Compliance Markov

Girard et al. (34) proposed a hierarchical Markov model for patient compliance with oral medications that was conditioned on a set of individual-specific nominal daily dose times. The individual random effects for the model were assumed to be multivariate normally distributed. Assuming first-order Markov hypothesis (see... 

Probabilistic models have been developed for characterizing compliance. The most commonly cited probabilistic approach is the hierarchical Markov model. Other more recently developed approaches range from a random sampling probabilistic model approach, to likelihood approaches, Bayesian approaches, and a missing dosing history approach. It is up to the pharmacometrician to choose the method that would best characterize his/her nonadherence data. The application example reinforces the importance of compliance to prescribed drug therapy, and how steady-state pharmacokinetics can be disrupted in the presence of noncompliance. 

P. Girard, T. E. Blaschke, H. Kastrissios, and L. B. Sheiner, A Markov mixed effect regression model for drug compliance. Stat Med 17 2313-2333 (1998). 

Markov models are used to describe disease as a series of probable transitions between health states. The methodology has considerable appeal for use in phar-macometrics since it offers a method to evaluate patient compliance with prescribed medication regimen, multiple health states simultaneously, and transitions between different sleep stages. An overview of the Markov model is provided together with the Markovian assumption. The most commonly used form of the Markov model, the discrete-time Markov model, is described as well as its application in the mixed effects modeling setting. The chapter concludes with a discussion of a hybrid Markov mixed effects and proportional odds model used to characterize an adverse effect that lends itself to this combination modeling approach. 

Failure to account for nonadherence to study drug administration schedules will lead to biased and imprecise trial simulation outcome measures (19). Models to assimilate compliance often involve a hierarchical Markov model, where the probability for an individual to take a scheduled dose is conditional on whether this individual had taken the previous dose (20,21). The model may also contain covariates as predictors of compliance. For example, compliance has been shown to be affected by dosing frequency, where an increased frequency (e.g., three times daily vs. once daily) has been associated with worse compliance (22, 23). Alternatively, the consequence of missing a once-a-day dose may have more significant impact on efficacy. PK/PD-based simulations play an important role in understanding the balance of these situations. 

In addition to the Markov model, compliance may be modeled using a more simplified model as a mixture (fraction) of patients who are either compliant or noncompliant (all-or-none) (24). Or, similar to drawing covariate distributions from databases of representative populations, a nonmodel-based option for compliance would be to draw from prior compliance data collected from a representative patient population. 

Cocozza-Thivent, Christiane (1997) Processus stochas-tiques etfiabUitedes syste mes, Berlin Springer CS-25 (2002) European Aviation Safety Agency Certification Specifications For Large Aeroplanes CS-25 Amendment I, BOOK 2 Acceptable Means of Compliance Freedman, David (1974) Markov Chains, San Francisco Holden-Day, 1971,p.l54ff... 

There are a large number of studies examining the reliability of websites or web applications. However, in most cases the reliability analysis is based on Markov processes (Barlow Proschan 1996) and the analyzed system is modelled as a simple serial one (Lipinski 2006). The Markov or Semi-Markov approach have significant limitations (Malinowski 2012) which includes the limited distributions (mostly exponential), narrow applicability (only to a special class of systems) and poor compliance with reality. That is why computer simulation (Juan et al. 2012) is used for availability analysis of complex systems. 

---