This is an important contribution to a modern area of applied probability that deals with nonstationary Markov chains in continuous time. This area is becoming increasingly useful in engineering, economics, communication theory, active networking, and so forth, where the Markov-chain system is subject to frequent  uctuations with clusters of states such that the chain  uctuates very rapidly among different states of a cluster but changes less rapidly from one cluster to another. The authors use the setting of singular perturbations, which allows them to study both weak and strong interactions among the states of the chain. This leads to simpli cations through the averaging principle, aggregation, and decomposition. The main results include asymptotic expansions of the corresponding probability distributions, occupations measures, limiting normality, and exponential rates. These results give the asymptotic behavior of many controlled stochastic dynamic systems when the perturbation parameter tends to 0. The classical analytical method employs the asymptotic expansions of onedimensional distributions of the Markov chain as solutions to a system of singularly perturbed ordinary differential equations. Indeed, the asymptotic behavior of solutions of such equations is well studied and understood. A more probabilistic approach also used by the authors is based on the tightness of the family of probability measures generated by the singularly perturbed Markov chain with the corresponding weak convergence properties. Both of these methods are illustrated by practical dynamic optimization problems, in particular by hierarchical production planning in a manufacturing system. An important contribution is the last chapter, Chapter 10, which describes numerical methods to solve various control and optimization problems involving Markov chains. Altogether the monograph consists of three parts, with Part I containing necessary, technically rather demanding facts about Markov processes (which in the nonstationary case are de ned through martingales.) Part II derives the mentioned asymptotic expansions, and Part III deals with several applications, including Markov decision processes and optimal control of stochastic dynamic systems. This technically demanding book may be out of reach of many readers of Technometrics. However, the use of Markov processes has become common for numerous real-life complex stochastic systems. To understand the behavior of these systems, the sophisticated mathematical methods described in this book may be indispensable.

Monte Carlo Methods in Bayesian Computation

Objective To compare the blood pressure (BP) effects of exercise alone (EXalone), medication alone (MEDSalone) and combined (EX+MEDScombined) among adults with hypertension. Data sources PubMed, Scopus, Cumulative Index to Nursing and Allied Health Literature, SPORTDiscus and the Cochrane Library. Eligibility criteria Randomised controlled trails (RCTs) or meta-analyses (MAs) of controlled trials that: (1) involved healthy adults>18 year with hypertension; (2) investigated exercise and BP; (3) reported preintervention and postintervention BP and (4) were published in English. RCTs had an EX+MEDScombined arm; and an EXalone arm and/or an MEDSalone arm; and MAs performed moderator analyses. Design A systematic network MA and meta-review with the evidence graded using the Physical Activity Guidelines for Americans Advisory Committee system. Outcome The BP response for EXalone, MEDSalone and EX+MEDScombined and compared with each other. Results Twelve RCTs qualified with 342 subjects (60% women) who were mostly physically inactive, middle-aged to older adults. There were 13 qualifying MAs with 28 468 participants (~50% women) who were mostly Caucasian or Asian. Most RCTs were aerobic (83.3%), while the MAs involved traditional (46%) and alternative (54%) exercise types. Strong evidence demonstrates EXalone, MEDSalone and EX+MEDScombined reduce BP and EX+MEDScombined elicit BP reductions less than the sum of their parts. Strong evidence indicates EX+MEDScombined potentiate the BP effects of MEDSalone. Although the evidence is stronger for alternative than traditional types of exercise, EXaloneelicits greater BP reductions than MEDSalone. Conclusions The combined BP effects of exercise and medications are not additive or synergistic, but when combined they bolster the antihypertensive effects of MEDSalone. PROSPERO registration number The protocol is registered at PROSPERO CRD42020181754.

https://bmjopensem.bmj.com/content/bmjosem/7/1/e000895.full.pdf

Do the combined blood pressure effects of exercise and antihypertensive medications add up to the sum of their parts? A systematic meta-review.

Low-density lipoprotein cholesterol (LDL-C) has been identified as a causative factor for atherosclerosis and related coronary heart disease, and as the main target for cholesterol- and lipid-lowering therapy. Statin drugs inhibit cholesterol synthesis in the liver and are typically the first line of therapy to lower elevated levels of LDL-C. On the other hand, a different drug, Ezetimibe, inhibits the absorption of cholesterol by the small intestine and provides a different mechanism of action. Many clinical trials have been carried out on safety and efficacy evaluation of cholesterol lowering drugs. To synthesize the results from different clinical trials, we examine treatment level (aggregate) network meta-data from 29 double-blind, randomized, active, or placebo-controlled statins +/$-$ Ezetimibe clinical trials on adult treatment-naive patients with primary hypercholesterolemia. In this article, we propose a new approach to carry out Bayesian inference for arm-based network meta-regression. Specifically, we develop a new strategy of grouping the variances of random effects, in which we first formulate possible sets of the groups of the treatments based on their clinical mechanisms of action and then use Bayesian model comparison criteria to select the best set of groups. The proposed approach is especially useful when some treatment arms are involved in only a single trial. In addition, a Markov chain Monte Carlo sampling algorithm is developed to carry out the posterior computations. In particular, the correlation matrix is generated from its full conditional distribution via partial correlations. The proposed methodology is further applied to analyze the network meta-data from 29 trials with 11 treatment arms.

/pdf/bayesian-inference-for-network-meta-regression-using-3tq67k343y.pdf

Bayesian inference for network meta-regression using multivariate random effects with applications to cholesterol lowering drugs

/pdf/drought-and-all-cause-mortality-in-nebraska-from-1980-to-gpqw3j7t.pdf

Drought and all-cause mortality in Nebraska from 1980 to 2014: Time-series analyses by age, sex, race, urbanicity and drought severity.

Évaluation de la qualité méthodologique et de communication des méta-analyses en réseau en anesthésiologie : revue systématique et étude méta-épidémiologique

Crohn's disease (CD) is a life-long condition associated with recurrent relapses characterized by abdominal pain, weight loss, anemia, and persistent diarrhea. In the US, there are approximately 780 000 CD patients and 33 000 new cases added each year. In this article, we propose a new network meta-regression approach for modeling ordinal outcomes in order to assess the efficacy of treatments for CD. Specifically, we develop regression models based on aggregate covariates for the underlying cut points of the ordinal outcomes as well as for the variances of the random effects to capture heterogeneity across trials. Our proposed models are particularly useful for indirect comparisons of multiple treatments that have not been compared head-to-head within the network meta-analysis framework. Moreover, we introduce Pearson residuals and construct an invariant test statistic to evaluate goodness-of-fit in the setting of ordinal outcome data. A detailed case study demonstrating the usefulness of the proposed methodology is carried out using aggregate ordinal outcome data from 16 clinical trials for treating CD.

May Mo

Papers

Network meta-regression for ordinal outcomes: Applications in comparing Crohn's disease treatments.