  Medication adherence is a major problem for patients with chronic diseases
that require long term pharmacotherapy. Many unanswered questions surround
adherence, including how adherence rates translate into treatment efficacy and
how missed doses of medication should be handled. To address these questions,
we formulate and analyze a mathematical model of the drug concentration in a
patient with imperfect adherence. We find exact formulas for drug concentration
statistics, including the mean, the coefficient of variation, and the deviation
from perfect adherence. We determine how adherence rates translate into drug
concentrations, and how this depends on the drug half-life, the dosing
interval, and how missed doses are handled. While clinical recommendations
require extensive validation and should depend on drug and patient specifics,
as a general principle our theory suggests that nonadherence is best mitigated
by taking double doses following missed doses if the drug has a long half-life.
This conclusion contradicts some existing recommendations that cite long drug
half-lives as the reason to avoid a double dose after a missed dose.
Furthermore, we show that a patient who takes double doses after missed doses
can have at most only slightly more drug in their body than a perfectly
adherent patient if the drug half-life is long. We also investigate other ways
of handling missed doses, including taking an extra fractional dose following a
missed dose. We discuss our results in the context of hypothyroid patients
taking levothyroxine.
