A0803
Title: Nonparametric estimation for a log-concave distribution function with interval-censored data
Authors: Brian Ling - Queens University (Canada) [presenting]
Chi Wing Chu - City University of Hong Kong (Hong Kong)
Chaoyu Yuan - Columbia University (United States)
Abstract: The nonparametric maximum likelihood estimation is considered for the underlying event time based on mixed-case interval-censored data under a log-concavity assumption on its distribution function. This generalized framework relaxes the assumptions of a log-concave density function or a concave distribution function considered in the literature. A log-concave distribution function is fulfilled by many common parametric families in survival analysis and also allows for multi-modal and heavy-tailed distributions. The existence, uniqueness, and consistency of the log-concave nonparametric maximum likelihood estimator are established. A computationally efficient procedure that combines an active set algorithm with the iterative convex minorant algorithm is proposed. Numerical studies demonstrate the advantages of incorporating additional shape constraints compared to the unconstrained nonparametric maximum likelihood estimator. The results also show that the method achieves a balance between efficiency and robustness compared to assuming log-concavity in the density. An R package iclogcondist is developed to implement the proposed method.
