On non-parametric maximum likelihood estimation of the bivariate survivor function

✍ Scribed by Ross L. Prentice

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 171 KB
• Volume: 18
• Category: Article
• ISSN: 0277-6715
• DOI: 10.1002/(sici)1097-0258(19990915/30)18:17/18<2517::aid-sim273>3.0.co;2-f

✦ Synopsis

The likelihood function for the bivariate survivor function F, under independent censorship, is maximized to obtain a non-parametric maximum likelihood estimator F K . F K may or may not be unique depending on the con"guration of singly-and doubly-censored pairs. The likelihood function can be maximized by placing all mass on the grid formed by the uncensored failure times, or half lines beyond the failure time grid, or in the upper right quadrant beyond the grid. By accumulating the mass along lines (or regions) where the likelihood is #at, one obtains a partially maximized likelihood as a function of parameters that can be uniquely estimated. The score equations corresponding to these point mass parameters are derived, using a Lagrange multiplier technique to ensure unit total mass, and a modi"ed Newton procedure is used to calculate the parameter estimates in some limited simulation studies. Some considerations for the further development of non-parametric bivariate survivor function estimators are brie#y described.