LOESS smoothed density estimates for multivariate survival data subject to censoring and masking

Abstract

Actuaries often encounter censored and masked survival data when constructing multiple-decrement tables. In this paper, we propose estimators for the cause-specific failure time density using LOESS smoothing techniques that are employed in the presence of left-censored data, while still allowing for right-censored and exact observations, as well as masked causes of failure. The smoothing mechanism is incorporated as part of an expectation-maximisation algorithm. The proposed models are applied to a bivariate African sleeping sickness data set.

Nonparametric modeling of multiple decrements subject to dependent censoring and masking

“…Partial masking can be introduced into the algorithm. For details, consult Adamic and Guse (2016). In terms of self-consistency, Adamic (2010) outlines a proof that the SC-CR Algorithms (for both the partially masked and completely masked cases) produce self-consistent estimators of the CIF's for each failure mode.…”

“…As opined in Hudgens et al (2001), estimators of this type will have the unwelcome property that the resulting estimators of the survival distribution will be undefined over a potentially large set of regions. Indeed, the problem is even more acute in the multiple-decrement environment: the SC-CR Algorithms of Adamic (2010) and Adamic and Guse (2016) can be seen to converge only over a class of intervals that were dubbed cause-specific innermost intervals. To remedy this problem, we have chosen to generalize a univariate kernel density estimator found in Braun et al (2005) that was used to fill in the gaps between the univariate innermost intervals that were created by invoking the self-consistent EM algorithm of Turnbull (1976).…”

“…Jewell et al (2003) and Groeneboom et al (2008) follow this trajectory with similar studies of nonparametric maximum likelihood estimators for current status data. More recently, Adamic (2010), Adamic et al (2010), and Adamic and Guse (2016) developed generalizations of Turnbull's (1974Turnbull's ( , 1976 classical univariate algorithms for modeling competing risks. These models, based on Turnbull's self-consistent algorithm, can be shown to be species of EM algorithms.…”