P.K. Sen Memorial Session

Due to recent use of digital health technologies (DHT) for remote data acquisition, the development of novel statistical methods for analyzing intensive longitudinal data is now very much needed. In statistical literature, joint modeling survival data and longitudinal covariates has been considered and studied, but almost all existing methods rely on parametric or semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are not justifiable or difficult to verify in practice. The kernel method based procedures and the slower convergence rate of the resulting estimator rely on choices of kernel function and bandwidth, which have not been studied. Without these parametric/semiparametric assumptions and without the use of kernel method, this article proposes a generalized latent proportional hazards (GLPH) model for right censored survival time and longitudinal covariates, which treats the longitudinal covariate process as a stochastic process with an unknown hidden random variable, i.e., the latent variable with unknown distribution, and takes into account of within-subject historic change patterns for the longitudinal covariates. The asymptotic properties of empirical likelihood MLE for the GLPH model are established here for intensive longitudinal covariates, and based on these results, a statistical analysis of a recent and very intensive longitudinal ABCD Study data via DHT is conducted here and produces some very interesting results. Moreover, a novel method for joint modeling survival time and sparse longitudinal covariates is constructed via a smooth version of empirical likelihood MLE for the GLPH model by adding some estimated longitudinal covariates to increase intensity, which gives very good and hugely improved simulation results.

Coauthor: Charles Zhao, University of North Carolina - Chapel Hill, USA

Keywords: Empirical likelihood, latent variable, generalized latent proportional hazards model, intensive longitudinal data, maximum likelihood estimator, right censored data, sparse longitudinal data. 

We examine distributional properties and predictive performance of the estimated maximum agreement linear predictor (MALP), which is the linear predictor maximizing Lin's concordance correlation coefficient (CCC) between the predictor and the predictand. It is compared and contrasted, theoretically and through computer experiments, with the estimated least-squares linear predictor (LSLP), with respect to some performance measures. Finite-sample and asymptotic properties are obtained, and confidence intervals and prediction intervals are also presented. The predictors are illustrated using two real data sets: an eye data set and a body fat data set. The results indicate that the estimated MALP is a viable alternative to the estimated LSLP if one desires a predictor whose predicted values possess higher agreement with the predictand values, as measured by the CCC.