Moments of the Product-Limit Estimator Under Left-Truncation and Right-Censoring

2005 ◽  
Vol 34 (8) ◽  
pp. 1833-1850
Author(s):  
Y.-T. Hwang
Keyword(s):  
Right Censoring ◽  
Left Truncation ◽  
Product Limit Estimator ◽  
Product Limit

A note on the product-limit estimator under right censoring and left truncation

Biometrika ◽  
1987 ◽  
Vol 74 (4) ◽  
pp. 883-886 ◽  
Author(s):  
WEI-YANN TSAI ◽  
NICHOLAS P. JEWELL ◽  
MEI-CHENG WANG
Keyword(s):  
Right Censoring ◽  
Left Truncation ◽  
Product Limit Estimator ◽  
Product Limit

Weak convergence of TJW product‐limit estimator under association

Stat ◽  
2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Amir Hossein Shabani ◽  
Hadi Jabbari ◽  
Vahid Fakoor
Keyword(s):  
Weak Convergence ◽  
Product Limit Estimator ◽  
Product Limit

EMPIRICAL FUZZY ESTIMATE OF THE SURVIVAL CURVE

2004 ◽  
Vol 12 (03) ◽  
pp. 347-356
Author(s):  
KIAN POKORNY ◽  
DILEEP SULE
Keyword(s):  
Expert Knowledge ◽  
Survival Curve ◽  
Complete Data ◽  
Point Estimate ◽  
Data Set ◽  
Fuzzy Membership Functions ◽  
Product Limit Estimator ◽  
Product Limit ◽  
Few Data ◽  
Fuzzy Estimate

In this paper, a computational system is developed that estimates a survival curve and a point estimate when very few data are available and a high proportion of the data are censored. Standard statistical methods require a more complete data set. With any less data expert knowledge or heuristic methods are required. The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The "fuzzy" data is then used to estimate a survival curve and the mean survival time is calculated from the curve. The new estimator converges to the Product-Limit estimator when a complete data set is available. In addition, this method allows for the incorporation of expert knowledge. Finally, simulation results are provided to demonstrate the performance of the new method and its improvement over the Product-Limit estimator.

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