International Journal of Biostatistics最新文献

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Estimating the Population Average Treatment Effect in Observational Studies with Choice-Based Sampling. 在基于选择抽样的观察性研究中估计总体平均治疗效果。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-04-16 DOI: 10.1515/ijb-2018-0093
Zhiwei Zhang, Zonghui Hu, Chunling Liu
{"title":"Estimating the Population Average Treatment Effect in Observational Studies with Choice-Based Sampling.","authors":"Zhiwei Zhang,&nbsp;Zonghui Hu,&nbsp;Chunling Liu","doi":"10.1515/ijb-2018-0093","DOIUrl":"https://doi.org/10.1515/ijb-2018-0093","url":null,"abstract":"<p><p>We consider causal inference in observational studies with choice-based sampling, in which subject enrollment is stratified on treatment choice. Choice-based sampling has been considered mainly in the econometrics literature, but it can be useful for biomedical studies as well, especially when one of the treatments being compared is uncommon. We propose new methods for estimating the population average treatment effect under choice-based sampling, including doubly robust methods motivated by semiparametric theory. A doubly robust, locally efficient estimator may be obtained by replacing nuisance functions in the efficient influence function with estimates based on parametric models. The use of machine learning methods to estimate nuisance functions leads to estimators that are consistent and asymptotically efficient under broader conditions. The methods are compared in simulation experiments and illustrated in the context of a large observational study in obstetrics. We also make suggestions on how to choose the target proportion of treated subjects and the sample size in designing a choice-based observational study.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0093","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37320863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Youden Index in the Generalized Receiver Operating Characteristic Curve Context. 广义受者工作特征曲线中的约登指数。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-04-03 DOI: 10.1515/ijb-2018-0060
Pablo Martínez-Camblor, Juan Carlos Pardo-Fernández
{"title":"The Youden Index in the Generalized Receiver Operating Characteristic Curve Context.","authors":"Pablo Martínez-Camblor,&nbsp;Juan Carlos Pardo-Fernández","doi":"10.1515/ijb-2018-0060","DOIUrl":"https://doi.org/10.1515/ijb-2018-0060","url":null,"abstract":"<p><p>The receiver operating characteristic (ROC) curve and their associated summary indices, such as the Youden index, are statistical tools commonly used to analyze the discrimination ability of a (bio)marker to distinguish between two populations. This paper presents the concept of Youden index in the context of the generalized ROC (gROC) curve for non-monotone relationships. The interval estimation of the Youden index and the associated cutoff points in a parametric (binormal) and a non-parametric setting is considered. Monte Carlo simulations and a real-world application illustrate the proposed methodology.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37117951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 79
A Joint Poisson State-Space Modelling Approach to Analysis of Binomial Series with Random Cluster Sizes. 随机簇大小二项序列分析的联合泊松状态空间建模方法。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-03-21 DOI: 10.1515/ijb-2018-0090
Guohua Yan, Renjun Ma, M Tariqul Hasan
{"title":"A Joint Poisson State-Space Modelling Approach to Analysis of Binomial Series with Random Cluster Sizes.","authors":"Guohua Yan,&nbsp;Renjun Ma,&nbsp;M Tariqul Hasan","doi":"10.1515/ijb-2018-0090","DOIUrl":"https://doi.org/10.1515/ijb-2018-0090","url":null,"abstract":"<p><p>Serially correlation binomial data with random cluster sizes occur frequently in environmental and health studies. Such data series have traditionally been analyzed using binomial state-space or hidden Markov models without appropriately accounting for the randomness in the cluster sizes. To characterize correlation and extra-variation arising from the random cluster sizes properly, we introduce a joint Poisson state-space modelling approach to analysis of binomial series with random cluster sizes. This approach enables us to model the marginal counts and binomial proportions simultaneously. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors. This estimation method is computationally efficient and robust since it depends only on the first- and second- moment assumptions of unobserved random effects. Our proposed approach is illustrated with analysis of birth delivery data.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37240012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Double Robust Efficient Estimators of Longitudinal Treatment Effects: Comparative Performance in Simulations and a Case Study. 纵向治疗效果的双稳健有效估计:模拟中的比较性能和案例研究。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-02-26 DOI: 10.1515/ijb-2017-0054
Linh Tran, Constantin Yiannoutsos, Kara Wools-Kaloustian, Abraham Siika, Mark van der Laan, Maya Petersen
{"title":"Double Robust Efficient Estimators of Longitudinal Treatment Effects: Comparative Performance in Simulations and a Case Study.","authors":"Linh Tran,&nbsp;Constantin Yiannoutsos,&nbsp;Kara Wools-Kaloustian,&nbsp;Abraham Siika,&nbsp;Mark van der Laan,&nbsp;Maya Petersen","doi":"10.1515/ijb-2017-0054","DOIUrl":"https://doi.org/10.1515/ijb-2017-0054","url":null,"abstract":"<p><p>A number of sophisticated estimators of longitudinal effects have been proposed for estimating the intervention-specific mean outcome. However, there is a relative paucity of research comparing these methods directly to one another. In this study, we compare various approaches to estimating a causal effect in a longitudinal treatment setting using both simulated data and data measured from a human immunodeficiency virus cohort. Six distinct estimators are considered: (i) an iterated conditional expectation representation, (ii) an inverse propensity weighted method, (iii) an augmented inverse propensity weighted method, (iv) a double robust iterated conditional expectation estimator, (v) a modified version of the double robust iterated conditional expectation estimator, and (vi) a targeted minimum loss-based estimator. The details of each estimator and its implementation are presented along with nuisance parameter estimation details, which include potentially pooling the observed data across all subjects regardless of treatment history and using data adaptive machine learning algorithms. Simulations are constructed over six time points, with each time point steadily increasing in positivity violations. Estimation is carried out for both the simulations and applied example using each of the six estimators under both stratified and pooled approaches of nuisance parameter estimation. Simulation results show that double robust estimators remained without meaningful bias as long as at least one of the two nuisance parameters were estimated with a correctly specified model. Under full misspecification, the bias of the double robust estimators remained better than that of the inverse propensity estimator under misspecification, but worse than the iterated conditional expectation estimator. Weighted estimators tended to show better performance than the covariate estimators. As positivity violations increased, the mean squared error and bias of all estimators considered became worse, with covariate-based double robust estimators especially susceptible. Applied analyses showed similar estimates at most time points, with the important exception of the inverse propensity estimator which deviated markedly as positivity violations increased. Given its efficiency, ability to respect the parameter space, and observed performance, we recommend the pooled and weighted targeted minimum loss-based estimator.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2017-0054","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37004195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Variational Inference for Coupled Hidden Markov Models Applied to the Joint Detection of Copy Number Variations. 耦合隐马尔可夫模型的变分推理在拷贝数变化联合检测中的应用。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-02-19 DOI: 10.1515/ijb-2018-0023
Xiaoqiang Wang, Emilie Lebarbier, Julie Aubert, Stéphane Robin
{"title":"Variational Inference for Coupled Hidden Markov Models Applied to the Joint Detection of Copy Number Variations.","authors":"Xiaoqiang Wang,&nbsp;Emilie Lebarbier,&nbsp;Julie Aubert,&nbsp;Stéphane Robin","doi":"10.1515/ijb-2018-0023","DOIUrl":"https://doi.org/10.1515/ijb-2018-0023","url":null,"abstract":"<p><p>Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this context, we define a hidden Markov process that underlies all individuals jointly in order to detect and to classify genomics regions in different states (typically, deletion, normal or amplification). Structural variations from different individuals may be dependent. It is the case in agronomy where varietal selection program exists and species share a common phylogenetic past. We propose to take into account these dependencies inthe HMM model. When dealing with a large number of series, maximum likelihood inference (performed classically using the EM algorithm) becomes intractable. We thus propose an approximate inference algorithm based on a variational approach (VEM), implemented in the CHMM R package. A simulation study is performed to assess the performance of the proposed method and an application to the detection of structural variations in plant genomes is presented.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36969092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
The Performance of Fixed-Horizon, Look-Ahead Procedures Compared to Backward Induction in Bayesian Adaptive-Randomization Decision-Theoretic Clinical Trial Design. 贝叶斯自适应随机化决策理论临床试验设计中固定视界、前视程序与后向归纳法的性能比较。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-02-06 DOI: 10.1515/ijb-2018-0014
Ari M Lipsky, Roger J Lewis
{"title":"The Performance of Fixed-Horizon, Look-Ahead Procedures Compared to Backward Induction in Bayesian Adaptive-Randomization Decision-Theoretic Clinical Trial Design.","authors":"Ari M Lipsky,&nbsp;Roger J Lewis","doi":"10.1515/ijb-2018-0014","DOIUrl":"https://doi.org/10.1515/ijb-2018-0014","url":null,"abstract":"<p><p>Designing optimal, Bayesian decision-theoretic trials has traditionally required the use of computationally-intensive backward induction. While methods for addressing this barrier have been put forward, few are both computationally tractable and non-myopic, with applications of the Gittins index being one notable example. Here we explore the look-ahead approach with adaptive-randomization, with designs ranging from the fully myopic to the fully informed. We compare the operating characteristics of the look-ahead designed trials, in which decision rules are based on a fixed number of future blocks, with those of trials designed using traditional backward induction. The less-myopic designs performed well. As the designs become more myopic or the trials longer, there were disparities in regions of the decision space that are transition zones between continuation and stopping decisions. The more myopic trials generally suffered from early stopping as compared to the less myopic and backward induction trials. Myopic trials with adaptive randomization also saw as many as 28 % of their continuation decisions change to a different randomization ratio as compared to the backward induction designs. Finally, early stages of myopic-designed trials may have disproportionate effect on trial characteristics.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36934203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hazard Ratio Estimators after Terminating Observation within Matched Pairs in Sibling and Propensity Score Matched Designs. 在兄弟姐妹和倾向分数匹配设计中终止观察后的风险比估计。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2019-01-15 DOI: 10.1515/ijb-2017-0103
Tomohiro Shinozaki, Mohammad Ali Mansournia
{"title":"Hazard Ratio Estimators after Terminating Observation within Matched Pairs in Sibling and Propensity Score Matched Designs.","authors":"Tomohiro Shinozaki,&nbsp;Mohammad Ali Mansournia","doi":"10.1515/ijb-2017-0103","DOIUrl":"https://doi.org/10.1515/ijb-2017-0103","url":null,"abstract":"<p><p>Similar to unmatched cohort studies, matched cohort studies may suffer from the censoring of events prior to the end of follow-up. Moreover, in some matched-pair cohort studies, observation time is prematurely terminated immediately after the follow-up of his/her matched member is completed by an event or censoring. Although the follow-up termination within matched pairs may or may not change the hazard ratio estimators, when and how the change occurs has not been clarified. We study the change in the estimates of the hazard ratio conditional on matched pairs and/or covariates by considering two types of matched-pair designs in cohort studies-sibling pair matching and propensity score matching-in which termination can be naturally considered. If all possible confounders are shared within the matched pairs, after termination, a wide range of hazard ratio estimators coincides with that obtained from a stratified Cox model. If unshared confounders should be adjusted for in the analysis, however, such coincidence is not observed. Simulation studies on sibling designs with unshared confounders suggested that the pair-stratified covariate-adjusted Cox model for the hazard ratio conditional on matched pairs and covariates is generally preferred, for which termination does not deteriorate the estimation. Conversely, the comparison between stratifying or not stratifying on pair is a more subtle issue in propensity score matching which targets a marginal or covariate-conditional hazard ratio. Based on simulation studies considering Cox models after matching based on estimated propensity scores, we discourage pair-stratified analysis and termination, particularly after data collection.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2017-0103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36867785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Parametric Regression Analysis with Covariate Misclassification in Main Study/Validation Study Designs. 主要研究/验证研究设计中协变量错误分类的参数回归分析。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2018-12-15 DOI: 10.1515/ijb-2017-0002
Grace Y Yi, Ying Yan, Xiaomei Liao, Donna Spiegelman
{"title":"Parametric Regression Analysis with Covariate Misclassification in Main Study/Validation Study Designs.","authors":"Grace Y Yi,&nbsp;Ying Yan,&nbsp;Xiaomei Liao,&nbsp;Donna Spiegelman","doi":"10.1515/ijb-2017-0002","DOIUrl":"https://doi.org/10.1515/ijb-2017-0002","url":null,"abstract":"<p><p>Measurement error and misclassification have long been a concern in many fields, including medicine, administrative health care data, epidemiology, and survey sampling. It is known that measurement error and misclassification may seriously degrade the quality of estimation and inference, and should be avoided whenever possible. However, in practice, it is inevitable that measurements contain error for a variety of reasons. It is thus necessary to develop statistical strategies to cope with this issue. Although many inference methods have been proposed in the literature to address mis-measurement effects, some important issues remain unexplored. Typically, it is generally unclear how the available methods may perform relative to each other. In this paper, capitalizing on the unique feature of discrete variables, we consider settings with misclassified binary covariates and investigate issues concerning covariate misclassification; our development parallels available strategies for handling measurement error in continuous covariates. Under a unified framework, we examine a number of valid inferential procedures for practical settings where a validation study, either internal or external, is available besides a main study. Furthermore, we compare the relative performance of these methods and make practical recommendations.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37211949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Optimal and/or Efficient Two treatment Crossover Designs for Five Carryover Models. 五种结转模型的最佳和/或有效的两种处理交叉设计。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2018-11-24 DOI: 10.1515/ijb-2018-0001
Jigneshkumar Gondaliya, Jyoti Divecha
{"title":"Optimal and/or Efficient Two treatment Crossover Designs for Five Carryover Models.","authors":"Jigneshkumar Gondaliya,&nbsp;Jyoti Divecha","doi":"10.1515/ijb-2018-0001","DOIUrl":"https://doi.org/10.1515/ijb-2018-0001","url":null,"abstract":"<p><p>Crossover designs robust to changes in carryover models are useful in clinical trials where the nature of carryover effects is not known in advance. The designs have been characterized for being optimal and efficient under no carryover-, traditional-, and, self and mixed carryover- models, however, ignoring the number of subjects, which has significant impact on both optimality and administrative convenience. In this article, adding two more practical models, the traditional, and, self and mixed carryover models having carryover effect only for the new or test treatment, a 5M algorithm is presented. The 5M algorithm based computer code searches all possible two treatment crossover designs under the five carryover models and list those which are optimal and /or efficient to all the five carryover models. The resultant exhaustive list consists of optimal and/or efficient crossover designs in two, three, and four periods, having 4 to 20 subjects of which 24 designs are new optimal for one of the established carryover models, and 34 designs are optimal for newly added models.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"14 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36711332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Serious Flaw in Nutrition Epidemiology: A Meta-Analysis Study. 营养流行病学的严重缺陷:一项荟萃分析研究。
IF 1.2 4区 数学
International Journal of Biostatistics Pub Date : 2018-11-22 DOI: 10.1515/ijb-2018-0079
Karl E Peace, JingJing Yin, Haresh Rochani, Sarbesh Pandeya, Stanley Young
{"title":"A Serious Flaw in Nutrition Epidemiology: A Meta-Analysis Study.","authors":"Karl E Peace,&nbsp;JingJing Yin,&nbsp;Haresh Rochani,&nbsp;Sarbesh Pandeya,&nbsp;Stanley Young","doi":"10.1515/ijb-2018-0079","DOIUrl":"https://doi.org/10.1515/ijb-2018-0079","url":null,"abstract":"<p><p>Background Many researchers have studied the relationship between diet and health. Specifically, there are papers showing an association between the consumption of sugar sweetened beverages and Type 2 diabetes. Many meta-analyses use individual studies that do not attempt to adjust for multiple testing or multiple modeling. Hence the claims reported in a meta-analysis paper may be unreliable as the base papers do not ensure unbiased statistics. Objective Determine (i) the statistical reliability of 10 papers and (ii) indirectly the reliability of the meta-analysis study. Method We obtained copies of each of the 10 papers used in a metaanalysis paper and counted the numbers of outcomes, predictors, and covariates. We estimate the size of the potential analysis search space available to the authors of these papers; i. e. the number of comparisons and models available. The potential analysis search space is the number of outcomes times the number of predictors times 2 c , where c is the number of covariates. This formula was applied to information found in the abstracts (Space A) as well as the text (Space T) of each base paper. Results The median and range of the number of comparisons possible across the base papers are 6.5 and (2 12,288), respectively for Space A, and 196,608 and (3072-117,117,952), respectively for Space T. It is noted that the median of 6.5 for Space A may be misleading as each study has 60-165 foods that could be predictors. Conclusion Given that testing is at the 5% level and the number of comparisons is very large, nominal statistical significance is very weak support for a claim. The claims in these papers are not statistically supported and hence are unreliable so the meta-analysis paper is also unreliable.</p>","PeriodicalId":49058,"journal":{"name":"International Journal of Biostatistics","volume":"14 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijb-2018-0079","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36755840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
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