RESUMEN
Objective Nonparametric maximum likelihood estimate(NPMLE)and Breslow-Fleming-Harrington estimate(BFH)are extremely sensitive to small risk set for left truncated and right censored data,this study aims to develop estimation methods to improve the estimation accuracy and compare the existing methods.Methods We introduced the NPMLE,weighted NPMLE,conditional NPMLE,BFH and a new weighted BFH estimate.Simulation studies were carried out to compare five methods via the integrated absolute error(IAE) and integrated average width(IAW).Results The IAE of NPMLE,BFH,weighted NPMLE,weighted BFH and conditional NPMLE is ascending in turn;The IAW of weighted BFH is the lowest and NPMLE is the largest,BFH,conditional NPMLE and weighted NPMLE is reversed under different censored rate.Conclusion According to the results of simulation and example,weighted BFH and weighted NPMLE is recommended in turn when the risk set is small.Otherwise,the results of five methods would be consistent.