The GMLE based on the Masked Mixed Case Interval-Censored Competing Risks Data.
Abstract
When estimating the survival time T of a series
system consisted of J components, one likes to know the survival
time T with each component C, which means the sub-distribution for
each component. It is frequent that T is interval-censored and C is
masked, which is called interval-censored masked competing
risks(ICMCR) model. In general, there is no explicit solution for
the GMLE from the ICMCR data. We take the self-consistency(SC)
algorithm to find the numerical solution. To apply the SC algorithm
to our GMLE, we develop an algorithm how to find the maximal
intersections(MIs) in the reduction step of this procedure, then use
self-consistency algorithm to obtain the simulation results to
support our theorem about the consistency of the GMLE for each
sub-distribution. Also we provide the empirical convergent rate for
the GMLEs based on the simulated data, suggesting the possible
theoretical convergent rate would be $O_P(n^{1\over 3})$ or
$O_P(n\log n)^{1/3}$. Finally we give the data analysis for a real
ICMCR data set.
