SkewTIOT

Joint modeling of multivariate longitudinal outcomes and informative observation times with multivariate skew-t random effects.

SkewTIOT is an R package implementing a Monte-Carlo ECM (MCECM) estimator for a joint model in which

• a multivariate longitudinal outcome (dimension K) is observed at irregular, subject-specific visit times, and
• those visit times are informative — they follow a recurrent-event Cox intensity whose frailty is the same subject-level random effect that drives the longitudinal mean.

The shared random effect is given a multivariate skew-t distribution, so the model accommodates heavy tails and asymmetry in the latent subject effects. The E-step uses a per-subject Gibbs sampler written in C++ (Rcpp + RcppArmadillo + OpenMP); the M-step updates are in R.

This repository is the companion code for the manuscript "Variance Estimation and Validation for a Joint Multivariate-Longitudinal / Informative-Observation- Time Model with Skew-t Random Effects."

Installation

The package contains compiled C++ and requires a working toolchain (Xcode command-line tools on macOS, build-essential on Linux, Rtools on Windows) plus the R packages listed under Imports in DESCRIPTION.

# install.packages("remotes")
remotes::install_github("dayusun/SkewTIOT")

Or from a local clone:

R CMD INSTALL .

Quick start

A self-contained demo simulates a small data set (200 subjects, two correlated outcomes, informative visit times) and fits the model:

Rscript demo/run_demo.R

It prints the recovered beta, eta, gamma, and skewness Del next to the true values (about a minute single-core). The script also shows, in comments, how to switch to stiot_fnu_est() for profile-likelihood standard errors, z-scores, AIC, and BIC.

Main functions

Function	Purpose
stiot_fnu_est_only()	MCECM point estimation at a fixed degrees-of-freedom nu (fastest).
stiot_fnu_est()	Point estimation plus profile-likelihood standard errors, z-scores, observed log-likelihood, AIC/BIC.
stiot_fnu_cv_loss()	Held-out marginal log-likelihood of a fitted model, for choosing nu by cross-validation.
stiot_est_init()	Warm-start initial values via sn::selm and reReg::reReg.
stiot_tr_est()	Variant that applies a user-supplied transformation to Y before the skew-t likelihood.

Input-shape contract

All estimators expect data grouped contiguously by subject:

• ID — length-all_n vector repeating the subject id per observation.
• Y — all_n × K matrix of longitudinal outcomes.
• X — all_n × p_X covariate matrix for the longitudinal mean. An intercept column is prepended internally when ifintercetp = TRUE (the default); pass ifintercetp = FALSE if X already has one.
• Z — subject-level covariate matrix, one row per unique subject (nrow(Z) == length(unique(ID))), used for the visit-intensity Cox model.
• Time — length-all_n observation times.
• censor — length-n per-subject end of follow-up (defaults to each subject's last Time if NULL).

A fitted object always carries beta, Sige, eta, gamma, lambda, Gam, Del, nu; stiot_fnu_est() adds SE, zres, Covmat, logl_obs, AIC, BIC.

Parallelism

The per-subject E-step parallelizes over subjects. Pass a parallel PSOCK cluster via the paracl argument to reuse it across calls, or leave paracl = NULL (with ifpar = TRUE) to have the estimator create and tear down its own cluster. OpenMP threading inside the C++ Gibbs sampler is controlled by OMP_NUM_THREADS.

License

GPL (>= 2). See DESCRIPTION.