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

How Missed Doses of Antibiotics Affect Bacteria Growth Dynamics

What should you do if you miss a dose of antibiotics? Despite the prevalence of missed antibiotic doses, there is vague or little guidance on what to do when a dose is forgotten. In this paper, we consider the effects of different patient responses after missing a dose using a mathematical model that links antibiotic concentration with bacteria dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose.

Evaluation and application of population pharmacokinetic models for optimising linezolid treatment in non-adherence multidrug-resistant tuberculosis patients

BACKGROUND

Population pharmacokinetic (popPK) models can optimise linezolid dosage regimens in patients with multidrug-resistant tuberculosis (MDR-TB); however, unknown cross-centre precision and poor adherence remain problematic. This study aimed to assess the predictive ability of published models and use the most suitable model to optimise dosage regimens and manage compliance.

METHODS

One hundred fifty-eight linezolid plasma concentrations from 27 patients with MDR-TB were used to assess the predictive performance of published models. Prediction-based metrics and simulation-based visual predictive checks were conducted to evaluate predictive ability. Individualised remedial dosing regimens for various delayed scenarios were optimised using the most suitable model and Monte Carlo simulations. The influence of covariates, scheduled dosing intervals, and patient compliance were assessed.

RESULTS

Seven popPK models were identified. Body weight and creatinine clearance were the most frequently identified covariates influencing linezolid clearance. The model with the best performance had a median prediction error (PE%) of -1.62 %, median absolute PE of 29.50 %, and percentages of PE within 20 % (F20, 36.97 %) and 30 % (F30, 51.26 %). Monte Carlo simulations indicated that a twice-daily 300 mg linezolid dose may be more efficient than 600 mg once daily. For the 'typical' patient treated with 300 mg twice daily, half the dosage should be taken after a delay of ≥ 3 h.

CONCLUSIONS

Monte Carlo simulations based on popPK models can propose remedial regimens for delayed doses of linezolid in patients with MDR-TB. Model-based compliance management patterns are useful for balancing efficacy, adverse reactions, and resistance suppression.

Handling delayed or missed direct oral anticoagulant doses: model-informed individual remedial dosing

ABSTRACT

Nonadherence to direct oral anticoagulant (DOAC) pharmacotherapy may increase the risk of thromboembolism or bleeding, and delayed or missed doses are the most common types of nonadherence. Current recommendations from regulatory agencies or guidelines regarding this issue lack evidence and fail to consider individual differences. This study aimed to develop individual remedial dosing strategies when the dose was delayed or missed for DOACs, including rivaroxaban, apixaban, edoxaban, and dabigatran etexilate. Remedial dosing regimens based on population pharmacokinetic (PK)-pharmacodynamic (PD) modeling and simulation strategies were developed to expeditiously restore drug concentration or PD biomarkers within the therapeutic range. Population PK-PD characteristics of DOACs were retrieved from previously published literature. The effects of factors that influence PK and PD parameters were assessed for their impact on remedial dosing regimens. A web-based dashboard was established with R-shiny to recommend remedial dosing regimens based on patient traits, dosing schedules, and delay duration. Addressing delayed or missed doses relies on the delay time and specific DOACs involved. Additionally, age, body weight, renal function, and polypharmacy may marginally affect remedial strategies. The proposed remedial dosing strategies surpass current recommendations, with less deviation time beyond the therapeutic range. The online dashboard offers quick and convenient solutions for addressing missed or delayed DOACs, enabling individualized remedial dosing strategies based on patient characteristics to mitigate the risks of bleeding and thrombosis.

How drug onset rate and duration of action affect drug forgiveness

Medication nonadherence is one of the largest problems in healthcare today, particularly for patients undergoing long-term pharmacotherapy. To combat nonadherence, it is often recommended to prescribe so-called "forgiving" drugs, which maintain their effect despite lapses in patient adherence. Nevertheless, drug forgiveness is difficult to quantify and compare between different drugs. In this paper, we construct and analyze a stochastic pharmacokinetic/pharmacodynamic (PK/PD) model to quantify and understand drug forgiveness. The model parameterizes a medication merely by an effective rate of onset of effect when the medication is taken (on-rate) and an effective rate of loss of effect when a dose is missed (off-rate). Patient dosing is modeled by a stochastic process that allows for correlations in missed doses. We analyze this "on/off" model and derive explicit formulas that show how treatment efficacy depends on drug parameters and patient adherence. As a case study, we compare the effects of nonadherence on the efficacy of various antihypertensive medications. Our analysis shows how different drugs can have identical efficacies under perfect adherence, but vastly different efficacies for adherence patterns typical of actual patients. We further demonstrate that complex PK/PD models can indeed be parameterized in terms of effective on-rates and off-rates. Finally, we have created an online app to allow pharmacometricians to explore the implications of our model and analysis.

Understanding and Quantifying Network Robustness to Stochastic Inputs

A variety of biomedical systems are modeled by networks of deterministic differential equations with stochastic inputs. In some cases, the network output is remarkably constant despite a randomly fluctuating input. In the context of biochemistry and cell biology, chemical reaction networks and multistage processes with this property are called robust. Similarly, the notion of a forgiving drug in pharmacology is a medication that maintains therapeutic effect despite lapses in patient adherence to the prescribed regimen. What makes a network robust to stochastic noise? This question is challenging due to the many network parameters (size, topology, rate constants) and many types of noisy inputs. In this paper, we propose a summary statistic to describe the robustness of a network of linear differential equations (i.e. a first-order mass-action system). This statistic is the variance of a certain random walk passage time on the network. This statistic can be quickly computed on a modern computer, even for complex networks with thousands of nodes. Furthermore, we use this statistic to prove theorems about how certain network motifs increase robustness. Importantly, our analysis provides intuition for why a network is or is not robust to noise. We illustrate our results on thousands of randomly generated networks with a variety of stochastic inputs.

Physicochemical properties as a function of lomefloxacin biological activity

OBJECTIVE

Aim: The goal is to discover QSAR of Lomefloxacin as antibacterial activity.

PATIENTS AND METHODS

Materials and Methods: A number of lomefloxacins analogs activities were studied by program Windows Chem SW. The analogues were obtained and energy minimization was carried out through Molecular Modeling Program, the calculations were performed using General Atomic and Molecular Electronic Structure System (GAMESS) software.

RESULTS

Results: There were six descriptions (N-quinoline more (-) ev charge, Kinetic Energy, Potential Energy, Log p, Log S, F6 charge) results have highly compatible of physicochemical properties with lomefloxacin analogs activities. It can be used to estimate the activities depending on QSAR equation of lomefloxacin analogs.

CONCLUSION

Conclusions: The parameters used for calculation were depending on the quantum chemical was employed in deriving from computational study of properties and can used to predict the activities of certain analogs of Lomefloxacins as antibacterial compounds.

Statistical Analysis of Two-Compartment Pharmacokinetic Models with Drug Non-adherence

Poor drug adherence is considered one of major barriers to achieving the clinical and public health benefits of many pharmacotherapies. In the current paper, we aim to investigate the impact of dose omission on the plasma concentrations of two-compartment pharmacokinetic models with two typical routes of drug administration, namely the intravenous bolus and extravascular first-order absorption. First, we reformulate the classical two-compartment pharmacokinetic models with a new stochastic feature, where a binomial random model of dose intake is integrated. Then, we formalize the explicit expressions of expectation and variance for trough concentrations and limit concentrations, with the latter proved of the existence and uniqueness for steady-state distribution. Moreover, we mathematically demonstrate the strict stationarity and ergodicity of trough concentrations as a Markov chain. In addition, we numerically simulate the impact of drug non-adherence to different extents on the variability and regularity of drug concentration and compare the drug pharmacokinetic preference between one and two compartment pharmacokinetic models. The results of sensitivity analysis also suggest the drug non-adherence as one of the most sensitive model parameters to the expectation of limit concentration. Our modelling and analytical approach can be integrated into the chronic disease models to estimate or quantitatively predict the therapy efficacy with drug pharmacokinetics presumably affected by random dose omissions.

Handling Delayed or Missed Dose of Antiseizure Medications: A Model-Informed Individual Remedial Dosing

BACKGROUND AND OBJECTIVES

Delayed or missed antiseizure medications (ASMs) doses are common during long-term or lifelong antiepilepsy treatment. This study aims to explore optimal individualized remedial dosing regimens for delayed or missed doses of 11 commonly used ASMs.

METHODS

To explore remedial dosing regimens, Monte Carlo simulation was used based on previously identified and published population pharmacokinetic models. Six remedial strategies for delayed or missed doses were investigated. The deviation time outside the individual therapeutic range was used to evaluate each remedial regimen. The influences of patients' demographics, concomitant medication, and scheduled dosing intervals on remedial regimens were assessed. RxODE and Shiny in R were used to perform Monte Carlo simulation and recommend individual remedial regimens.

RESULTS

The recommended remedial regimens were highly correlated with delayed time, scheduled dosing interval, and half-life of the ASM. Moreover, the optimal remedial regimens for pediatric and adult patients were different. The renal function, along with concomitant medication that affects the clearance of the ASM, may also influence the remedial regimens. A web-based dashboard was developed to provide individualized remedial regimens for the delayed or missed dose, and a user-defined module with all parameters that could be defined flexibly by the user was also built.

DISCUSSION

Monte Carlo simulation based on population pharmacokinetic models may provide a rational approach to propose remedial regimens for delayed or missed doses of ASMs in pediatric and adult patients with epilepsy.

Should patients skip late doses of medication? A pharmacokinetic perspective

Missed doses, late doses, and other dosing irregularities are major barriers to effective pharmacotherapy, especially for the treatment of chronic conditions. What should a patient do if they did not take their last dose at the prescribed time? Should they take it late or skip it? In this paper, we investigate the pharmacokinetic effects of taking a late dose. We consider a single compartment model with linear absorption and elimination for a patient instructed to take doses at regular time intervals. We suppose that the patient forgets to take a dose and then realizes some time later and must decide what remedial steps to take. Using mathematical analysis, we derive several metrics which quantify the effects of taking the dose late. The metrics involve the difference between the drug concentration time courses for the case that the dose is taken late and the case that the dose is taken on time. In particular, the metrics are the integral of the absolute difference over all time, the maximum of the difference, and the maximum of the integral of the difference over any single dosing interval. We apply these general mathematical formulas to levothyroxine, atorvastatin, and immediate release and extended release formulations of lamotrigine. We further show how population variability can be immediately incorporated into these results. Finally, we use this analysis to propose general principles and strategies for dealing with dosing irregularities.

Designing Drug Regimens that Mitigate Nonadherence

Medication adherence is a well-known problem for pharmaceutical treatment of chronic diseases. Understanding how nonadherence affects treatment efficacy is made difficult by the ethics of clinical trials that force patients to skip doses of the medication being tested, the unpredictable timing of missed doses by actual patients, and the many competing variables that can either mitigate or magnify the deleterious effects of nonadherence, such as pharmacokinetic absorption and elimination rates, dosing intervals, dose sizes, and adherence rates. In this paper, we formulate and analyze a mathematical model of the drug concentration in an imperfectly adherent patient. Our model takes the form of the standard single compartment pharmacokinetic model with first-order absorption and elimination, except that the patient takes medication only at a given proportion of the prescribed dosing times. Doses are missed randomly, and we use stochastic analysis to study the resulting random drug level in the body. We then use our mathematical results to propose principles for designing drug regimens that are robust to nonadherence. In particular, we quantify the resilience of extended release drugs to nonadherence, which is quite significant in some circumstances, and we show the benefit of taking a double dose following a missed dose if the drug absorption or elimination rate is slow compared to the dosing interval. We further use our results to compare some antiepileptic and antipsychotic drug regimens.