Study On The Correlation Coefficient Of Binary Censored Random Variables

In the study of survival analysis,the time from the observation time to the occurrence of the event of interest is called the failure time or survival time.In the study of the actual problems of survival time,it is often necessary to study the correlation between the two survival times.If you can obtain a complete sample of survival time,you can consider using the Pearson correlation coefficient to analyze the linear relationship between the two survival time variables.However,due to the failure of follow-up,the existence of competitive risks,or the limited duration of the study,the observation of these two survival time variables cannot obtain complete data,which results in the deletion of data.For the correlation study of binary censored data,traditional methods cannot be used for analysis.At present,statisticians have conducted some studies on the correlation of binary censored data,mainly based on empirical likelihood and semi parametric estimation methods.When using these methods,it is usually necessary to use an iterative method to solve the approximate solution of the estimated quantity.The calculation process is complicated and the operation is difficult.This article proposes a relatively simple and easy to operate method.Based on the idea of "unbiased transformation",a set of estimates of Pearson correlation coefficients for a set of binary survival time variables are constructed.This method can simultaneously solve the correlation estimation problem of binary right censored data and binary interval censored data.The main purpose of "unbiased conversion" is to construct a statistic based on the censored data,so that the statistic is the same as the original mean of the time-to-live variable.The mean is estimated.The estimates obtained by the "unbiased conversion" method have many excellent statistical properties similar to the sample mean.Based on the censored data,this paper uses the "unbiased conversion" method to construct the mathematical expectation,variance and mathematical expectation of the product of the two survival time variables.Substituting these estimates into the corresponding parameter positions of Pearson correlation coefficients,an estimate of correlation coefficients is obtained.Since the estimator constructed by "unbiased transformation" has consistency and asymptotic normality,it can be deduced that the estimator of the Pearson correlation coefficient under this censored data has good statistical properties such as consistency and asymptotic normality.It can be seenfrom the simulation calculation that the result of the Pearson correlation coefficient calculated under "unbiased conversion" is very close to the result calculated from the Pearson correlation coefficient under full data,which verifies the feasibility of the "unbiased conversion" method used in this paper and effectiveness.