Joint Modeling and Analysis of Longitudinal Data with Informative Observation Times

Abstract

In analysis of longitudinal data, it is often assumed that observation times are predetermined and are the same across study subjects. Such an assumption, however, is often violated in practice. As a result, the observation times may be highly irregular. It is well known that if the sampling scheme is correlated with the outcome values, the usual statistical analysis may yield bias. In this article, we propose joint modeling and analysis of longitudinal data with possibly informative observation times via latent variables. A two-step estimation procedure is developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, and that the asymptotic variance can be consistently estimated using the bootstrap method. Simulation studies and a real data analysis demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use.

Multiple outputation for the analysis of longitudinal data subject to irregular observation

“…By contrast, semi‐parametric joint models assume that the visit and outcome processes are conditionally independent given random effects and covariates, that is, that where η i =( η i 1 , η i 2 ) is a vector of random effects. Generally, methods assume that Z i ( t ) is a baseline covariate or else a subset of X i ( t ), for example, the Liang model where W i is a subset of the covariates X i , Z i is a baseline auxiliary covariate and for identifiability, we assume that E ( η i 1 ∣ X i ( t )) = 0 and E ( η i 2 | Z i ) = 1∀ t . This approach is helpful when there are unobserved time‐invariant patient factors that influence both the visit and outcome processes; for example, socioeconomic status might influence both outcomes and the ability to attend follow‐up appointments.…”

Accelerated intensity frailty model for recurrent events data

“…Given α i , C i and X i , the number of observed recurrent events n i for subject i is generated from a poisson distribution with mean ${\alpha }_i{\mathrm{\Lambda }}_{0}false(C_i{e}^{{\beta }_0^{\prime }{\mathbf{X}}_i}false)$. Following similar arguments given inLiang et al (2009), conditional on ( C i , X i , n i ), the recurrent event times 0 < T i 1 < ⋯ < T in i < C i of subject i are obtained as the order statistics of a set of i.i.d random variables with the joint density function $$pfalse(t_{i1},\cdots t_{i{n}_i}|C_i,{\mathbf{X}}_i,n_{i}false)=n_i!\prod _{j=1}^{n_i}\frac{{\lambda }_{0}false(t_{ij}{e}^{{\beta }_0^{\prime }{\mathbf{X}}_i}false)e^{{\beta }_0^{\prime }{\mathbf{X}}_i}}{{\mathrm{\Lambda }}_{0}false(C_i{e}^{{\beta }_0^{\prime }{\mathbf{X}}_i}false)}.$$…”

Dynamic optimal strategy for monitoring disease recurrence

“…In this two-stage approach, the first step addresses the question how to distinguish groups of patients with distinct patterns of longitudinal biomarker measurements and patient and disease characteristics, and the second step addresses the question how monitoring schedules would differ across classes of patients. Two-stage estimation has been used in the analysis of correlated survival data (for example, [26], [27], [28]), and has also been used in the latent class joint modeling literature (for example, [29], [30], [31], [32], [33]). As pointed out by Putter et al (2008) ([31]) for a given number of classes, the two-stage procedure guarantees consistent estimates in both stages.…”