A necessary and sufficient condition for justifying non-parametric likelihood with censored data

Qiqing Yu (), Yuting Hsu and Kai Yu

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 8, 995-1011

Abstract: The non-parametric likelihood L(F) for censored data, including univariate or multivariate right-censored, doubly-censored, interval-censored, or masked competing risks data, is proposed by Peto (Appl Stat 22:86–91, 1973 ). It does not involve censoring distributions. In the literature, several noninformative conditions are proposed to justify L(F) so that the GMLE can be consistent (see, for examples, Self and Grossman in Biometrics 42:521–530 1986 , or Oller et al. in Can J Stat 32:315–326, 2004 ). We present the necessary and sufficient (N&S) condition so that $$L(F)$$ L ( F ) is equivalent to the full likelihood under the non-parametric set-up. The statement is false under the parametric set-up. Our condition is slightly different from the noninformative conditions in the literature. We present two applications to our cancer research data that satisfy the N&S condition but has dependent censoring. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Right-censoring; Doubly-censoring; Masked competing risks data; Interval-censorship model; Multivariate censorship models; Primary 62 G05; Secondary 62 G20 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00184-014-0482-z

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