coxmeg: Fit a Cox mixed-effects model

In coxmeg: Cox Mixed-Effects Models for Genome-Wide Association Studies

Fit a Cox mixed-effects model

Description

coxmeg returns the estimates of the variance component(s) along with the HRs and p-values of the predictors.

Usage

coxmeg(
  outcome,
  corr,
  type,
  X = NULL,
  eps = 1e-06,
  min_tau = 1e-04,
  max_tau = 5,
  order = 1,
  detap = NULL,
  opt = "bobyqa",
  solver = NULL,
  spd = TRUE,
  verbose = TRUE,
  mc = 100
)

Arguments

outcome	A matrix contains time (first column) and status (second column). The status is a binary variable (1 for events / 0 for censored).
corr	A relatedness matrix or a List object of matrices if there are multiple relatedness matrices. They can be a matrix or a 'dgCMatrix' class in the Matrix package. The matrix (or the sum if there are multiple) must be symmetric positive definite or symmetric positive semidefinite. The order of subjects must be consistent with that in outcome.
type	A string indicating the sparsity structure of the relatedness matrix. Should be 'bd' (block diagonal), 'sparse', or 'dense'. See details.
X	An optional matrix of the preidctors with fixed effects. Can be quantitative or binary values. Categorical variables need to be converted to dummy variables. Each row is a sample, and the predictors are columns.
eps	An optional positive scalar indicating the relative convergence tolerance in the optimization algorithm. Default is 1e-6.
min_tau	An optional positive scalar indicating the lower bound in the optimization algorithm for the variance component tau. Default is 1e-4.
max_tau	An optional positive scalar indicating the upper bound in the optimization algorithm for the variance component tau Default is 5.
order	An optional integer starting from 0. Only valid when dense=FALSE. It specifies the order of approximation used in the inexact newton method. Default is 1.
detap	An optional string indicating whether to use an approximation for log-determinant. Can be 'exact', 'diagonal', 'gkb', or 'slq'. Default is NULL, which lets the function select a method based on 'type' and other information. See details.
opt	An optional logical scalar for the Optimization algorithm for estimating the variance component(s). Can be one of the following values: 'bobyqa', 'Brent', 'NM', or 'L-BFGS-B' (only for >1 variance components). Default is 'bobyqa'.
solver	An optional bianry value that can be either 1 (Cholesky Decomposition using RcppEigen) or 2 (PCG). Default is NULL, which lets the function select a solver. See details.
spd	An optional logical value indicating whether the relatedness matrix is symmetric positive definite. Default is TRUE. See details.
verbose	An optional logical scalar indicating whether to print additional messages. Default is TRUE.
mc	An optional integer scalar specifying the number of Monte Carlo samples used for approximating the log-determinant when detap='gkb' or detap='slq'. Default is 100.

Value

beta: The estimated coefficient for each predictor in X.

HR: The estimated HR for each predictor in X.

sd_beta: The estimated standard error of beta.

p: The p-value.

iter: The number of iterations until convergence.

tau: The estimated variance component.

int_ll: The marginal likelihood (-2*log(lik)) of tau evaluated at the estimate of tau.

rank: The rank of the relatedness matrix.

nsam: Actual sample size.

About type

Specifying the type of the relatedness matrix (whether it is block-diagonal, general sparse, or dense). In the case of multiple relatedness matrices, it refers to the type of the sum of these matrices.

• "bd" - used for a block-diagonal relatedness matrix, or a sparse matrix the inverse of which is also sparse.

• "sparse" - used for a general sparse relatedness matrix the inverse of which is not sparse.

• "dense" - used for a dense relatedness matrix.

About spd

When spd=TRUE, the relatedness matrix is treated as SPD. If the matrix is SPSD or not sure, use spd=FALSE.

About solver

Specifying which method is used to solve the linear system in the optimization algorithm.

• "1" - Cholesky decompositon (RcppEigen:LDLT) is used to solve the linear system.

• "2" - PCG is used to solve the linear system. When type='dense', it is recommended to set solver=2 to have better computational performance.

About detap

Specifying the method to compute the log-determinant for estimating the variance component(s).

• "exact" - the exact log-determinant is computed for estimating the variance component.

• "diagonal" - uses diagonal approximation and is only effective for a sparse relatedness matrix.

• "slq" - uses stochastic lanczos quadrature approximation. It uses the Lanczos algorithm to compute the weights and nodes. When type is 'bd' or 'sparse', it is often faster than 'gkb' and has the same accuracy. When type='dense', it is faster than 'gkb' by around half, but can be inaccurate if the relatedness matrix is (almost) singular.

• "gkb" - uses stochastic lanczos quadrature approximation. It uses the Golub-Kahan bidiagonalization algorithm to compute the weights and nodes. It is robust against an (almost) singular relatedness matrix when type='dense', but it is generally slower than 'slq'.

Examples

library(Matrix)
library(MASS)
library(coxmeg)

## simulate a block-diagonal relatedness matrix
tau_var <- 0.2
n_f <- 100
mat_list <- list()
size <- rep(10,n_f)
offd <- 0.5
for(i in 1:n_f)
{
  mat_list[[i]] <- matrix(offd,size[i],size[i])
  diag(mat_list[[i]]) <- 1
}
sigma <- as.matrix(bdiag(mat_list))
n <- nrow(sigma)

## simulate random effects and outcomes
x <- mvrnorm(1, rep(0,n), tau_var*sigma)
myrates <- exp(x-1)
y <- rexp(n, rate = myrates)
cen <- rexp(n, rate = 0.02 )
ycen <- pmin(y, cen)
outcome <- cbind(ycen,as.numeric(y <= cen))

## fit a Cox mixed-effects model
re = coxmeg(outcome,sigma,type='bd',detap='diagonal',order=1)
re

coxmeg documentation built on Jan. 13, 2023, 5:07 p.m.