Nonparametric estimation for censored mixture data with application to the Cooperative Huntington's Observational Research Trial

We present methods for estimating genotype-specific distributions from genetic epidemiology studies where event times are subject to right censoring, the genotypes are not observed, and the data arise from a mixture of scientifically meaningful subpopulations.   Current methods for analyzing censored mixture data include two types of nonparametric maximum likelihood estimators (NPMLEs) which do not make parametric assumptions on the genotype-specific density functions. Although both NPMLEs are commonly used, we show that one is inefficient and the other inconsistent. To overcome these deficiencies, we propose three classes of consistent nonparametric estimators which do not assume parametric density models and are easy to implement. They are based on the inverse probability weighting (IPW), augmented IPW (AIPW), and nonparametric imputation. The AIPW achieves the efficiency bound without additional modeling assumptions.  Extensive simulation experiments demonstrate satisfactory performance of these estimators even when the data are heavily censored.  We apply these estimators to the Cooperative Huntington's Observational Research Trial, and for the first time in the literature, provide age-specific estimates of the mortality effect from mutation in the Huntington gene using a sample of family members.  Our analyses underscore an elevated risk of death in Huntington gene mutation carriers compared to non-carriers for a wide age range, and suggest that the disease equally affects survival rates in both genders.  The estimated survival rates are useful in genetic counseling as guidelines on interpreting the risk of death associated with a positive test, and in facilitating subjects at risk to decide whether to undergo genetic mutation testings.