Weibull prediction of event times in clinical trials

In clinical trials with interim analyses planned at pre-specified event counts, one may wish to predict the times of these landmark events as a tool for logistical planning. Currently available methods use either a parametric approach based on an exponential model for survival (Bagiella and Heitjan, Statistics in Medicine 2001; 20:2055) or a non-parametric approach based on the Kaplan-Meier estimate (Ying et al., Clinical Trials 2004; 1:352). Ying et al. (2004) demonstrated the trade-off between bias and variance in these models; the exponential method is highly efficient when its assumptions hold but potentially biased when they do not, whereas the non-parametric method has minimal bias and is well calibrated under a range of survival models but typically gives wider prediction intervals and may fail to produce useful predictions early in the trial. As a potential compromise, we propose here to make predictions under a Weibull survival model. Computations are somewhat more difficult than with the simpler exponential model, but Monte Carlo studies show that predictions are robust under a broader range of assumptions. We demonstrate the method using data from a trial of immunotherapy for chronic granulomatous disease.     

How to exert the student-center approach in middle school English teaching

In order to train a student to be a person with ability,who can self-study,use knowledge flexibly and bring firth new ideas constantly,the constant development of society demands a full exertion of student-center approach in the process of education.Therefore,how to exert the student-center approach is a question that every teacher is facing.I think that we can exert the student-center approach from the following aspects.One,a teacher must change his teaching conception.He should know that it's the students who are the main body of teaching and the teacher can act as a guider.The other,by all means,we ought to make the students know the purpose of their study and the function of themselves in learning.We also ought to culture their interest in learning,inspire and strengthen their main body consciousness.the teacher should,on the basis of full understanding his students and textbook,exert the leading function of himself.In the course of teaching,the teacher can exert the advantage of advanced teaching method,such as situational language teaching,and advanced teaching instrument,such as multimedia,which will inspire the students' interest and conscious activities.We can train the students' imagining ability through encouragement 、guiding and extracurricular activities.We can improve the students' ability of self-study.Thus,the students' main body function will reach a better exertion and the effect of teaching will be improved.This will train the students to suit the need of society.