  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 level in a patient
with imperfect adherence. We find exact formulas for drug level statistics,
including the mean, the coefficient of variation, and the deviation from
perfect adherence. We determine how adherence rates translate into drug levels,
and how this depends on the drug half-life, the dosing interval, and how missed
doses are handled. While clinical recommendations should depend on drug and
patient specifics, as a general principle we find 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.
