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various other sources. When mutation status is missing, the available data take the form of censored mixture data. Recently, various methods have been proposed for risk estimation using such data, but none is efficient for estimating a nonparametric distribution. We propose a fully efficient sieve maximum likelihood estimation method, in which we estimate the logarithm of the hazard ratio between genetic mutation groups using B-splines, while applying nonparametric maximum likelihood estimation to the reference baseline hazard function. Our estimator can be calculated via an expectation-maximization algorithm which is much faster than existing methods. We show that our estimator is consistent and semiparametrically efficient and establish its asymptotic distribution. Simulation studies demonstrate the superior performance of the proposed method, which is used to estimate the distribution of the age-at-onset of Parkinson's disease for carriers of mutations in the leucine-rich repeat kinase 2, LRRK2, gene. [ABSTRACT FROM AUTHOR]