Shared parameter models for joint analysis of longitudinal and survival data with left truncation due to delayed entry – Applications to cystic fibrosis

Abstract

Many longitudinal studies observe time to occurrence of a clinical event such as death, while also collecting serial measurements of one or more biomarkers that are predictive of the event, or are surrogate outcomes of interest. Joint modeling can be used to examine the relationship between the biomarker and the event, and also as a way of adjusting analyses of the biomarker for non-ignorable dropout. In settings such as registry studies, an additional complexity is caused when follow-up of subjects is delayed, referred to as left-truncation of follow-up in the survival analysis setting. If not adjusted for, this can cause bias in estimation of parameters of the survival distribution for the clinical event and in parameters of the longitudinal outcome such as the profile or rate of change over time because subjects may die or have the clinical event before follow-up starts. This paper illustrates how a broad class of shared parameter models can be used to jointly model a time to event outcome along with a longitudinal marker using available nonlinear mixed modeling software, when follow-up times are left truncated. Methods are applied to jointly model survival and decline in lung function in cystic fibrosis patients.

Modelling of viral load dynamics and CD4 cell count progression in an antiretroviral naive cohort: using a joint linear mixed and multistate Markov model

“…There was a total of 8760 follow-up visits recorded from 219 HIV infected black women with a median age of 25 years (Interquartile range, IQR, [22][23][24][25][26][27][28][29][30]. Of these patients, 9.2% of them were co-infected with TB.…”

“…The goals of joint modelling are to improve inference for the time to transition between multistate events, whilst taking into account the endogenous nature of a biomarker [21]. It also examines the association between the two correlated outcomes [22]. This will lead to an improvement in estimation for a longitudinal biomarker response variable, subject to an informative dropout mechanism that is not of direct interest [23] and will improve inferences as compared to the separate analysis of the two response variables [24].…”

Flexible link functions in a joint hierarchical Gaussian process model

“…Focusing on PE recurrence is important because prior literature suggests that some patients may not be able to recover baseline levels prior to PE onset (Sanders et al., 2010). Other applications specific to joint models applied to CF have focused on characterizing the association between longitudinal and risk of death (Schluchter and Piccorelli, 2019).…”

Explaining the Sex Effect on Survival in Cystic Fibrosis: a Joint Modeling Study of UK Registry Data

“…A recent study has illustrated how left truncation can lead to biased estimates in the context of joint models. 30 We aimed to limit the impact of left truncation by including the birth year as a covariate in the longitudinal and survival submodels. The effect of birth year here is driven by both cohort effects and left truncation.…”