JointCSsurv

JointCSsurv (which stands for Joint model for Cluster Size and survival outcome) is a package that performs semiparametric estimation and inference for clustered interval-censored data with informative cluster size using the method proposed by Lee et al. (2022) <DOI: 10.1111/biom.13795>.

JointCSsurv relies on the R-packages splines2, numDeriv, statmod, which are hosted on CRAN.

How to import the Functions

install.packages("devtools")
library(devtools)
source_url("https://github.com/lcyjames/JointCSsurv/blob/main/JointCSsurv.R?raw=TRUE")

Usage

The package contains 2 functions:

Functions	Description
JointCSsurvSIM	Generate a data set according to the simulation study in Lee et al. (2022)
JointCSsurvEST	Perform the semiparametric estimation methods of Lee et al. (2022)

JointCSsurvSIM

JointCSsurvSIM(seed = NA, n, m, beta, alpha, kappa, sigma)

This function generates a data set according to the model under scenario I of the simulation study in Lee et al. (2022) that takes the arguments:

• n is the sample size
• m is the maximum cluster size in the binomial distribution
• beta is the coefficient in the proportional hazards model
• alpha is the coefficients in the binomial model
• kappa is the coefficient of the random effect
• sigma is the standard deviation of the random effect

Example:

Data <- JointCSsurvSIM(seed = 1234, n = 50, m = 10, beta = 1, alpha = c(1,log(2)), kappa = -0.5, sigma = 1)
head(Data)

#   id cs       Lij      Rij DL DI           X          Z
# 1  1  3 1.5548184 2.194611  0  1  0.08005964 -1.2070657
# 2  1  3        NA 4.000000  0  0 -0.63140930 -1.2070657
# 3  1  3 2.3650486 3.344980  0  1 -1.51328812 -1.2070657
# 4  2  8 0.4422604 1.384112  0  1  1.84246363  0.3592891
# 5  2  8 1.7613718 2.400782  0  1  1.11236284  0.3592891
# 6  2  8 1.7778747 2.428052  0  1  0.03266396  0.3592891

This data structure is as follows:

• id is the sample identifier
• cs is the size within a specific cluster
• Lij is the left endpoint of an observed interval, which takes the value NA for right-censored observations
• Rij is the right endpoint of an observed interval, which takes the value NA for left-censored observations
• DL is the left censoring indicator
• DI is the interval censoring indicator
• X is a covariate in the proportional hazards model, which can have multiple columns
• Z is a covariate in the binomial model without an intercept, which can have multiple columns

JointCSsurvEST

JointCSsurvEST(data, K = 7, P, Q, deg = 3, max.m, M = 20, tolerance = 10^{-3}, 
               gam_0 = NA, beta_0 = NA, alpha_0 = NA, kappa_0 = NA, sigma_0 = NA, TRACE = FALSE)

This function performs the semiparametric estimation methods of Lee et al. (2022). The details of the arguments are as follows:

• data is a data.frame object shown in the above, with columns id, cs, Lij, Rij, DL,DI,X[1],...,X[P],Z[1],...,Z[Q-1]
• K is the dimension of parameter gamma; the order of the I-splines equal to (K-deg+1); K must be greater than or equal to deg
• P is the dimension of covariate X in the proportional hazards model
• Q is the dimension of covariate Z (without an intercept) plus 1 in the binomial model
• deg is the degree of polynomial used in the I-splines, set to 3 by default
• max.m is the maximum cluster size in the binomial distribution
• M is the number of nodes used in adaptive Gauss-Hermite quadrature, set to 20 by default
• tolerance is the stopping criterion for the EM algorithm, set to 10^{-3} by default
• gam_0 is a vector of positive constants of size K for the initial values of gamma, set to be rep(2,K) by default (gam_0=NA)
• beta_0 is a vector of constants of size P for the initial values of parameter beta, set to be rep(0,P) by default (beta_0=NA)
• alpha_0 is a vector of constants of size Q for the initial values of parameter alpha, set to be rep(0,Q) by default (alpha_0=NA)
• kappa_0 is a constant for the initial value of parameter kappa, set to be 0 by default (kappa_0=NA)
• sigma_0 is a constant for the initial value of parameter sigma, set to be 2 by default (sigma_0=NA)
• TRACE is an option for tracking the converging path of the parameter estimation, set to be FALSE by default

Example:

Data<-JointCSsurvSIM(seed = 1234, n = 50, m = 10, beta = 1, alpha = c(1,log(2)), kappa = -0.5, sigma= 1)
Result <-JointCSsurvEST(data = Data, K = 7, P = 1, Q = 2, deg = 3, max.m = 10, tolerance = 10^{-3}, M = 20, TRACE = FALSE)
Result

# $loglik
# [1] -943.2061
# 
# $gam.hat
# [1] 0.1006968 0.0913659 0.4115768 0.5069621 0.8006600 0.3812705 0.5546317
# 
# $alpha.hat
# [1] 1.09652 0.53590
# 
# $kappa.hat
# [1] -0.5807313
# 
# $beta.hat
# [1] 0.901442
# 
# $sigma.hat
# [1] 0.8442931
# 
# $alpha.hat.se
# [1] 0.1303666 0.1338147
# 
# $kappa.hat.se
# [1] 0.173564
# 
# $beta.hat.se
# [1] 0.07883315
# 
# $sigma.hat.se
# [1] 0.1251456

Contact

Lee Chun Yin, James <james-chun-yin.lee@polyu.edu.hk>

Reference

Lee, C. Y., Wong, K. Y., Lam, K. F., and Bandyopadhyay, D. (2022). A semiparametric joint model for cluster size and subunit-specific interval-censored outcomes. Biometrics [online], DOI: 10.1111/biom.13795.