduce information loss, compliance-based designs and compliance improvement measures are suggested.

Methods: In the simulation, the same patients are instructed to take a drug at a specified time before each of their three clinical visits. At the clinic, a single sample is taken at the beginning of each visit. The distributions of administration times with non-compliance were based on the data from actual clinical trials. The data contained patients’ dosing histories collected by an electronic monitoring device, the use of which is also assumed in the simulated trial. Consequently, the actual administration times are random at the design stage, but known for estimation purposes.

For the assumed first-order absorption one-compartment PK model (cf. Retout and Mentré, 2003) with perfect compliance, a three-point D-optimal population design was found using Matlab. The optimality criterion value was calculated for both perfect and empirically-based compliance, assuming that the three-point D-optimal design is used.

Results: The criterion value dropped between 25% and 40%, depending on the pattern of non-compliance. The largest decrease occurred at about the first optimal time post-dose. The smallest decrease occurred at about the third optimal time, suggesting varying significance of compliance for different visits.

The next stage of the research considers compliance-based adjustments to optimal design algorithms. First, the D-optimality criterion was optimised over a prior population distribution of administration times. The algorithm thus differed from current standard methods, which assume fixed design times. For the considered empirical-based distributions, designs different from the standard D-optimal one were obtained, and the criterion value increased by between 6% and 10%. Second, since the same patients attended all three clinical visits, an optimal design with respect to individual distributions of administration times was considered. The optimisation resulted in individualised time specifications, based on the mean and variance of each patient’s administration time. The individualised optimisation produced a higher increase in the criterion value than did the first, population-based, algorithm. The drawback is that collection of patients’ dosing histories is required before conducting a PK trial. However, such collection may be feasible in clinical trials, especially since compliance itself can be an important end-point, and is crucial for determining the efficacy of a drug.

In addition to design adjustments, cost-efficient measures aimed at compliance improvement are considered. Based on individual dosing histories, patients can be classified into compliers and non-compliers, and group-specific motivational measures implemented. For instance, medical personnel can make phone calls reminding the non-compliers to take the medication at the specified time. Alternatively, since compliance is particularly crucial for the earliest post-dose measurement time, the drug could be administered at the clinic before the first sample is taken. If the number of visits is limited to one or two per patient, the earliest part of the drug concentration profile (when compliance has the most effect on the accuracy of the results) should be constructed using the measurements from compliers, whereas the later part constructed predominantly from non-compliers’ data.   

Conclusion: The simulations using empirically-based non-compliance showed up to a 40% decrease in the D-optimality criterion value. Designs based on a prior distribution of random administration times can mitigate some of the decrease. The design approach considered in the research may be applicable to the specification of the optimal sampling intervals, as in the sampling windows examples. The compliance improvement measures suggested may also enhance trial results. The decision to implement a particular improvement measure would depend on prior compliance information, available resources, and the trial’s objectives. The accuracy of Phase 2/3 PK trial results should be substantially improved by making provision for patients’ imperfect administration time compliance in trial design.

References:
B. Green and S. Duffull. Prospective Evaluation of a D-Optimal Designed Population Pharmacokenetic Study. J. Pharmacokin. Pharmacodyn. 30: 145 – 161 (2003)
P. Johnson, B. Jones, B. Bogacka and O. Volkov. Optimising PK sampling under the constraint imposed in later phase clinical trials. PAGE presentation (2005)
L. Pronzato. Information Matrices with Random Regressors. Application to Experimental Design. Journal of Statistical Planning and Inference. 108: 189 – 200 (2002)
S. Retout and F. Mentré, Optimization of Individual and Population Designs Using SPlus. J. Pharmacokin. Pharmacodyn. 30: 417 – 443 (2003)

Acknowledgement: The author is grateful to Dr Bernard Vrijens (Aardex Ltd) for providing the data sets used in the simulations