Runs, scans and URN model distributions: A unified Markov chain approach

ABSTRACT. Lack of adherence is a frequent cause of hospitalizations, but its effects on dosing patterns have not been extensively investigated. The purpose of this work was to critically evaluate a novel pharmacometric model for deriving the relationships of adherence to dosing patterns and the dosing interval distribution. The hybrid, stochastic model combines a Markov chain process with the von Mises distribution. The model was challenged with electronic medication monitoring data from 207 hypertension patients and against 5-year persistence data. The model estimates distributions of dosing runs, drug holidays, and dosing intervals. Drug holidays, which can vary between individuals with the same adherence, were characterized by the patient cooperativity index parameter. The drug holiday and dosing run distributions deviate markedly from normality. The dosing interval distribution exhibits complex patterns of multimodality and can be long-tailed. Dosing patterns are an important but under recognized covariate for explaining within-individual variance in drug concentrations.

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“…It was calculated using the computationally efficient triangular matrix decomposition method (13). The exact distribution of runs (e.g., for Fig.…”

Section: Modeling the Dosing Runs Distributionmentioning

confidence: 99%

A Hybrid Markov Chain–von Mises Density Model for the Drug-Dosing Interval and Drug Holiday Distributions

Fellows

Rodriguez-Cruz

Covelli

et al. 2015

AAPS J

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“…Recently, researchers have partially extended the definitions of the binary consecutive-k-out-of-n system to the multi-state (M.S) case by allowing the system to remain binary and its components to have more than two possible states, for example, see Zuo and Liang [13] and Malinowski and Preuss [14,15]. Koutras [16] extends the binary consecutive-k-out-of-n: F system to the dual failure mode environment whereas the system and each component may experience one working state and two different failure states.…”

Section: Introductionmentioning

confidence: 99%

On the Reliability of Multi-State m-consecutive-at least-k-out-of-n: F Systems

Mokhlis¹,

Hassan²,

Sayed³

2013

IJCA

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Reliability importance of a component is a quantitative measure of the importance of the individual component in contributing to system reliability.In this paper, an appropriate Markov chain imbedding technique is employed to obtain the reliability of an multi-state m-consecutive-at least-k-out-of-n: F systems when the system components are independently functioning with not necessarily equal reliability. Finally, an illustrative is given example.

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“…Koutras and Alexandrou (1995) have described a method to obtain the exact distribution of W n,k,r by invoking a Markov chain embedding technique; however, this approach becomes unwieldy for k and r of moderate size, while its computational complexity for large k, r and n renders the whole procedure as non-feasible. Therefore, the development of asymptotic results for the distribution of W n,k,r is of special interest.…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Results for Scan Statistics

2009

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Abstract:In the first part of this paper we focus on the classical scan and multiple scan statistic, defined on a sequence of independent and identically distributed (i.i.d.) binary trials and review a number of bounds and approximations for their distributions which have been developed by the aid of distance measures. Moreover, we discuss briefly a number of asymptotic results that have been established by setting up appropriate conditions guaranteeing the convergence (to zero) of the distance measures' upper bounds. In the second part, we study a multiple scan statistic enumerating variable by considering a general threshold-based framework, defined on i.i.d. continuous random variables. More specifically, we prove first a compound Poisson approximation for the total number of fixed length overlapping moving windows containing prespecified number of threshold exceedances. The classical scan and multiple scan statistic may be treated as a special case of this general model. Next we exploit the previous result to gain some new extreme value results for the scan enumerating statistic under the assumption that the continuous random variables belong to the maximum domain of attraction of one of the three extreme value distributions (Frechet, reversed Weibull, Gumbel). Finally, we elucidate how the general results can be applied in a number of classical continuous distributions (Pareto, Uniform, Exponential and Normal).

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Runs, scans and URN model distributions: A unified Markov chain approach

Abstract: Success runs, scan statistics, urn models, Markov chains, triangular multidimensional recurrence relations, distributions of orderk ,

Cited by 142 publications

References 38 publications

A Hybrid Markov Chain–von Mises Density Model for the Drug-Dosing Interval and Drug Holiday Distributions

A Hybrid Markov Chain–von Mises Density Model for the Drug-Dosing Interval and Drug Holiday Distributions

On the Reliability of Multi-State m-consecutive-at least-k-out-of-n: F Systems

Extreme Value Results for Scan Statistics

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