groupedSurvFam {groupedSurv}

Compute the Efficient Score Statistic for the Frailty Model

Description

A method to compute the efficient score statistic for a frailty model, accounting for family structure of related individuals (e.g., trios). The input data is assumed to be organized such that records for each family occur consecutively, and that records for offspring precede those for parents. The variance matrix for the random effects is assumed to be of the form var*K, where K is a matrix of kinship coefficients between family members. The following groupings are permitted: (Individual), (Offspring, Offspring), (Offspring, Parent), (Offspring, Parent, Parent), and (Offspring, Offspring, Parent, Parent). Other family structures have not been implemented.

Usage

  groupedSurvFam(x, fam_group, fam_role, alpha, var, gtime, delta, beta=0, nCores=1)  	

Arguments

x

Vector or matrix of numeric variables of interest for each sample.

fam_group

Vector of family IDs for each sample.

fam_role

Vector of indicators for the role within a family of each sample, i.e., {"Offspring","Mother","Father"}, or {"o","m","f"}.

alpha

Vector of baseline survival rates for each time interval.

var

Scalar for frailty variance.

gtime

Vector of observed survival times for each sample.

delta

Vector of event indicators for each sample: 1 indicates observed event, 0 indicates censored.

beta

Scalar for the fixed effect size. Default is 0.

nCores

Integer representing the number of cores to be used for multi-threaded computation. Default is 1.

Value

Matrix of contributions of each family to the efficient score statistics of each variable of interest. Rows correspond to families, and columns correspond to the variables of interest.

Examples

# Generate dummy data
set.seed(111)
n <- 24

# effect size
beta <- 0.3

# covariate parameters
theta <- c(0.2, 0.2)

# variable of interest
MAF <- 0.05
x <- matrix(rbinom(n, 2, MAF), ncol = 1)

# covariate data (centered at 0)
z1 <- rnorm(n)
z2 <- rbinom(n, 1, 0.5) - 0.5
Z  <- matrix(cbind(z1, z2), ncol = 2)

# continuous survival time
lam0 <- 1
cmax <- 3
lami <- lam0 * exp(x*beta + Z[,1]*theta[1]+Z[,2]*theta[2])
stime <- rexp(n, lami)
ctime <- runif(n, 0, cmax)
delta <- stime < ctime
otime <- pmin(stime, ctime)

# number of observation times
ntps <- 5

# number of intervals
r <- ntps + 1

# last observation time
maxbreakq <- 0.85
maxbreak <- qexp(maxbreakq, lam0)

# grouped failure times
breaks <- (1:ntps) * (maxbreak/ntps)
gtime <- findInterval(otime, breaks) + 1
delta[gtime == r] <- FALSE
dctime <- findInterval(ctime, breaks) + 1
delta[gtime == dctime] <- FALSE
delta <- as.numeric(delta)

# family-specific information
m <- n/3
fam_role <- rep(c("o","f","m"),m)
fam_group <- as.character(rep(1:m,rep(3,m)))

# nuisance parameters
#alpha <- thetaEst(Z, gtime,delta)$alpha
#var <- 0.2

# compute efficient score statistics
#res   <- groupedSurvFam(x, fam_group, fam_role, alpha, var, gtime, delta) 
#res