What should patients do if they miss a dose of medication? A theoretical approach

TL;DR

This paper develops a mathematical model to analyze medication adherence, providing formulas for drug concentration and suggesting that taking double doses after missed doses may be beneficial for drugs with long half-lives.

Contribution

It introduces a novel theoretical framework to quantify how missed doses affect drug levels and offers new insights into dose management strategies based on drug half-life.

Findings

Double doses after missed doses are beneficial for long half-life drugs.

Patients taking double doses do not accumulate significantly more drug than adherent patients.

The model applies to hypothyroid patients on levothyroxine.

Abstract

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.