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Abstract:
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This research aims to solve constrained nonparametric maximum likelihood estimator (NPMLE) of survival function for interval censored data under distributional ordering. For right censored data, there have been literatures on constrained NPMLE of survival function under distributional orderings. For example, Dykstra (1982) obtained NPMLE of stochastically ordered survival functions for two populations. Feltz and Dykstra (1985) developed an iterative algorithm to compute NPMLE of stochastically ordered survival functions for several populations. Lim, Kim, and Wang (2009) adopted geometric programming to solve NPMLE of several survival functions. However, for interval censored data, the constrained NPMLE of stochastically ordered survival functions was rarely studied. In this study, Turnbull (1976) type of iterative algorithm and Iterative Convex Minorant algorithm are considered to compute constrained NPMLE for interval-censored survival data under stochastic ordering. The obtained constrained NPMLE will be utilized to test the stochastic ordering. Comparisons will be made through real data and simulated data. In addition, uniform stochastic ordering will also be considered.
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