PROFILE MM ALGORITHMS for GAMMA FRAILTY MODELS

• Activity Number: 486 - Computing Kaleidoscope
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:12 AM
• Sponsor: Section on Statistical Computing
• Author(s): Xifen Huang* and jinfeng Xu
• Companies: University of Hong Kong and The University of Hong Kong
• Keywords: MM algorithm; Nonparametric maximum likelihood; Survival data

Abstract

Gamma frailty survival models have been extensively used for the analysis of multivariate failure time data such as clustered failure time data and recurrent event data. Estimation and inference procedures in these models often center on the nonparametric maximum likelihood method and its numerical implementation via the EM algorithm. Despite its popularity and well celebrated success in dealing with incomplete data problems, the EM algorithm uses Newton's method and involves matrix inversion and hence may not fare well in high-dimensional situations. To address this problem, we propose a class of profile MM algorithms with good convergence properties. As a key step in constructing minorizing functions, the high-dimensional objective function is decomposed into a sum of separable low-dimensional functions. This allows the algorithm to bypass the difficulty of inverting large matrix and facilitates its pertinent use in high-dimensional problems. Simulation studies show that the proposed algorithms perform well in various situations and converge reliably with practical sample sizes. The method is illustrated using data from a colorectal cancer study.