linear mixed effect Cox model with clinical covariates and gene expressions levels (coxlmm) is a R procedure to access the prognosis of different cancers and estimate the partition of clinical variance and genetic variance.
Specifically, denote the observed survival time by ti and the true survival time by Ti with di indicating the censored status, Xi is a p-dimensional vector for available clinical covariates (e.g. disease stage, age and gender) for individual i, and Gi be an m-dimensional vector for a set of gene expression levels for individual. To link the survival risk with the clinical information and all the genetic information, we employ Cox model within the framework of linear mixed models:
where is the variance for gene expressions
The coxlmm model is fitted with the R coxme (version 2.2-10) package (https://CRAN.R-project.org/package=coxme), in which the Laplace approximation method is implemented based on the second order Taylor series. However, fitting coxlmm with coxme directly is time-consuming due to the high-dimensional problem. Instead, we fit coxlmm in an efficient alternative way. Specifically, note that the genetic component
can be re-expressed as
Based on the above relationship, we construct an equivalent Cox mixed model
where Zi is the ith row vector of K1/2 with K = GGT, which is often referred to as the genetic relationship matrix (GRM) in genetic prediction; δ is an n-dimensional vector for the effect sizes of Zi.
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R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2013 (https://www.R-project.org/).
I am very grateful to any questions, comments, or bugs reports; and please contact Xinghao Yu via xinghaoyu@stu.xzhmu.edu.cn or Ping Zeng via zpstat@xzhmu.edu.cn.