Sequential Selection Procedure Research Articles

Adaptive Sequential Procedures for Quantile Selection with Importance Sampling

In this paper, we consider the problem of identifying the simulated system configuration with optimal quantile performance among a finite set of alternative systems. We first propose adaptive sequential selection procedures via direct simulation, where the point and variance estimators for quantiles are sequentially updated. For the sake of extreme quantiles, we develop adaptive quantile selection procedures using importance sampling. Our procedures apply sample average approximation and stochastic approximation for iteratively computing the optimal importance-sampling parameter and the importance-sampling quantile estimators. The statistical validity of the proposed selection procedures is proven in the asymptotic regime. We particularly investigate the consistency and the central limit convergence using both sample average and stochastic approximation for quantile estimation during the adaptive procedures. Empirical results and an illustrative example show the efficiency of the developed procedures.

IsoFrog: a reversible jump Markov Chain Monte Carlofeature selection-based method for predicting isoform functions.

A single gene may yield several isoforms with different functions through alternative splicing. Continuous efforts are devoted to developing machine-learning methods to predict isoform functions. However, existing methods do not consider the relevance of each feature to specific functions and ignore the noise caused by the irrelevant features. In this case, we hypothesize that constructing a feature selection framework to extract the function-relevant features might help improve the model accuracy in isoform function prediction. In this article, we present a feature selection-based approach named IsoFrog to predict isoform functions. First, IsoFrog adopts a reversible jump Markov Chain Monte Carlo (RJMCMC)-based feature selection framework to assess the feature importance to gene functions. Second, a sequential feature selection procedure is applied to select a subset of function-relevant features. This strategy screens the relevant features for the specific function while eliminating irrelevant ones, improving the effectiveness of the input features. Then, the selected features are input into our proposed method modified domain-invariant partial least squares, which prioritizes the most likely positive isoform for each positive MIG and utilizes diPLS for isoform function prediction. Tested on three datasets, our method achieves superior performance over six state-of-the-art methods, and the RJMCMC-based feature selection framework outperforms three classic feature selection methods. We expect this proposed methodology will promote the identification of isoform functions and further inspire the development of new methods. IsoFrog is freely available at https://github.com/genemine/IsoFrog.

Feature selection in ultrahigh-dimensional additive models with heterogeneous frequency component functions

In this paper, we consider feature selection in ultrahigh-dimensional additive models with heterogeneous frequency component functions. Firstly, we introduce a new concept, weighted sum of squared conditional correlations (WSSCC), which measures the correlation between a random variable and its function. Afterwards, we propose a sure independence screening procedure based on WSSCC (WSSCCSIS), whose sure screening property is established. Furthermore, a sequential feature selection procedure based on WSSCC (WSSCCFR) is proposed. Numerical studies including comprehensive simulation and a real data analysis are carried out to demonstrate the advantage of our method over other existing approaches.

Classification of Alzheimer's disease and frontotemporal dementia using routine clinical and cognitive measures across multicentric underrepresented samples: A cross sectional observational study.

Global brain health initiatives call for improving methods for the diagnosis of Alzheimer's disease (AD) and frontotemporal dementia (FTD) in underrepresented populations. However, diagnostic procedures in upper-middle-income countries (UMICs) and lower-middle income countries (LMICs), such as Latin American countries (LAC), face multiple challenges. These include the heterogeneity in diagnostic methods, lack of clinical harmonisation, and limited access to biomarkers. This cross-sectional observational study aimed to identify the best combination of predictors to discriminate between AD and FTD using demographic, clinical and cognitive data among 1794 participants [904 diagnosed with AD, 282 diagnosed with FTD, and 606 healthy controls (HCs)] collected in 11 clinical centres across five LAC (ReDLat cohort). A fully automated computational approach included classical statistical methods, support vector machine procedures, and machine learning techniques (random forest and sequential feature selection procedures). Results demonstrated an accurate classification of patients with AD and FTD and HCs. A machine learning model produced the best values to differentiate AD from FTD patients with an accuracy = 0.91. The top features included social cognition, neuropsychiatric symptoms, executive functioning performance, and cognitive screening; with secondary contributions from age, educational attainment, and sex. Results demonstrate that data-driven techniques applied in archival clinical datasets could enhance diagnostic procedures in regions with limited resources. These results also suggest specific fine-grained cognitive and behavioural measures may aid in the diagnosis of AD and FTD in LAC. Moreover, our results highlight an opportunity for harmonisation of clinical tools for dementia diagnosis in the region. This work was supported by the Multi-Partner Consortium to Expand Dementia Research in Latin America (ReDLat), funded by NIA/NIH (R01AG057234), Alzheimer's Association (SG-20-725707-ReDLat), Rainwater Foundation, Takeda (CW2680521), Global Brain Health Institute; as well as CONICET; FONCYT-PICT (2017-1818, 2017-1820); PIIECC, Facultad de Humanidades, Usach; Sistema General de Regalías de Colombia (BPIN2018000100059), Universidad del Valle (CI 5316); ANID/FONDECYT Regular (1210195, 1210176, 1210176); ANID/FONDAP (15150012); ANID/PIA/ANILLOS ACT210096; and Alzheimer's Association GBHI ALZ UK-22-865742.

Proof of a Key Inequality for Lattice Event Probabilities with Equal Odds

Levin and Leu (2021) introduced some key inequalities that underlie the lower bound formula for the probability of lattice events when using adaptive members of the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. Here we provide a rigorous proof of the key inequality for each adaptive procedure in the special case of equal odds parameters. We also provide some further insight into why the key inequality holds for arbitrary odds parameters and we present a complete proof in that case for a simple yet non-trivial prototype example. Two errata in the abovementioned publication are also corrected herein.

Sequential sensor selection for the localization of acoustic sources by sparse Bayesian learning.

This paper deals with the design of sensor arrays in the context involving the localization of a few acoustic sources. Sparse approximation is known to be effective to find the source locations, but it depends on different array characteristics, such as the number of sensors and the array geometry. The present paper tackles this array design problem under the form of a sequential sensor selection procedure. The proposed method alternates between two steps. One step involves a source localization estimator, given a current set of measurement points, to obtain the estimation variance. Then, the other step selects the new point where a future measurement will maximally decrease the variance from the previous step. As such, the procedure can be applied online. Both numerical and experimental studies are conducted in an indoor nearfield configuration. Results show that the proposed approach performs better than offline state-of-the-art methods, and the presented empirical study reveals a better robustness to the model mismatches originating from the room reflections.

Adaptive fully sequential selection procedures with linear and nonlinear control variates

A decision-making process often involves selecting the best solution from a finite set of possible alternatives regarding some performance measure, which is known as Ranking-and-Selection (R&S) when the performance is not explicitly available and can only be estimated by taking samples. Many R&S procedures have been proposed considering different problem formulations. In this article, we adopt the classic fully sequential Indifference-Zone (IZ) formulation developed in the statistical literature, and take advantage of the control variates, a well-known variance reduction technique in the simulation literature, to investigate the potential benefits as well as the statistical guarantee by designing a new type of R&S procedure in an adaptive fashion. In particular, we propose a generic adaptive fully sequential procedure that can employ both linear and nonlinear control variates, in which both the control coefficient and sample variance can be sequentially updated as the sampling process progresses. We demonstrate that the proposed procedures provide the desired probability of correct selection in the asymptotic regime as the IZ parameter goes to zero. We then compare the proposed procedures with various existing procedures through the simulation experiments on practical illustrative examples, in which we observe several interesting findings and demonstrate the advantage of our proposed procedures.

A sequential feature selection procedure for high-dimensional Cox proportional hazards model

A sequential feature selection procedure for high-dimensional Cox proportional hazards model

Informative Power Evaluation of Clinical Parameters to Predict Initial Therapeutic Response in Patients with Advanced Pleural Mesothelioma: A Machine Learning Approach.

Malignant pleural mesothelioma (MPM) is a rare neoplasm whose early diagnosis is challenging and systemic treatments are generally administered as first line in the advanced disease stage. The initial clinical response may represent a useful parameter in terms of identifying patients with a better long-term outcome. In this report, the initial therapeutical response in 46 patients affected with advanced/unresectable pleural mesothelioma was investigated. The initial therapeutic response was assessed by CT scan and clinical examination after 2–3 treatment cycles. Our preliminary evaluation shows that the group of patients treated with regimens including antiangiogenetics and/or immunotherapy had a significantly better initial response as compared to patients only treated with standard chemotherapy, exhibiting a disease control rate (DCR) of 100% (95% IC, 79.40–100%) and 80.0% (95% IC, 61.40–92.30%), respectively. Furthermore, the therapeutic response was correlated with the disease stage, blood leukocytes and neutrophils, high albumin serum levels, and basal body mass index (BMI). Specifically, the patients with disease stage III showed a DCR of 95.7% (95% IC, 78.1–99.9%), whereas for disease stage IV the DCR decreased to 66.7% (95% IC, 34.9–9.1%). Moreover, a better initial response was observed in patients with a higher BMI, who reached a DCR of 96.10% (95% IC, 80.36–99.90%). Furthermore, in order to evaluate in the predictive power of the collected features a multivariate way, we report the preliminary results of a machine learning model for predicting the initial therapeutic response. We trained a state-of-the-art algorithm combined to a sequential forward feature selection procedure. The model reached a median AUC value, accuracy, sensitivity, and specificity of 77.0%, 75%, 74.8%, and 83.3%, respectively. The features with greater informational power were gender, histotype, BMI, smoking habits, packs/year, and disease stage. Our preliminary data support the possible favorable correlation between innovative treatments and therapeutic response in patients with unresectable/advanced pleural mesothelioma. The small sample size does not allow concrete conclusions to be drawn; nevertheless, this work is the basis of an ongoing study that will also involve radiomics in a larger dataset.

Abstract P4-11-04: A randomized adaptive sequential selection trial of cryotherapy, compression therapy, and placebo to prevent taxane inducted peripheral neuropathy in patients with breast cancer

Abstract Background: Taxane-induced peripheral neuropathy (TIPN) is one of the most common and debilitating adverse effects of taxane therapy for early-stage breast cancer (ESBC). TIPN is difficult to treat, and there are no known effective prevention strategies. Small non-randomized studies in patients with ESBC, have suggested both cryotherapy and compression therapy to the hands and feet may be effective for TIPN prevention. However, is unknown which therapy, if either, is more effective at prevention of TIPN compared to placebo. Methods: We conducted a randomized phase IIB adaptive sequential selection trial of cryotherapy vs. compression therapy vs. placebo among participants with ESBC during taxane chemotherapy (NCT03873272). Participants were randomized in triplets to either frozen gloves/socks [NatraCure] refrigerated for at least 3 hours to -25 to -30°C prior to use (cryotherapy); compression gloves/socks [Sigvaris] with a pressure of 20-30 mmHg on the upper extremity, 20-30 mmHg on the lower leger, and 15 mmHg on the toes/feet (compression therapy); or “loose” gloves/socks [Sigvaris] with a maximum pressure of 3 mmHg on the upper/lower extremities (placebo arm). All garments were worn for a total of 90-120 minutes, beginning 15 minutes prior to the start of taxane infusion and until 15 minutes after completion of the taxane infusion. The primary goal was to select the best intervention to be carried forward to a larger phase III trial, with a high probability of correct selection if one intervention is truly superior using a novel sequential design based on the Levin-Robbins-Leu family of sequential selection procedures. The primary endpoint was change in Functional Assessment of Cancer Therapy Neurotoxicity (FACT-NTX) at 12-weeks; success was defined as <5-point decrease from baseline (minimal TIPN). The tally of success was compared starting from the 15th triplet. An arm would be eliminated if it had ≥4 successes less than the leading arm. The trial stopped the first time two arms were eliminated. Secondary endpoints included staff assessed adherence (defined as wearing study garments for ≥80% of infusions) and patient reported comfort (4-point Likert scale) to the study intervention. Results: Between 4/2019-4/2021 64 patients were randomized (n=20 cryotherapy; n=22 compression therapy; n=22 placebo). The stopping criterion was met after the 17th triplet (51 patients) had been evaluated for the primary endpoint. For the 51 patients, the median age was 50 years (range, 28-78), and the majority of patients (58.8%) were treated with docetaxel every 3-weeks, whereas 41.2% were treated with weekly paclitaxel. Success (i.e., minimal TIPN) at 12-weeks occurred in 11 (64.7%) patients treated with compression therapy, 7 (41.1%) patients treated with cryotherapy, and 7 (41.1%) patients treated with placebo. Adherence to the study intervention occurred in 82.4% of patients treated with compression therapy, 29.4% of patients treated with cryotherapy, and 76.5% treated with placebo. In regards to comfort, 87.4% of patients treated with compression therapy reported being satisfied/very satisfied with the study garments, compared to 56.3% treated with cryotherapy, and 73.3% treated with placebo. Conclusion: Compression therapy was found to be the most effective and tolerable intervention in this phase IIB selection trial to prevent TIPN, and has the greatest probability of being a successful intervention to prevent TIPN in a future randomized phase III study. Cryotherapy was not successful, which is likely related to poor tolerability due to the cold, which resulted in poor adherence to the study garments. Compression therapy for the prevention of TIPN should be further evaluated in a larger randomized phase III study. Citation Format: Melissa K Accordino, Shing Lee, Cheng-Shiun Leu, Meghna S Trivedi, Katherine D Crew, Kevin M Kalinsky, Rohit Rajhunathan, Alessandra Taboada, Lauren Franks, Erin Honan, Erik Harden, Cynthia Law, Dawn L Hershman. A randomized adaptive sequential selection trial of cryotherapy, compression therapy, and placebo to prevent taxane inducted peripheral neuropathy in patients with breast cancer [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P4-11-04.

Sequential adaptive design for jump regression estimation

Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this article presents a strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. The first example we undertook was to accelerate imaging speed in high-resolution material imaging, and the second was to use sequential design for mapping a chemical phase diagram. In both examples, the underlying regression functions have discontinuities, and thus many existing design optimization approaches cannot be used, as they assume a continuous regression function. Although some existing adaptive design strategies developed from the treed regression models can handle the discontinuities, the related Bayesian model estimation approaches come with computationally expensive Markov Chain Monte Carlo algorithms for posterior inferences and the subsequent design point selections, which may not be applicable for the first motivating example that requires the computation to be faster than the original imaging speed. In addition, the treed models are based on domain partitioning and are inefficient in cases when the discontinuities occur at complex sub-domain boundaries. In this article, we propose a simple and effective adaptive design strategy for regression analysis with discontinuities. After some statistical properties of the estimated regression model are derived in cases with a fixed design, a new criterion for sequentially selecting the design points is suggested. The suggested sequential design selection procedure is then evaluated using a comprehensive simulation study and demonstrated using two motivating examples.

Improving R Peak Detection in ECG Signal Using Dynamic Mode Selected Energy and Adaptive Window Sizing Algorithm with Decision Tree Algorithm.

R peak detection is crucial in electrocardiogram (ECG) signal analysis to detect and diagnose cardiovascular diseases (CVDs). Herein, the dynamic mode selected energy (DMSE) and adaptive window sizing (AWS) algorithm are proposed for detecting R peaks with better efficiency. The DMSE algorithm adaptively separates the QRS components and all non-objective components from the ECG signal. Based on local peaks in QRS components, the AWS algorithm adaptively determines the Region of Interest (ROI). The Feature Extraction process computes the statistical properties of energy, frequency, and noise from each ROI. The Sequential Forward Selection (SFS) procedure is used to find the best subsets of features. Based on these characteristics, an ensemble of decision tree algorithms detects the R peaks. Finally, the R peak position on the initial ECG signal is adjusted using the R location correction (RLC) algorithm. The proposed method has an experimental accuracy of 99.94%, a sensitivity of 99.98%, positive predictability of 99.96%, and a detection error rate of 0.06%. Given the high efficiency in detection and fast processing speed, the proposed approach is ideal for intelligent medical and wearable devices in the diagnosis of CVDs.

A key inequality for lower bound formulas for lattice event probabilities

We introduce and discuss some key inequalities that underlie the lower bound formula for the probability of lattice events in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. The present work combines the notion of lattice events—as previously discussed for the nonadaptive member of the family—with the positive cumulative sum property for the adaptive members—as previously discussed for the special lattice event of correct selection, thereby extending the key inequality to its broadest scope.

Modeling Multivariate Time Series With Copula-Linked Univariate D-Vines

This article proposes a novel multivariate time series model named copula-linked univariate D-vines (CuDvine), which enables the simultaneous copula-based modeling of both temporal and cross-sectional dependence for multivariate time series. To construct CuDvine, we first build a semiparametric univariate D-vine time series model (uDvine) based on a D-vine. The uDvine generalizes the existing first-order copula-based Markov chain models to Markov chains of an arbitrary-order. Building upon uDvine, we construct CuDvine by linking multiple uDvines via a parametric copula. As a simple and tractable model, CuDvine provides flexible models for marginal behavior and temporal dependence of time series, and can also incorporate sophisticated cross-sectional dependence such as time-varying and spatio-temporal dependence for high-dimensional applications. Robust and computationally efficient procedures, including a sequential model selection method and a two-stage MLE, are proposed for model estimation and inference, and their statistical properties are investigated. Numerical experiments are conducted to demonstrate the flexibility of CuDvine, and to examine the performance of the sequential model selection procedure and the two-stage MLE. Real data applications on the Australian electricity price data demonstrate the superior performance of CuDvine to traditional multivariate time series models.

Machine learning for suicide risk prediction in children and adolescents with electronic health records

Accurate prediction of suicide risk among children and adolescents within an actionable time frame is an important but challenging task. Very few studies have comprehensively considered the clinical risk factors available to produce quantifiable risk scores for estimation of short- and long-term suicide risk for pediatric population. In this paper, we built machine learning models for predicting suicidal behavior among children and adolescents based on their longitudinal clinical records, and determining short- and long-term risk factors. This retrospective study used deidentified structured electronic health records (EHR) from the Connecticut Children’s Medical Center covering the period from 1 October 2011 to 30 September 2016. Clinical records of 41,721 young patients (10–18 years old) were included for analysis. Candidate predictors included demographics, diagnosis, laboratory tests, and medications. Different prediction windows ranging from 0 to 365 days were adopted. For each prediction window, candidate predictors were first screened by univariate statistical tests, and then a predictive model was built via a sequential forward feature selection procedure. We grouped the selected predictors and estimated their contributions to risk prediction at different prediction window lengths. The developed predictive models predicted suicidal behavior across all prediction windows with AUCs varying from 0.81 to 0.86. For all prediction windows, the models detected 53–62% of suicide-positive subjects with 90% specificity. The models performed better with shorter prediction windows and predictor importance varied across prediction windows, illustrating short- and long-term risks. Our findings demonstrated that routinely collected EHRs can be used to create accurate predictive models for suicide risk among children and adolescents.

Positivity of cumulative sums for multi-index function components explains the lower bound formula in the Levin-Robbins-Leu family of sequential subset selection procedures

We exhibit some strong positivity properties of a certain function that implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. These properties provide a more direct and comprehensive demonstration of the key inequality than was discussed in Levin and Leu (2013a).

A curtailed selection procedure for comparing Bernoulli outcomes with a control

ABSTRACT A sequential selection procedure is proposed for comparing experimental Bernoulli populations with a controlled Bernoulli population. The comparison is made according to the success probability. Based on the numbers of successes of the populations, the indifference zone formulation and the subset selection formulation are integrated to select either the best population or a random-sized subset that contains the best population. Observations are taken one at a time and the populations that are no longer comparable are eliminated until either the best is identified or the total number of observations in at least one population reaches a specific upper bound. We show that the proposed sequential procedure satisfies the same probability requirements as does the corresponding fixed-sample-size procedure. Furthermore, the expected sample size from each population for the proposed procedure is significantly smaller than the sample size required by the fixed-sample-size procedure.

Algorithm for Calculating the Initial Sample Size in a Fully Sequential Ranking and Selection Procedure

In some fully sequential ranking and selection procedures, such as the KN procedure and Rinott’s procedure, some initial samples must be taken to estimate the variance. We analyze the impact of the initial sample size (ISS) on the total sample size and propose an algorithm to calculate the ISS in this type of procedure. To better illustrate our approach, we implement this algorithm on the KN procedure and propose the KN-ISS procedure. Comprehensive numerical experiments reveal that this procedure can significantly improve the efficiency compared with the KN procedure and still deliver the desired probability of correct selection.

Developing and using statistical tools to estimate observer effect for ordered class data: The case of the IBP (Index of Biodiversity Potential)

Abstract Ecological indicators based on measurements made by individual observers often include extra noise associated with the observer herself (observer effect). The literature on this subject has used a variety of analytical tools to account for this variation, but few analyses have used a hierarchical statistical model approach that can account for the variation and bias among observers on both the mean and variance of the data. We used the Index of Biodiversity Potential (IBP), a rapid habitat assessment method widely used in France, in a case study to propose latent variable hierarchical models to assess the impact of observer effect while accounting for other sources of variation. For seven of the ten factors constituting the IBP, we used a sequential model selection procedure to analyze observers’ scores, then analyzed the final models. The structure of the best models varied according to the related factor. Our analyses confirm: (i) that the expert reference observer provided lower variability in his observations than did the other observers for all factors except the one related to standing deadwood; (ii) that all but two factors showed at least a moderate level of systematic random observer variations; (iii) that the absence of leaves in winter led to increased variations when tree-species identification was required; and (iv) that evaluation of stand openness was highly variable and should therefore be assessed by an expert. Overall, the data were coherent with our best models from various points of view for which we diagnosed goodness-of-fit. Our work is a further illustration of the interest of adopting fully parametric statistical modelling of observer-based variations.

A worst‐case formulation for constrained ranking and selection with input uncertainty

AbstractIn this research, we consider robust simulation optimization with stochastic constraints. In particular, we focus on the ranking and selection problem in which the computing time is sufficient to evaluate all the designs (solutions) under consideration. Given a fixed simulation budget, we aim at maximizing the probability of correct selection (PCS) for the best feasible design, where the objective and constraint measures are assessed by their worst‐case performances. To simplify the complexity of PCS, we develop an approximated probability measure and derive the asymptotic optimality condition (optimality condition as the simulation budget goes to infinity) of the resulting problem. A sequential selection procedure is then designed within the optimal computing budget allocation framework. The high efficiency of the proposed procedure is tested via a number of numerical examples. In addition, we provide some useful insights into the efficiency of a budget allocation procedure.