scholarly journals 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

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Nobuhle N. Mchunu ◽  
Henry G. 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.

scholarly journals 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

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

scholarly journals Joint longitudinal and time-to-event models for multilevel hierarchical data

2018 ◽  
Vol 28 (12) ◽  
pp. 3502-3515 ◽  
Author(s):  
Samuel L Brilleman ◽  
Michael J Crowther ◽  
Margarita Moreno-Betancur ◽  
Jacqueline Buros Novik ◽  
James Dunyak ◽  
...  
Keyword(s):  
Tumor Burden ◽  
Repeated Measurements ◽  
Patient Specific ◽  
Complex Data ◽  
Event Data ◽  
Time To Event ◽  
Joint Modelling ◽  
Risk Of Death ◽  
Patient Level ◽  
Time To Event Data

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation.

scholarly journals ODACH: A One-shot Distributed Algorithm for Cox model with Heterogeneous Multi-center Data

2021 ◽  
Author(s):  
Chongliang Luo ◽  
Rui Duan ◽  
Yong Chen
Keyword(s):  
Likelihood Function ◽  
Cox Model ◽  
Meta Analysis ◽  
Event Data ◽  
Time To Event ◽  
Hazard Functions ◽  
Patient Level ◽  
Time To Event Data ◽  
Level Data ◽  
Center Time

Objective: We developed and evaluated a privacy-preserving One-shot Distributed Algorithm for Cox model to analyze multi-center time-to-event data without sharing patient-level information across sites, while accounting for heterogeneity across sites by allowing site-specific baseline hazard functions and feature distributions. Materials and Methods: We constructed a surrogate likelihood function to approximate the Cox log partial likelihood function which is stratified by site, using patient-level data from a single site and aggregated information from other sites. The ODAC estimator was obtained by maximizing the surrogate likelihood function. We evaluated and compare the performance of ODACH with meta-analysis by extensive numerical studies. Results: The simulation study showed that ODACH provided estimates close to the pooled estimator, which is obtained by directly analyzing patient-level data from all sites via a stratified Cox model. The relative bias was <1% across all scenarios. As a comparison, the meta-analysis estimator, which was obtained by the inverse variance weighted average of the site-specific estimates, had substantial bias when the event rate is <5%, with the relative bias reaching 12% when the event rate is 1%. Conclusions: ODACH is a privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data, which allows the baseline hazard functions as well as the distribution of covariate variables to vary across sites. It provides estimates that is close to the pooled estimator and substantially outperforms the meta-analysis estimator when the event is rare. It is thus extremely suitable for studying rare events with heterogeneous baseline hazards across sites in a distributed manner.

scholarly journals Proposals on Kaplan–Meier plots in medical research and a survey of stakeholder views: KMunicate

BMJ Open ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. e030215 ◽  
Author(s):  
Tim P Morris ◽  
Christopher I Jarvis ◽  
William Cragg ◽  
Patrick P J Phillips ◽  
Babak Choodari-Oskooei ◽  
...  
Keyword(s):  
Outcome Measures ◽  
Event Data ◽  
Time To Event ◽  
Web Based ◽  
Time To Event Data ◽  
Kaplan Meier ◽  
Starting Point ◽  
Wide Range ◽  
International Participation ◽  
Over Time

ObjectivesTo examine reactions to the proposed improvements to standard Kaplan–Meier plots, the standard way to present time-to-event data, and to understand which (if any) facilitated better depiction of (1) the state of patients over time, and (2) uncertainty over time in the estimates of survival.DesignA survey of stakeholders’ opinions on the proposals.SettingA web-based survey, open to international participation, for those with an interest in visualisation of time-to-event data.Participants1174 people participated in the survey over a 6-week period. Participation was global (although primarily Europe and North America) and represented a wide range of researchers (primarily statisticians and clinicians).Main outcome measuresTwo outcome measures were of principal importance: (1) participants’ opinions of each proposal compared with a ‘standard’ Kaplan–Meier plot; and (2) participants’ overall ranking of the proposals (including the standard).ResultsMost proposals were more popular than the standard Kaplan–Meier plot. The most popular proposals in the two categories, respectively, were an extended table beneath the plot depicting the numbers at risk, censored and having experienced an event at periodic timepoints, and CIs around each Kaplan–Meier curve.ConclusionsThis study produced a high response number, reflecting the importance of graphics for time-to-event data. Those producing and publishing Kaplan–Meier plots—both authors and journals—should, as a starting point, consider using the combination of the two favoured proposals.

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