A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia

Abstract

We consider the problem of estimating the intensity functions for a continuous time 'illness-death' model with intermittently observed data. In such a case, it may happen that a subject becomes diseased between two visits and dies without being observed. Consequently, there is an uncertainty about the precise number of transitions. Estimating the intensity of transition from health to illness by survival analysis (treating death as censoring) is biased downwards. Furthermore, the dates of transitions between states are not known exactly. We propose to estimate the intensity functions by maximizing a penalized likelihood. The method yields smooth estimates without parametric assumptions. This is illustrated using data from a large cohort study on cerebral ageing. The age-specific incidence of dementia is estimated using an illness-death approach and a survival approach.

Orthostatic Hypotension and Risk of Incident Dementia

“…23 Therefore, it incorporates the different transition states applicable to this study. 24 The first transition (baseline to dementia) is adjusted for the center, using only univariate analysis, and for the adjustment variables from model 2 of the principal multivariate analysis. The second transition (baseline to death) is adjusted in univariate analysis for sex and center.…”

Statistical Issues in Modeling Chronic Disease in Cohort Studies

“…Undertaking such an analysis requires careful thought about how best to formulate models, including how to define states, which time scale to adopt, how to formulate the dependence on covariates, etc. Fitting semiparametric models is particularly challenging with interval-censored data but convenient flexible alternatives include methods based on piecewiseconstant baseline intensities; Joly et al (2002) develop intensity-based methods based on splines. Heterogeneity poses another modeling challenge and when random effects models are adopted care must be taken to ensure inferences about heterogeneity are not unduly influenced by misspecification of the model conditional on the random effects.…”

Sieve estimation in a Markov illness-death process under dual censoring

“…We express these and other assumptions throughout this paper more precisely in Appendix A of the supplementary material, but essentially this means U hj must be dense in (σ, τ ) as n → ∞. Such a requirement is stronger than the ones imposed by Joly et al (2002) and Frydman and Szarek (2009), which allow for unobservable terminal event times with negative progression status: U 02,n = ∅. A consequence of this is that the support for the distribution of T 02 is not apparent from the available data, so imposing at least a weakly parametric model for Λ 02 is needed to achieve consistency.…”

“…Bebchuk and Betensky (2001) combine local likelihood and multiple imputation to estimate transition intensities under progression times right-censored before death. Joly et al (2002) propose spline-based penalized likelihood for the (Cox, 1972) proportional hazards model for an interval-censored variant of this observation scheme. Jackson (2011) considers a piecewise exponential analog by way of time-dependent covariates.…”