Joint modeling of longitudinal and time-to-event data with missing time-varying covariates in targeted therapy of oncology

Longitudinal and time to event data are frequently encountered in many medical studies. Clinicians are more interested in how longitudinal outcomes influences the time to an event of i nterest. To study the association between longitudinal and time to event data, joint modeling approaches were found to be the most appropriate techniques for such data. The approaches involves the choice of the distribution of the survival times which in most cases authors prefer either exponential or Weibull distribution. However, these distributions have some shortcomings. In this paper, we propose an alternative joint model approach under Bayesian prospective. We assumed that survival times follow a Gompertz distribution. One of the advantages of Gompertz distribution is that its cumulative distribution function has a closed form solution and it accommodates time varying covariates. A Bayesian approach through Gibbs sampling procedure was developed for parameter estimation and inferences. We evaluate the finite samples performance of the joint model through an extensive simulation study and apply the model to a real dataset to determine the association between markers(tumor sizes) and time to death among cancer patients without recurrence. Our analysis suggested that the proposed joint modeling approach perform well in terms of parameter estimations when correlation between random intercepts and slopes is considered.

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Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

Statistical Methods in Medical Research ◽

10.1177/09622802211002868 ◽

2021 ◽

pp. 096228022110028

Author(s):

T Baghfalaki ◽

M Ganjali

Keyword(s):

Linear Model ◽

Joint Modeling ◽

Partially Linear Model ◽

Event Data ◽

Time To Event ◽

Data Set ◽

Partially Linear ◽

Time To Event Data ◽

Count Response ◽

Approximate Bayesian

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

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Joint modelling of longitudinal and time-to-event data: An illustration using CD4 count and mortality in a cohort of patients initiated on antiretroviral therapy

10.21203/rs.2.19995/v1 ◽

2020 ◽

Author(s):

Nobuhle Nokubonga Mchunu ◽

Henry Mwambi ◽

Tarylee Reddy ◽

Nonhlanhla Yende-Zuma ◽

Kogieleum Naidoo

Keyword(s):

Cox Model ◽

Joint Model ◽

Cd4 Count ◽

Time Varying ◽

Event Data ◽

Time To Event ◽

Joint Modelling ◽

Risk Of Death ◽

Time To Event Data ◽

Over Time

Abstract Background: Modelling of longitudinal biomarkers and time-to-event data are important to monitor disease progression. However, these two variables are traditionally analyzed separately or time-varying Cox models are used. The former strategy fails to recognize the shared random-effects from the two processes while the latter assumes that longitudinal biomarkers are exogenous covariates, resulting in inefficient or biased estimates for the time-to-event model. Therefore, we used joint modelling for longitudinal and time-to-event data to assess the effect of longitudinal CD4 count on mortality. Methods: We studied 4014 patients from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) who initiated ART between June 2004 and August 2013. We used proportional hazards regression model to assess the effect of baseline characteristics (excluding CD4 count) on mortality, and linear mixed effect models to evaluate the effect of baseline characteristics on the CD4 count evolution over time. Thereafter, the two analytical approaches were amalgamated to form an advanced joint model for studying the effect of longitudinal CD4 count on mortality. To illustrate the virtues of the joint model, the results from the joint model were compared to those from the time-varying Cox model. Results: Using joint modelling, we found that lower CD4 count over time was associated with a 1.3-fold increase in the risk of death, (HR: 1.34, 95% CI: 1.27-1.42). Whereas, results from the time-varying Cox model showed lower CD4 count over time was associated with a 1.2-fold increase in the risk of death, (HR: 1.17, 95% CI: 1.12-1.23). Conclusions: Joint modelling enabled the assessment of the effect of longitudinal CD4 count on mortality while correcting for shared random effects between longitudinal and time-to-event models. In the era of universal test and treat, the evaluation of CD4 count is still crucial for guiding the initiation and discontinuation of opportunistic infections prophylaxis and assessment of late presenting patients. CD4 count can also be used when immunological failure is suspected as we have shown that it is associated with mortality. Keywords: Time-to-event data; longitudinal data; joint models; CD4 count; mortality; bias

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