Modelling imperfect adherence to HIV induction therapy

Abstract

Background: Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis.

Methods: We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase?

Results: For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration.

Conclusions: Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials.

Figure 1

Dose-effect curves. Example of dose-effect curves for the wild-type (solid blue curve) and 10-fold resistance (dashed green curve) virus strains. When drug concentration levels are in Region 1, the amount of drug is insufficient to either control wild-type or mutant strains. When drug concentration levels are in Region 2, the amount of drug is sufficient to block the wild-type virus but resistant virus may emerge. When drug concentration levels are in Region 3, both virus strains are controlled. This example is for the reverse transcriptase inhibitor Stavudine (d4T).

Figure 2

Drug concentrations. Drug concentrations using impulsive differential equations. A. Example of drug concentration levels with perfect adherence to therapy. Drug concentration levels fluctuate from lower endpoints to upper endpoints . Drug concentration levels increase instantaneously after a dose is taken and decrease exponentially between doses. If all doses are taken, drug concentration levels monotonically approach an impulsive orbit. B. Example of fluctuating drug concentration levels when missing drug doses. Once drug concentration levels have reached the impulsive orbit , missing h doses results in a long exponential decay. Subsequent adherence returns drug concentration levels to the impulsive periodic orbit before the next drug holiday occurs . In this example, a patient has two drug holidays within a 30 day period.

Figure 3

Determining the prescribed tolerance. Difference between a prescribed tolerance of (A) 0.1 μM and (B) 0.01 μM for the reverse transcriptase inhibitor Didanosine (ddI). The red line plotted on both graphs is the average drug concentration while taking drug holidays. This was calculated using the data from Table 2. The average drug concentration in (A) is around 11 μM and has not reached the trough values when drug holidays are excluded, whereas the average drug concentration in (B) is around 12 μM and thus exceeds the trough values during therapy.

Figure 4

Adherence to ABC monotherapy. A. Long-term effects of adherence to ABC monotherapy, using the prescribed adherence breaks. The wild type (solid blue curve, left axes) and mutant (dashed green curve, right axes) populations are shown. The overall effect of the mutant remains low. Parameters used, in addition to those in Table 1, were n_I = 262.5 day^-1, ω = 0.7, r_I = 0.01 day^-1, r_Y = 0.001 day^-1, d_V = 3 day^-1, d_S = 0.1 day^-1, d_I = 0.5 day^-1, ψ = 0.2, p_L = 0.05, r_R = r_Q = 80 μM^-1, day^-1, λ = 180 cells μL^-1 and m_RI = m_RY = log(2) day^-1. Initial conditions were V_I (0) = 22000 virions mL^-1, V_Y (0) = 5 × 10^-3 virions mL^-1, T_S (0) = 1000 cells day^-1 and all other initial conditions were zero. B. The effects of missing one extra dose per drug holiday. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 5

Adherence to 3TC monotherapy. A. Long-term effects of adherence to 3TC monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters are as in Table 1, while all other parameters are as in Figure 4. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 6

Adherence to d4T monotherapy. A. Long-term effects of adherence to d4T monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters are as in Table 1, while all other parameters are as in Figure 4. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 7

Adherence to FTC monotherapy. A. Long-term effects of adherence to FTC monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters are as in Table 1, while all other parameters are as in Figure 4. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 8

Adherence to ZDV monotherapy. A. Long-term effects of adherence to ZDV monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters are as in Table 1, while all other parameters are as in Figure 4. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 9

Adherence to ddI monotherapy. A. Long-term effects of adherence to ddI monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters are as in Table 1, while all other parameters are as in Figure 4. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 10

Adherence to NVP monotherapy. A. Long-term effects of adherence to NVP monotherapy, using prescribed adherence breaks. B. The effects of missing one extra dose. Drug parameters as as in Table 1, while all other parameters are as in Figure 4. In this case, both strains are controlled. Inset: The effects of missing three extra doses. In this case, the wild-type strain is controlled, but the resistant strain emerges. The proportions of each type of uninfected T cell at the end of the simulation are shown in the insets.

Figure 11

Sensitivity to other parameters. Sensitivity of length of drug holiday to (A) the drug decay rate, d_r, (B) the Region 2 threshold, R₂, and (C) the drug concentration, Rⁱ. Dashed lines indicate values used in our calculations. This example is for ABC.