A fast algorithm for the nonparametric maximum likelihood estimate in the cox-gene model

[[abstract]]The Cox model with the gene effect for age at onset was introduced and studied by Li, Thompson and Wijsman (1998) and Li and Thompson (1997). This paper concerns the numerical performance of the nonparametric maximum likelihood estimate of the environmental effects and the genetic effect in this model. Based on the self-consistency equations derived from the score functions, we propose a fast iterative algorithm for the computations of the nonparametric maximum likelihood estimate and its asymptotic variance. Simulation studies conducted using these algorithms indicate that the profile likelihood-based normal approximations for the estimates are valid with reasonable sample sizes, and the bootstrap methods work well also for smaller sample sizes, and are computationally feasible