Composite likelihood for joint analysis of multiple multistate processes via copulas

Abstract

A copula-based model is described which enables joint analysis of multiple progressive multistate processes. Unlike intensity-based or frailty-based approaches to joint modeling, the copula formulation proposed herein ensures that a wide range of marginal multistate processes can be specified and the joint model will retain these marginal features. The copula formulation also facilitates a variety of approaches to estimation and inference including composite likelihood and two-stage estimation procedures. We consider processes with Markov margins in detail, which are often suitable when chronic diseases are progressive in nature. We give special attention to the setting in which individuals are examined intermittently and transition times are consequently interval-censored. Simulation studies give empirical insight into the different methods of analysis and an application involving progression in joint damage in psoriatic arthritis provides further illustration.

Marginal clustered multistate models for longitudinal progressive processes with informative cluster size

“…However, we recognize that in more general situations where the true conditional parameters differ, such that 𝜆 12,0 ≠ 𝜆 23,0 and 𝛽 12 ≠ 𝛽 23 , obtaining marginal inferences for clustered multistate processes becomes challenging due to the influence of historical processes on the marginal transition hazards. To address this issue, Diao and Cook [20] proposed a copula-based model TA B L E 2 Simulation results of marginal approaches when there exists frailties but no ICS in the generated data (𝜏 = 1, 𝜂 u = 0). that ensures correct specification of marginal multistate processes.…”

“…However, we recognize that in more general situations where the true conditional parameters differ, such that $$$ {\lambda}_{12,0}\ne {\lambda}_{23,0} $$$ and $$$ {\beta}_{12}\ne {\beta}_{23} $$$, obtaining marginal inferences for clustered multistate processes becomes challenging due to the influence of historical processes on the marginal transition hazards. To address this issue, Diao and Cook [20] proposed a copula‐based model that ensures correct specification of marginal multistate processes. They employed composite likelihood and a two‐stage estimation approach to estimate the parameters and derive appropriate inferences.…”

Modeling multiple correlated end‐organ disease trajectories: A tutorial for multistate and joint models with applications in diabetes complications

“…Random effects have also been used to jointly model separate marginal multistate processes 32 . Copula models can be used to investigate marginal features of high‐dimensional multivariate processes 46 . In our tutorial, we did not explore the effects of time and used time‐homogeneous Markov models; in multistate models under intermittent observation, piecewise‐constant intensity functions can be used to investigate how transition rates vary with time 4 .…”

“…32 Copula models can be used to investigate marginal features of high-dimensional multivariate processes. 46 In our tutorial, we did not explore the effects of time and used time-homogeneous Markov models; in multistate models under intermittent observation, piecewise-constant intensity functions can be used to investigate how transition rates vary with time. 4 We did not fully-explore the incorporation of covariates in the eight-state multistate model; we note that like the standard Cox proportional hazards model, fixed baseline covariates and time-dependent exogenous covariates are straightforward to incorporate in proportional intensities models.…”

Clustered Multistate Models with Observation Level Random Effects, Mover–Stayer Effects and Dynamic Covariates: Modelling Transition Intensities and Sojourn Times in a Study of Psoriatic Arthritis

“…Such observations are less likely to result in unobserved heterogeneity being time-invariant or time-varying but deterministic (which is enforced by patient-level random effects). We also note that along with generalised estimating equations, copulas (Diao and Cook, 2014) and expanded state space models (Tom and Farewell, 2011) have been proposed to handle clustering. Although there are considerable advantages to such models, they are particularly difficult to formulate and implement when more than two intermittently observed nonprogressive multi-state processes are of interest.…”