Non-parametric estimation of bivariate survival function
Abeysundara, Hemalika T.
Estimating bivariate and marginal densities of paired survival data becomes more challenging when only one component is censored. If both components are cencored or both are not censored, a bivariate version of Kaplan-Meier remains as a consistent estimator. But if only one variable is censored, Kaplan-Meier fails to take advantage of the information of the remaining variable. The method proposed by Akritas and Keilegom (2003) considered the case of single censoring as well as double censoring, a situation that is typical in medical studies. Our objective is to estimate the correlation between two variables in paired survival data at the presense of double and single censoring via nonparametric approaches. We use the estimates of nonparametric bivariate distribution and marginal distribution of each variable proposed by Akritas and Keilegom (2003) .These estimates are based on conditional distribution functions considering only those pairs where the value of conditioning variable is uncensored. We then apply above method on Diabetic Macular Edema (DME) data to estimate densities and correlation between time to cure for right and left eye.