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One of the appropriate and efficient tools in the field of productivity measurement and evaluation is data envelopment analysis, which is used as a non-parametric method to calculate the efficiency of decision-making units. Today, the use of data envelopment analysis technique is expanding rapidly and is used in the evaluation of various organizations and industries such as banks, postal service, hospitals, training centers, power plants, refineries, etc.In real-world problems, the values observed from input and output data are often ambiguous and random. To solve this problem, data envelopment analysis in stochastic fuzzy environment was proposed. Although the DEA has many advantages, one of the disadvantages of this method is that the classic DEA does not actually give us a definitive conclusion and does not allow random changes in input and output. In this paper, we review some of the proposed models in data envelopment analysis with fuzzy and random inputs and outputs.

In this paper, we investigate the fuzzification of zero forcing process. For this, first we introduce a new embedding of a graph [Formula: see text] by considering a minimal zero forcing set of [Formula: see text] and an arbitrary list of maximal forcing chains of this zero forcing set. Then we get a comparison between zero forcing sets of a graph by using fuzzy concepts. Finally, we give an application for this procedure.

ObjectiveTo provide an understanding of the role of common genetic variations in colorectal cancer (CRC) risk, we report an updated field synopsis and comprehensive assessment of evidence to catalogue all genetic markers for CRC (CRCgene2).DesignWe included 869 publications after parallel literature review and extracted data for 1063 polymorphisms in 303 different genes. Meta-analyses were performed for 308 single nucleotide polymorphisms (SNPs) in 158 different genes with at least three independent studies available for analysis. Scottish, Canadian and Spanish data from genome-wide association studies (GWASs) were incorporated for the meta-analyses of 132 SNPs. To assess and classify the credibility of the associations, we applied the Venice criteria and Bayesian False-Discovery Probability (BFDP). Genetic associations classified as ‘positive’ and ‘less-credible positive’ were further validated in three large GWAS consortia conducted in populations of European origin.ResultsWe initially identified 18 independent variants at 16 loci that were classified as ‘positive’ polymorphisms for their highly credible associations with CRC risk and 59 variants at 49 loci that were classified as ‘less-credible positive’ SNPs; 72.2% of the ‘positive’ SNPs were successfully replicated in three large GWASs and the ones that were not replicated were downgraded to ‘less-credible’ positive (reducing the ‘positive’ variants to 14 at 11 loci). For the remaining 231 variants, which were previously reported, our meta-analyses found no evidence to support their associations with CRC risk.ConclusionThe CRCgene2 database provides an updated list of genetic variants related to CRC risk by using harmonised methods to assess their credibility.

Habitat heterogeneity is a main factor determining the geographical distribution of species. For plant and particularly trees and shrubs, topography (microtopography) is an applicable predictor of habitat, slope, and aspect that often correlate with distribution of water and nutrients availability and spatial pattern of species. However, there is lack on exploring this relationship in different plant communities through different environments. In this research, the spatial pattern of woody species in relation to microtopography was investigated in Chahartagh forest, Chahar Mahal, and Bakhtiari province, Iran. The location of the trees and shrubs of a 53-ha forest reserve in Chartagh was measured and the type of microtopography including (i) slope A without microtopography and (ii) slope B composed of three microtopography types: crest (degree of tilt is≥60%), intermediate area (30–40%), and gully (10–20%) were recorded. The effects of microtopography on the spatial pattern of species were analyzed using O-ring statistic. The results showed that the main distribution pattern for the woodiest species in the study area in all platforms is aggregated pattern, while for larger scales, the pattern tended to become random. Also, the pattern was strongly influenced by the scale that the distribution type was assessed. From the other hand, our results revealed that for steeper platforms, the patterns tend to be more aggregated which indicates the non-uniformity of water and nutrition distribution in steeper platforms. Also, this can be a result of seed distribution behavior which is affected by microtopography in a way that in steep platforms, rolling of the seed results in patchy accumulation of the seeds and finally patchy regeneration.

Int. J. Epidemiol. Advance Access published October 7, 2015 International Journal of Epidemiology, 2015, 1–20 doi: 10.1093/ije/dyv185 Original article Original article Systematic meta-analyses and field synopsis of genetic association studies in colorectal adenomas Downloaded from http://ije.oxfordjournals.org/ at Serials RecordsSerials on October 14, 2015 Zahra Montazeri, 1† Evropi Theodoratou, 2† Christine Nyiraneza, 1 Maria Timofeeva, 3 Wanjing Chen, 2 Victoria Svinti, 3 Shanya Sivakumaran, 2 Gillian Gresham, 1 Laura Cubitt, 2 Luis Carvajal-Carmona, 4 Monica M. Bertagnolli, 5 Ann G. Zauber, 6 Ian Tomlinson, 7 Susan M. Farrington, 3 Malcolm G. Dunlop, 3 Harry Campbell 2,3 and Julian Little 1 * School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, Ottawa, Canada, 2 Centre for Population Health Sciences, University of Edinburgh, Edinburgh, UK, 3 Colon Cancer Genetics Group and Academic Coloproctology, Institute of Genetics and Molecular Medicine, University of Edinburgh and MRC Human Genetics Unit Western General Hospital, Edinburgh, UK Biochemistry and Molecular Medicine, Genome and Biomedical Sciences Facility, UC Davis School of Medicine, University of California Davis, Davis, CA, USA, 5 Department of Surgery, Brigham and Women’s Hospital, Boston, MA, USA 6 Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, New York, NY, USA and 7 Wellcome Trust Centre for Human Genetics, Oxford, UK *Corresponding author. School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, 451 Smyth Road, Ottawa, Canada. E-mail: jlittle@uottawa.ca Joint first authors. Accepted 20 August 2015 Abstract Background: Low penetrance genetic variants, primarily single nucleotide polymorph- isms, have substantial influence on colorectal cancer (CRC) susceptibility. Most CRCs develop from colorectal adenomas (CRA). Here we report the first comprehensive field synopsis that catalogues all genetic association studies on CRA, with a parallel online database [http://www.chs.med.ed.ac.uk/CRAgene/]. Methods: We performed a systematic review, reviewing 9750 titles, and then extracted data from 130 publications reporting on 181 polymorphisms in 74 genes. We conducted meta-analyses to derive summary effect estimates for 37 polymorphisms in 26 genes. We applied the Venice criteria and Bayesian False Discovery Probability (BFDP) to assess the levels of the credibility of associations. Results: We considered the association with the rs6983267 variant at 8q24 as ‘highly cred- ible’, reaching genome-wide statistical significance in at least one meta-analysis model. We identified ‘less credible’ associations (higher heterogeneity, lower statistical power, BFDP > 0.02) with a further four variants of four independent genes: MTHFR c.677C>T p.A222V C The Author 2015; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association V

Background Low back pain (LBP) as a musculoskeletal disorder is one of the most common occupational injuries in nurses but there isn’t any valid measure of the prevalence of LBP in Iranian nursing. In order to increase the power and improve the estimates of the prevalence of LBP in Iranian nurses, a comprehensive meta-analysis was carried out. A summary measure of all studies conducted in this field was found and distributions of LBP were evaluated based on different variables. Methods Inclusion criteria included articles with prevalence of LBP in Iranian nurses, who had at least six months of work experience without any trauma, injuries to spine, or any underlying disease. The keywords“prevalence, low back pain, nurses”, and “Iran” were used as part of this search. Databases such as Pubmed, Web of Science, Science direct, Scopus, IranMedex, Irandoc, Magiran, SID, CIVILICA, IMEMR and Google scholar were searched up to and including 15 June 2016. For data extraction a form was designed that included the following variables: Author names, province, sample size, age, gender, marital status, work experience, body mass index, job type, smoking status, work schedule, year of publication, type of standard questionnaire, prevalence of LBP, studies’ quality score and climate classifications. Data analysis was carried out using fixed and random effects model. Heterogeneity between studies was assessed by using the I 2 and Q tests. Results In all 1250 articles were identified and 22 articles with 9347 participants met the inclusion criteria for meta-analyses after filtering. The prevalence of low back pain during their working life and during the last year, was estimated at 63% (95% Confidence Interval (CI): 57.4–68.5) and 61.2% (95% CI: 55.7–66.7) respectively. The prevalence rate of this disorder was 58.7% (95% CI: 35.8–81.7) and 60.4% (95% CI: 52.2–68.6) among men and women respectively. Furthermore, prevalence’s of LBP were 59.5% in wards nurses, 50.3% in operating room technicians, and 39.4% in aid nurses. Conclusions The results showed the high prevalence of LBP injury in nurses, especially female nurses. The effect of musculoskeletal disorders such as LBP may be reduced by considering proper observation of the principles of ergonomics in the workplace, performing physical examinations on a regular basis, identifying risk factors in the advancement of musculoskeletal disorders and then trying to fix them.

Methods are proposed to combine several individual classifiers in order to develop more accurate classification rules. The proposed algorithm uses Rademacher–Walsh polynomials to combine M (≥2) individual classifiers in a nonlinear way. The resulting classifier is optimal in the sense that its misclassification error rate is always less than, or equal to, that of each constituent classifier. A number of numerical examples (based on both real and simulated data) are also given. These examples demonstrate some new, and far-reaching, benefits of working with combined classifiers.

Procedures are proposed to perform classification when a covariate vector may have missing values. The proposed methods use a combination of least-squares and kernel imputation to construct a classifier. The associated function-indexed empirical processes provide the right theoretical tool to assess the performance of the resulting classifiers. This is done by obtaining exponential bounds on the probability of the deviations of the conditional errors of the constructed classifier from that of the best (optimal) classifier. Such bounds, in conjunction with the Borel–Cantelli lemma, yield various strong consistency results.

SummarySome results related to statistical classification in the presence of missing covariates are presented. We derive representations for the best (Bayes) classifier when some of the covariates can be missing; this is done without imposing any assumptions on the underlying missing probability mechanism. Furthermore, without assuming any missingness-at-random type of conditions, we also construct Bayes consistent classifiers that do not require any imputation-based techniques. Both parametric and non-parametric situations are considered but the emphasis is on the latter. In addition to simple missingness patterns, we also consider the full Swiss cheese model, where the missing covariates can be anywhere. Both mechanics and the theoretical validity of our results are discussed.

General procedures are proposed for nonparametric classification in the presence of missing covariates. Both kernel-based imputation as well as Horvitz–Thompson-type inverse weighting approaches are employed to handle the presence of missing covariates. In the case of imputation, it is a certain regression function which is being imputed (and not the missing values). Using the theory of empirical processes, the performance of the resulting classifiers is assessed by obtaining exponential bounds on the deviations of their conditional errors from that of the Bayes classifier. These bounds, in conjunction with the Borel–Cantelli lemma, immediately provide various strong consistency results.

Objective Although accumulating evidence suggests harmful effects of waterpipe smoking, there is limited information about its direct association with chronic diseases, notably cancer. We provide an up-to-date systematic review and meta-analysis of the association between waterpipe smoking and cancer. Data sources Systematic search of articles indexed in main biomedical databases: Pubmed, EmBase, Google Scholar and Web of Science, published between 1962 and September 2014. Search keywords included a combination of waterpipe or hookah, sheesha, nargile, hubble-bubble, goza or gaylan, and cancer. Study selection Focus on observational studies (cohort, case–control, cross-sectional) that evaluated the association between waterpipe smoking and cancer. Studies with mixed exposures excluded. Data extraction Two investigators independently extracted data and reached consensus on all items. Data synthesis 13 case–control studies met the inclusion criteria and were considered for meta-analysis. The methodological quality of included studies was assessed using the Newcastle-Ottawa Scale (NOS). Meta-analysis revealed a positive association between waterpipe smoking and lung cancer (OR=4.58 (2.61 to 8.03); I 2 =44.67%), and oesophageal cancer (OR=3.63 (1.39 to 9.44); I 2 =94.49%). The majority of studies had a NOS score of 5–6 or 7, indicating ‘fair’ or ‘good’ quality, respectively. Conclusions Our findings support a positive association between waterpipe smoking and cancer risk. However, high-quality studies with standardised exposure measurements are needed to clarify the contribution of waterpipe smoking to chronic diseases. More investments in initiatives for surveillance, intervention and regulatory policy for waterpipe smoking are urgently warranted.

Objective: Family history (FH) provides insights into the effects of shared genomic susceptibilities, environments and behaviors, making it a potentially valuable risk assessment tool for chronic diseases. We assessed whether coronary heart disease (CHD) risk assessment is improved when FH information is added to other clinical information recommended in guidelines. Methods: We applied logistic regression analyses to cross-sectional data originally obtained from a UK study of women who delivered a live-born infant between 1951 and 1970. We developed 3 models: Model 1 included only the covariates in a guideline applicable to the population, Model 2 added FH to Model 1, and Model 3 included a fuller range of risk factors. For each model, its ability to discriminate between study subjects with and those without CHD was evaluated and its impact on risk classification examined using the net reclassification index. Results: FH was an independent risk factor for CHD (odds ratio = 1.7, 95% confidence interval = 1.26-2.47) and improved discrimination beyond guideline-defined clinical factors (p < 0.0006). However, the difference in the area under the curve of 2.8% and the extent of patient reclassification resulting from the inclusion of FH were small (p = 0.11). Conclusion: While FH were a significant independent risk factor for CHD, it added little to risk factors typically included in guidelines.

Background Colorectal cancer is a major global public health problem, with approximately 950,000 patients newly diagnosed each year. We report the first comprehensive field synopsis and creation of a parallel publicly available and regularly updated database (CRCgene) that catalogs all genetic association studies on colorectal cancer (http://www.chs.med.ed.ac.uk/CRCgene/). Methods We performed two independent systematic reviews, reviewing 10e145 titles, then collated and extracted data from 635 publications reporting on 445 polymorphisms in 110 different genes. We carried out meta-analyses to derive summary effect estimates for 92 polymorphisms in 64 different genes. For assessing the credibility of associations, we applied the Venice criteria and the Bayesian False Discovery Probability (BFDP) test. Results We consider 16 independent variants at 13 loci (MUTYH, MTHFR, SMAD7, and common variants tagging the loci 8q24, 8q23.3, 11q23.1, 14q22.2, 1q41, 20p12.3, 20q13.33, 3q26.2, 16q22.1, and 19q13.1) to have the most highly credible associations with colorectal cancer, with all variants except those in MUTYH and 19q13.1 reaching genome-wide statistical significance in at least one meta-analysis model. We identified less-credible (higher heterogeneity, lower statistical power, BFDP >0.2) associations with 23 more variants at 22 loci. The meta-analyses of a further 20 variants for which associations have previously been reported found no evidence to support these as true associations. Conclusion The CRCgene database provides the context for genetic association data to be interpreted appropriately and helps inform future research direction.

Methods are proposed to construct empirical measures when there are missing terms among the components of a random vector. Fur- thermore, Vapnik-Chevonenkis type exponential bounds are obtained on the uniform deviations of these estimators, from the true probabilities. These results can then be used to deal with classical problems such as statistical classification, via empirical risk minimization, when there are missing covariates among the data. Another application involves the uni- form estimation of a distribution function. AMS 2000 subject classifications: Primary 60G50, 62G15; secondary 62H30.