The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in...The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. In this work we consider how individual observations in a data set can influence the value of various R2 measures proposed for survival analysis including local influence to assess mathematically the effect of small changes. We discuss methodologies for assessing influence on Graf et al.＇s R2G measure, Harrell＇s C-index and Nagelkerke＇s R2N. The ideas are illustrated on data on 1391 patients diagnosed with Diffuse Large B-cell Lymphoma （DLBCL）, a major subtype ofNon-Hodgkin＇s Lymphoma （NHL）.展开更多
This paper is concerned with a mutualism ecological model with stochastic perturba- tions. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavio...This paper is concerned with a mutualism ecological model with stochastic perturba- tions. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic perma- nence. The sufficient conditions for the system to be extinct are given and the conditionsfor the system to be persistent are also established. At last, some figures are presented to illustrate our main results.展开更多
文摘The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. In this work we consider how individual observations in a data set can influence the value of various R2 measures proposed for survival analysis including local influence to assess mathematically the effect of small changes. We discuss methodologies for assessing influence on Graf et al.＇s R2G measure, Harrell＇s C-index and Nagelkerke＇s R2N. The ideas are illustrated on data on 1391 patients diagnosed with Diffuse Large B-cell Lymphoma （DLBCL）, a major subtype ofNon-Hodgkin＇s Lymphoma （NHL）.
文摘This paper is concerned with a mutualism ecological model with stochastic perturba- tions. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic perma- nence. The sufficient conditions for the system to be extinct are given and the conditionsfor the system to be persistent are also established. At last, some figures are presented to illustrate our main results.
