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The X-linked genetic association is overlooked in most of the genetic studies because of the complexity of X-chromosome inactivation process. In fact, the biological process of the gene at the same locus can vary across different subjects. Besides, the skewness of X-chromosome inactivation is inherently subject-specific (even tissue-specific within subjects) and cannot be accurately represented by a population-level parameter. To tackle this issue, a new model is proposed to incorporate the X-linked genetic association into right-censored survival data. The novel model can present that the X-linked genes on different subjects may go through different biological processes via a mixed distribution. Further, a random effect is employed to describe the uncertainty of the biological process for every subject. The proposed method can derive the probability for the escape of X-chromosome inactivation and derive the unbiased estimates of the model parameters. The Legendre-Gauss Quadrature method is used to approximate the integration over the random effect. Finite sample performance of this method is examined via extensive simulation studies. An application is illustrated with the implementation on a cancer genetic study with right-censored survival data.

Random effects two-part models have been applied to longitudinal studies for zero-inflated (or semi-continuous) data, characterized by a large portion of zero values and continuous non-zero (positive) values. Examples include monthly medical costs, daily alcohol drinks, relative abundance of microbiome, etc. With the advance of information technology for data collection and storage, the number of variables available to researchers can be rather large in such studies. To avoid curse of dimensionality and facilitate decision making, it is critically important to select covariates that are truly related to the outcome. However, owing to its intricate nature, there is not yet a satisfactory variable selection method available for such sophisticated models. In this paper, we seek a feasible way of conducting variable selection for random effects two-part models on the basis of the recently proposed "minimum information criterion" (MIC) method. We demonstrate that the MIC formulation leads to a reasonable formulation of sparse estimation, which can be conveniently solved with SAS Proc NLMIXED. The performance of our approach is evaluated through simulation, and an application to a longitudinal alcohol dependence study is provided.