Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a ...Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.展开更多
AIM： To pool data currently available to determine the association between statin use and the risk of liver cancer.METHODS： A computerized literature search was conducted to identify those relevant studies between J...AIM： To pool data currently available to determine the association between statin use and the risk of liver cancer.METHODS： A computerized literature search was conducted to identify those relevant studies between Janu-ary 1966 and March 2013. Stata 11.0 （Stata Corp, College Station, Texas） was used for statistical analyses. Pooled relative risk （RR） estimates with 95%CI were calculated for overall analysis and subgroup analyses, using the random- and fxed-effects models. Heteroge-neities between studies were evaluated by Cochran’s Q test and I^2 statistic. The Begg’s funnel plot and Egger’s regression asymmetry test were used to detect the publication bias.RESULTS： Seven studies were included in our meta-analysis according to the selection criteria, including four cohort studies and three case-control studies. These studies involved 4725593 people and 9785 liver cancer cases. The overall analysis showed that statin use was statistically associated with a signifcantly reduced risk of liver cancer （random-effects model, RR=0.61, 95%CI： 0.49-0.76, P 〈 0.001; fxed-effects mod-el, RR=0.64, 95%CI： 0.57-0.71, P 〈 0.001）; however, significant heterogeneity was found between studies （Cochran’s Q statistic=19.13, P=0.004; I^2 = 68.6%）. All subgroup analyses provided supporting evidence for the results of overall analysis. Begg’s （Z=0.15, P=0.881） and Egger’s test （ t=-0.44, P=0.681） showed no signifcant risk of having a publication bias.CONCLUSION： Statin use was associated with the reduced risk of liver cancer. To clearly clarify this relationship, more high quality studies are required.展开更多
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes...The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.展开更多
文摘Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.
基金Supported by Beijing NOVA Programme,No.Z131107000413067the Research Fund of the China-Japan Friendship Hospital,Nos.2013-QN-07 and 2013-QN-06
文摘AIM： To pool data currently available to determine the association between statin use and the risk of liver cancer.METHODS： A computerized literature search was conducted to identify those relevant studies between Janu-ary 1966 and March 2013. Stata 11.0 （Stata Corp, College Station, Texas） was used for statistical analyses. Pooled relative risk （RR） estimates with 95%CI were calculated for overall analysis and subgroup analyses, using the random- and fxed-effects models. Heteroge-neities between studies were evaluated by Cochran’s Q test and I^2 statistic. The Begg’s funnel plot and Egger’s regression asymmetry test were used to detect the publication bias.RESULTS： Seven studies were included in our meta-analysis according to the selection criteria, including four cohort studies and three case-control studies. These studies involved 4725593 people and 9785 liver cancer cases. The overall analysis showed that statin use was statistically associated with a signifcantly reduced risk of liver cancer （random-effects model, RR=0.61, 95%CI： 0.49-0.76, P 〈 0.001; fxed-effects mod-el, RR=0.64, 95%CI： 0.57-0.71, P 〈 0.001）; however, significant heterogeneity was found between studies （Cochran’s Q statistic=19.13, P=0.004; I^2 = 68.6%）. All subgroup analyses provided supporting evidence for the results of overall analysis. Begg’s （Z=0.15, P=0.881） and Egger’s test （ t=-0.44, P=0.681） showed no signifcant risk of having a publication bias.CONCLUSION： Statin use was associated with the reduced risk of liver cancer. To clearly clarify this relationship, more high quality studies are required.
基金supported by National Science Foundation of USA (Grant No. DMS1265202)National Institutes of Health of USA (Grant No. 1-U54AI117924-01)
文摘The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.
