Comparator Sequence Research Articles

Non-stationary Projection-Free Online Learning with Dynamic and Adaptive Regret Guarantees

Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static regret, which unfortunately fails to capture the challenge of changing environments. In this paper, we investigate non-stationary projection-free online learning, and choose dynamic regret and adaptive regret to measure the performance. Specifically, we first provide a novel dynamic regret analysis for an existing projection-free method named BOGD_IP, and establish an O(T^¾ (1+P_T)) dynamic regret bound, where P_T denotes the path-length of the comparator sequence. Then, we improve the upper bound to O(T^¾ (1+P_T)^¼) by running multiple BOGD_IP algorithms with different step sizes in parallel, and tracking the best one on the fly. Our results are the first general-case dynamic regret bounds for projection-free online learning, and can recover the existing O(T^¾) static regret by setting P_T = 0. Furthermore, we propose a projection-free method to attain an O(?^¾) adaptive regret bound for any interval with length ?, which nearly matches the static regret over that interval. The essential idea is to maintain a set of BOGD_IP algorithms dynamically, and combine them by a meta algorithm. Moreover, we demonstrate that it is also equipped with an O(T^¾ (1+P_T)^¼) dynamic regret bound. Finally, empirical studies verify our theoretical findings.

Nonstationary online convex optimization with multiple predictions

This work focuses on dynamic regret for non-stationary online convex optimization with full information. State-of-the-art analysis shows that Implicit Online Mirror Descent (IOMD) combined with Hedge achieves an O˜(min⁡{VT,(1+PT)T}) dynamic regret, where VT denotes the temporal variability of the loss functions and PT measures the path length reflecting the non-stationarity of the comparator sequence, and Optimistic IOMD (OptIOMD) enjoys the dynamic regret of O(min⁡{VT′,(1+P)T}), where VT′ denotes the cumulative distance from the loss functions to an arbitrary predictor sequence, and P is an upper bound of the path-length PT. In order to further suppress dynamic regret, we propose an algorithm named Hedge-OptIOMD, which achieves an O˜(min⁡{minj∈1:n⁡VTj,(1+PT)T}) dynamic regret via multiple predictors, where VTj represents the cumulative distance from the loss functions to the j-th predictor sequence. We also verify the advantages of Hedge-OptIOMD through numerical experiments.

Distributed Bandit Online Convex Optimization With Time-Varying Coupled Inequality Constraints

Distributed bandit online convex optimization with time-varying coupled inequality constraints is considered, motivated by a repeated game between a group of learners and an adversary. The learners attempt to minimize a sequence of global loss functions and at the same time satisfy a sequence of coupled constraint functions, where the constraints are coupled across the distributed learners at each round. The global loss and the coupled constraint functions are the sum of local convex loss and constraint functions, respectively, which are adaptively generated by the adversary. The local loss and constraint functions are revealed in a bandit manner, i.e., only the values of loss and constraint functions are revealed to the learners at the sampling instance, and the revealed function values are held privately by each learner. Both one- and two-point bandit feedback are studied with the two corresponding distributed bandit online algorithms used by the learners. We show that sublinear expected regret and constraint violation are achieved by these two algorithms, if the accumulated variation of the comparator sequence also grows sublinearly. In particular, we show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{\theta })$</tex-math></inline-formula> expected static regret and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{7/4-\theta })$</tex-math></inline-formula> constraint violation are achieved in the one-point bandit feedback setting, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{\max \lbrace \kappa,1-\kappa \rbrace })$</tex-math></inline-formula> expected static regret and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{1-\kappa /2})$</tex-math></inline-formula> constraint violation in the two-point bandit feedback setting, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta \in (3/4,5/6]$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa \in (0,1)$</tex-math></inline-formula> are user-defined tradeoff parameters. Finally, the tightness of the theoretical results is illustrated by numerical simulations of a simple power grid example, which also compares the proposed algorithms to algorithms existing in the literature.

Tofacitinib in the Treatment of Moderate-to-Severe Rheumatoid Arthritis in China: A Cost-Effectiveness Analysis Basedon a Mapping Algorithm Derived from a Chinese Population.

To estimate the cost-effectiveness of tofacitinib for patients with moderate-to-severe rheumatoid arthritis (RA) who failed conventional synthetic disease-modifying antirheumatic drugs from the Chinese healthcare system perspective. An individual patient simulation model was used to estimate the lifetime cost and effectiveness. The comparator sequence commenced with etanercept, followed by rituximab-tocilizumab- non-biologic therapy. The intervention sequences were assumed to add tofacitinib to different positions in the comparator sequence. Quality-of-life estimates were generated by mapping Health Assessment Questionnaire scores to utility with the algorithm derived from a Chinese population. Scenario analyses, univariable and probabilistic sensitivity analyses were performed to evaluate the model uncertainty. Compared with the comparator sequence, patients receiving tofacitinib as the first-, second-, third- and fourth-line treatment gained additional 0.49, 0.59, 0.44 and 0.53 QALYs, respectively, and the use of tofacitinib as the first- and second-line treatment was less costly, whereas the use of tofacitinib as the third- and fourth-line treatment cost an additional $234,998 and $381,116, respectively. This produced an incremental cost-effectiveness ratio of $333.73 and $9669.34/QALY, respectively. Tofacitinib is estimated to be dominant in both the first- and second-line settings and to be highly cost-effective in both the third- and fourth-line settings.

Cost-effectiveness Comparison of Ceftazidime/Avibactam Versus Meropenem in the Empirical Treatment of Hospital-acquired Pneumonia, Including Ventilator-associated Pneumonia, in Italy

PurposeCeftazidime/avibactam (CAZ-AVI) is a fixed-dose combination antibiotic approved in Europe and the United States for patients with hospital-acquired pneumonia, including ventilator-associated pneumonia (HAP/VAP). The economic benefits of a new drug such as CAZ-AVI are required to be assessed against those of available comparators, from the perspective of health care providers and payers, through cost-effectiveness and cost-utility analyses. The objective of this analysis was to compare the cost-effectiveness of CAZ-AVI versus meropenem in the empirical treatment of appropriate hospitalized patients with HAP/VAP caused by gram-negative pathogens, from the perspective of publicly funded health care in Italy (third-party perspective, based on the data from the REPROVE (Ceftazidime-Avibactam Versus Meropenem In Nosocomial Pneumonia, Including Ventilator-Associated Pneumonia) clinical study; ClinicalTrials.gov NCT01808092). MethodsA patient-level, sequential simulation model of the HAP/VAP clinical course was developed using spreadsheet software. The analysis focused on direct medical costs. The time horizon of the model selected was 5 years, with an annual discount rate of 3% on costs and quality-adjusted life-years (QALYs). Clinical inputs for treatment comparisons were mainly obtained from the REPROVE clinical study data. In addition to clinical outcomes observed in the trial, the model incorporated impact of resistance pathogens, based on data from published studies and expert opinion. Certain assumptions were made for some model parameters due to a lack of data. FindingsThe analysis demonstrated that the intervention sequence (CAZ-AVI followed by colistin + high-dose meropenem) versus the comparator sequence (meropenem followed by colistin + high-dose meropenem) provided a better clinical cure rate (+13.52%), which led to a shorter hospital stay (−0.40 days per patient), and gains in the number of life-years (+0.195) and QALYs (+0.350) per patient. The intervention sequence had an estimated net incremental total cost of €1254 ($1401) per patient, and the estimated incremental cost-effectiveness ratio was €3581 ($4000) per QALY gained, well below the willingness-to-pay threshold of €30,000 ($33,507) per QALY in Italy. ImplicationsThe model results showed that CAZ-AVI is expected to provide clinical benefits in hospitalized patients with HAP/VAP in Italy at an acceptable cost compared to meropenem.

Recognition of Brain Metastases Using Gadolinium-Enhanced SWI MRI: Proof-of-Concept Study.

Background and purpose: SWI MRI, a T2*-dominant MRI sequence with T1 shine-through effect, uses intrinsic structural susceptibility to create enhancement among brain structures. We evaluated whether gadolinium-enhanced SWI (SWI-Gd) improves brain metastasis detection in combination with other MRI sequences.Materials and methods: MRI images of 24 patients (46 studies) were prospectively acquired using a 1.5-T scanner. T1-weighted, unenhanced SWI (SWI-U) and SWI-Gd were evaluated blindly to clinical features by two board-certified radiologists.Results: SWI-Gd revealed more significant metastatic lesions than either T1-Gd or SWI-U (p = 0.0004 for either comparator sequence). Moreover, SWI-Gd revealed more lesions only for those patients with ≤5 lesions on T1-Gd (n = 30 studies from 16 patients; p = 0.046). Performing SWI-Gd added <5 min of scanning time with no further additional risk.Conclusions: Our findings suggest that, when added to T1-Gd and other common sequences, SWI-Gd may improve the diagnostic yield of brain metastases with only a few extra minutes of scanning time and no further risk than that of a regular gadolinium-enhanced MRI.

Distributed Online Convex Optimization With Time-Varying Coupled Inequality Constraints

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. Without assuming Slater's condition, we first derive regret and constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated dynamic variation of the comparator sequence, the number of agents, and the network connectivity. As a result, under some natural decreasing stepsize sequences, we prove that the algorithm achieves sublinear dynamic regret and constraint violation if the accumulated dynamic variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and constraint violation under mild conditions. Assuming Slater's condition, we show that the algorithm achieves smaller bounds on the constraint violation. In addition, smaller bounds on the static regret are achieved when the objective function is strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Cost-effectiveness analysis comparing ceftazidime/avibactam (CAZ-AVI) as empirical treatment comparing to ceftolozane/tazobactam and to meropenem for complicated intra-abdominal infection (cIAI)

BackgroundThe rising incidence of resistance to currently available antibiotics among pathogens, particularly Gram-negative pathogens, in complicated intra-abdominal infections (cIAIs) has become a challenge for clinicians. Ceftazidime/avibactam (CAZ-AVI) is a fixed-dose antibiotic approved in Europe and the United States for treating (in combination with metronidazole) cIAI in adult hospitalised patients who have limited or no alternative treatment options. The approval was based on the results of RECLAIM, a Phase III, parallel-group, comparative study (RECLAIM 1 [NCT01499290] and RECLAIM 2 [NCT01500239]). The objective of our study was to assess the cost-effectiveness of CAZ-AVI plus metronidazole compared with 1) ceftolozane/tazobactam plus metronidazole and 2) meropenem, as an empiric treatment for the management of cIAI in Italy.MethodsA sequential, patient-level simulation model, with a 5-year time horizon and 3% annual discount rate (applied to both costs and health benefits), was developed using Microsoft Excel® to demonstrate the clinical course of the disease. The impact of resistant pathogens was included as an additional factor.ResultsIn the base-case analysis, the CAZ-AVI sequence (CAZ-AVI plus metronidazole followed by a colistin + tigecycline + high-dose meropenem combination after treatment failure), when compared to sequences for ceftolozane/tazobactam (ceftolozane/tazobactam plus metronidazole followed by colistin + tigecycline + high-dose meropenem after treatment failure) and meropenem (meropenem followed by colistin + tigecycline + high-dose meropenem after treatment failure), had better clinical outcomes with higher cure rates (93.04% vs. 91.52%; 92.98% vs. 90.24%, respectively), shorter hospital stays (∆ = − 0.38 and ∆ = − 1.24 days per patient, respectively), and higher quality-adjusted life years (QALYs) gained per patient (4.021 vs. 3.982; 4.019 vs. 3.960, respectively). The incremental cost effectiveness ratio in the CAZ-AVI sequence was €4099 and €15,574 per QALY gained versus each comparator sequence, respectively, well below the willingness-to-pay threshold of €30,000 per QALY accepted in Italy.ConclusionsThe model results demonstrated that CAZ-AVI plus metronidazole could be a cost-effective alternative when compared with other antibiotic treatment options, as it is expected to provide better clinical benefits in hospitalised patients with cIAI in Italy.

Adaptive online distributed optimization in dynamic environments

ABSTRACT This paper presents a dynamic regret analysis on the decentralized online convex optimization problems computed over a network of agents. The goal is to distributively optimize a global function which can be decomposed into the summation of local cost functions associated with each agent. By exploiting the convexity of cost functions, previous studies have shown that the dynamic regret of a decentralized gradient-based algorithm can be upper bounded by the path-length of the comparator sequence and the connectivity in the underlying network. In this paper, we illustrate that the dynamic regret can be further improved by allowing the learner to use a class of adaptive search directions and step-sizes from estimates of first and second moments of the gradients. Specifically, we develop a new class of decentralized and stochastic algorithms based on the adaptive gradient method in the dynamic environment and show that their regret bounds for certain realistic classes of loss functions are considerably better than existing bounds. Numerical simulations verify the theoretical results and demonstrate the efficiency of the new proposed method in practice.

Cost-effectiveness analysis of ceftazidime/avibactam compared to imipenem as empirical treatment for complicated urinary tract infections

Ceftazidime/avibactam (CAZ-AVI) is a novel, fixed-dose combination antibiotic that has been approved in Europe and the United States for patients with complicated urinary tract infections (cUTIs) based on results of a Phase III, randomized, comparative study (RECAPTURE study). The present analysis evaluated cost-effectiveness of CAZ-AVI as an empirical treatment for hospitalized patients with cUTIs from the Italian publicly funded healthcare (third-party payer) perspective. A sequential, patient-level simulation model was developed that followed the clinical course of cUTI and generated 5000 pairs of identical patients (CAZ-AVI or imipenem as empirical treatment). The model included additional impact of resistant pathogens; patients who did not respond to empirical treatment were switched to second-line treatment of colistin+high dose carbapenem in both groups. The time horizon of the model was five years, with an annual discount rate of 3% applied to both costs and quality-adjusted life-years (QALYs). The analysis demonstrated that an intervention sequence (CAZ-AVI followed by colistin+high dose carbapenem) compared with a comparator sequence (imipenem followed by colistin+high dose carbapenem) was associated with a net incremental cost of €1015 per patient but provided better health outcomes in terms of clinical cure (97.65% vs. 91.08%; ∆ = 6.57%), shorter hospital stays (10.65 vs. 12.55 days; ∆ = 1.90 days), and QALYs gained per patient (4.190 vs. 4.063; ∆ = 0.126). The incremental cost-effectiveness ratio was €8039/QALY, which is well below the willingness-to-pay threshold of €30 000/QALY in Italy. The results showed that CAZ-AVI is expected to be a cost-effective treatment compared with imipenem for cUTI in Italy.

Worst-Case Prediction Performance Analysis of the Kalman Filter

In this paper, we study the prediction performance of the Kalman filter (KF) in a worst case minimax setting as studied in online machine learning, information, and game theory. The aim is to predict the sequence of observations almost as well as the best reference predictor (comparator) sequence in a comparison class. We prove worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence. In fact, the performance of the KF is derived as a function of the performance of the best reference predictor and the total amount of drift that occurs in the schedule of the best comparator.

The Clinical and Cost Effectiveness of Apremilast for Treating Active Psoriatic Arthritis: A Critique of the Evidence.

As part of the National Institute for Health and Clinical Excellence (NICE) single technology appraisal (STA) process, the manufacturer of apremilast was invited to submit evidence for its clinical and cost effectiveness for the treatment of active psoriatic arthritis (PsA) for whom disease-modifying anti-rheumatic drugs (DMARDs) have been inadequately effective, not tolerated or contraindicated. The Centre for Reviews and Dissemination and Centre for Health Economics at the University of York were commissioned to act as the independent Evidence Review Group (ERG). This paper provides a description of the ERG review of the company's submission, the ERG report and submission and summarises the NICE Appraisal Committee's subsequent guidance (December 2015). In the company's initial submission, the base-case analysis resulted in an incremental cost-effectiveness ratio (ICER) of £14,683 per quality-adjusted life-year (QALY) gained for the sequence including apremilast (positioned before tumour necrosis factor [TNF]-α inhibitors) versus a comparator sequence without apremilast. However, the ERG considered that the base-case sequence proposed by the company represented a limited set of potentially relevant treatment sequences and positions for apremilast. The company's base-case results were therefore not a sufficient basis to inform the most efficient use and position of apremilast. The exploratory ERG analyses indicated that apremilast is more effective (i.e. produces higher health gains) when positioned after TNF-α inhibitor therapies. Furthermore, assumptions made regarding a potential beneficial effect of apremilast on long-term Health Assessment Questionnaire (HAQ) progression, which cannot be substantiated, have a very significant impact on results. The NICE Appraisal Committee (AC), when taking into account their preferred assumptions for HAQ progression for patients on treatment with apremilast, placebo response and monitoring costs for apremilast, concluded that the addition of apremilast resulted in cost savings but also a QALY loss. These cost savings were not high enough to compensate for the clinical effectiveness that would be lost. The AC thus decided that apremilast alone or in combination with DMARD therapy is not recommended for treating adults with active PsA that has not responded to prior DMARD therapy, or where such therapy is not tolerated.

Biases in preferences for sequences of outcomes in monkeys

Movies, vacations, and meals are all examples of events composed of a sequence of smaller events. How do we go from our evaluations of each scene in a movie to an evaluation of the sequence as a whole? In theory, we should simply average the values of the individual events. In practice, however, we are biased towards sequences where each element tends to be better than the previous, where the last value is large, and we overweight the best (or worst) part of the sequence. To study how general these biases are we examined monkeys’ preferences for sequences of rewards in a novel reward repeat task. Monkeys were first given a sequence of rewards and then chose between repeating the sequence or receiving a standard comparator sequence. We found that, like humans, monkeys overweight events that happen later in a sequence, so much so that adding a small reward to the end of a sequence can paradoxically reduce its value. Monkeys were also biased towards sequences with large peak values (the highest value in the sequence), but only following a working memory challenge, suggesting that this preference may be driven by memory limitations. These results demonstrate the cross-species nature of biases in preferences for sequences of outcomes. In addition, monkeys’ consistent preference for sequences in which large values occur later challenges the generality of discounting models of intertemporal choice in animals.

FAVR (Filtering and Annotation of Variants that are Rare): methods to facilitate the analysis of rare germline genetic variants from massively parallel sequencing datasets

BackgroundCharacterising genetic diversity through the analysis of massively parallel sequencing (MPS) data offers enormous potential to significantly improve our understanding of the genetic basis for observed phenotypes, including predisposition to and progression of complex human disease. Great challenges remain in resolving genetic variants that are genuine from the millions of artefactual signals.ResultsFAVR is a suite of new methods designed to work with commonly used MPS analysis pipelines to assist in the resolution of some of the issues related to the analysis of the vast amount of resulting data, with a focus on relatively rare genetic variants. To the best of our knowledge, no equivalent method has previously been described. The most important and novel aspect of FAVR is the use of signatures in comparator sequence alignment files during variant filtering, and annotation of variants potentially shared between individuals. The FAVR methods use these signatures to facilitate filtering of (i) platform and/or mapping-specific artefacts, (ii) common genetic variants, and, where relevant, (iii) artefacts derived from imbalanced paired-end sequencing, as well as annotation of genetic variants based on evidence of co-occurrence in individuals. We applied conventional variant calling applied to whole-exome sequencing datasets, produced using both SOLiD and TruSeq chemistries, with or without downstream processing by FAVR methods. We demonstrate a 3-fold smaller rare single nucleotide variant shortlist with no detected reduction in sensitivity. This analysis included Sanger sequencing of rare variant signals not evident in dbSNP131, assessment of known variant signal preservation, and comparison of observed and expected rare variant numbers across a range of first cousin pairs. The principles described herein were applied in our recent publication identifying XRCC2 as a new breast cancer risk gene and have been made publically available as a suite of software tools.ConclusionsFAVR is a platform-agnostic suite of methods that significantly enhances the analysis of large volumes of sequencing data for the study of rare genetic variants and their influence on phenotypes.