Simultaneous monitoring for regression coefficients and baseline hazard profile in Cox modeling of time-to-event data

Biostatistics ◽  
2020 ◽  
Author(s):  
Yishu Xue ◽  
Jun Yan ◽  
Elizabeth D Schifano
Keyword(s):  
Control Chart ◽  
Hazard Function ◽  
Cox Model ◽  
Regression Coefficients ◽  
Event Data ◽  
Time To Event ◽  
Baseline Hazard ◽  
Baseline Hazard Function ◽  
Time To Event Data ◽  
Profile Control

Summary The Cox model is the most popular tool for analyzing time-to-event data. The nonparametric baseline hazard function can be as important as the regression coefficients in practice, especially when prediction is needed. In the context of stochastic process control, we propose a simultaneous monitoring method that combines a multivariate control chart for the regression coefficients and a profile control chart for the cumulative baseline hazard function that allows for data blocks of possibly different censoring rates and sample sizes. The method can detect changes in either the parametric or the nonparametric part of the Cox model. In simulation studies, the proposed method maintains its size and has substantial power in detecting changes in either part of the Cox model. An application in lymphoma survival analysis in which patients were enrolled by 2-month intervals in the Surveillance, Epidemiology, and End Results program identifies data blocks with structural model changes.

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 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

Simulating Duration Data for the Cox Model

2018 ◽  
Vol 7 (04) ◽  
pp. 921-928 ◽  
Author(s):  
Jeffrey J. Harden ◽  
Jonathan Kropko
Keyword(s):  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Simulation Studies ◽  
Baseline Hazard ◽  
Baseline Hazard Function ◽  
Time Varying Covariates

The Cox proportional hazards model is a popular method for duration analysis that is frequently the subject of simulation studies. However, no standard method exists for simulating durations directly from its data generating process because it does not assume a distributional form for the baseline hazard function. Instead, simulation studies typically rely on parametric survival distributions, which contradicts the primary motivation for employing the Cox model. We propose a method that generates a baseline hazard function at random by fitting a cubic spline to randomly drawn points. Durations drawn from this function match the Cox model’s inherent flexibility and improve the simulation’s generalizability. The method can be extended to include time-varying covariates and non-proportional hazards.

Estimating the Cutoff Points of Time-Dependent Risk Factors by Using Joint Modeling of Longitudinal and Time-to-Event Data: A 14-Year Follow-up Study—Tehran Lipid and Glucose Study

2019 ◽  
Vol 31 (8) ◽  
pp. 728-736
Author(s):  
Nezhat Shakeri ◽  
Fereidoun Azizi
Keyword(s):  
Risk Factors ◽  
Cox Model ◽  
Joint Modeling ◽  
Time Dependent ◽  
Estimation Methods ◽  
Event Data ◽  
Time To Event ◽  
Time To Event Data ◽  
Cutoff Points

Diagnostic accuracy and optimal cutoff points of risk factors is one of the important issues in medical decisions. In order to reassess the cutoff points of markers, longitudinal and time-to-event data of elderly individuals were collected repeatedly through 3 follow-up stages in the Tehran Lipid and Glucose Study. Time-dependent area under the ROC (receiver operating characteristic) curves (AUCs) based on the joint modeling of longitudinal and time-to-event data technique were measured. AUCs were considered to evaluate the discriminative potential of the models. The joint model produced higher AUC values than the Cox model; therefore, accuracy was improved although it is computationally complicated. The results had some differences with the thresholds reported in guidelines due to specificity to the population and/or the means of estimation methods. The estimated cutoff points with regard to sex can be used as a guideline for the Iranian elderly population.

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.

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

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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