A comparison of time dependent Cox regression, pooled logistic regression and cross sectional pooling with simulations and an application to the Framingham Heart Study

Abstract Background: Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods: In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy, and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results: Simulation results demonstrate that the Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. The Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years.Conclusions: Traditional methods for modeling longitudinal and survival data, such as the time dependent covariate method, that use the observed longitudinal data, tend to provide downwardly biased estimates. The two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

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Cross-sectional relations of urinary sodium excretion to cardiac structure and hypertrophyThe Framingham Heart Study

American Journal of Hypertension ◽

10.1016/s0895-7061(04)00869-6 ◽

2004 ◽

Vol 17 (10) ◽

pp. 891-896 ◽

Cited By ~ 1

Author(s):

R DHINGRA ◽

M PENCINA ◽

E BENJAMIN ◽

D LEVY ◽

M LARSON ◽

...

Keyword(s):

Framingham Heart Study ◽

Sodium Excretion ◽

Urinary Sodium Excretion ◽

Urinary Sodium ◽

Cardiac Structure ◽

Cross Sectional ◽

Heart Study

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Revisiting Methods For Modeling Longitudinal and Survival Data: The Framingham Heart Study

10.21203/rs.3.rs-33952/v1 ◽

2020 ◽

Author(s):

Julius S Ngwa ◽

Howard J Cabral ◽

Debbie M Cheng ◽

David R Gagnon ◽

Michael P LaValley ◽

...

Keyword(s):

Maximum Likelihood ◽

Longitudinal Data ◽

Survival Data ◽

Framingham Heart Study ◽

Time Dependent ◽

Time To Event ◽

Longitudinal Measure ◽

Heart Study ◽

Longitudinal And Survival Data ◽

Joint Method

Abstract Background Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results Simulation results demonstrate that Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years. Conclusions Traditional methods for modeling longitudinal and survival data, such as time dependent covariate method, that use the observed longitudinal data, tend to provide downward bias estimates. Two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

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Association Between Sex Hormones and Visual Field Progression in Women With Primary Open Angle Glaucoma: A Cross-Sectional and Prospective Cohort Study

Frontiers in Aging Neuroscience ◽

10.3389/fnagi.2021.756186 ◽

2021 ◽

Vol 13 ◽

Author(s):

Yichao Qiu ◽

Jian Yu ◽

Li Tang ◽

Jun Ren ◽

Mingxi Shao ◽

...

Keyword(s):

Logistic Regression ◽

Cohort Study ◽

Sex Hormones ◽

Cox Regression ◽

Cross Sectional Study ◽

Rank Test ◽

Regression Analyses ◽

Sectional Study ◽

Cross Sectional ◽

The Cross

Purpose: We evaluated the level of sex hormones in female patients with primary open angle glaucoma (POAG) to determine whether they are associated with the onset and/or progression of POAG.Methods: The cross-sectional study enrolled 63 women with POAG and 56 healthy women as normal control subjects. Furthermore, 57 women with POAG were included and followed-up for at least 2 years in the cohort study. All subjects were evaluated for serum concentration of sex hormones [prolactin (PRL), luteinizing hormone (LH), testosterone (TESTO), follicle-stimulating hormone (FSH), progesterone (PROG), and estrogen (E2)] and underwent visual field (VF) examination. In the cross-sectional study, Spearman analysis, linear regression analysis, and logistic regression analysis were performed to assess risk factors for POAG in women. In the cohort study, Cox regression analyses and Kaplan–Meier survival analysis were performed to identify factors associated with VF progression in women with POAG.Results: In the cross-sectional study, the level of E2 was significantly lower in the POAG group than in the normal group (p < 0.05). Multiple logistic regression showed that the decreased level of E2 was a risk factor of POAG (OR = 0.27, 95% CI = 0.09–0.78, p < 0.05), especially in premenopausal subjects. In the cohort study, there were 29 non-progression subjects and 28 progression subjects. Patients in the progression group had significantly lower levels of E2 than those in the no progression group (p < 0.01). The decreased level of E2 at baseline was associated with POAG progression (HR = 0.08, 95% CI = 0.02–0.46, p < 0.05), especially in premenopausal subjects. Patients with POAG and with lower baseline E2 levels had significantly lower VF non-progression rates than patients with higher E2 levels (log-rank test p < 0.001), especially premenopausal subjects (log-rank test p < 0.05). Additionally, logistic regression analyses, Cox regression analyses, and Kaplan–Meier survival analysis showed that PROG, LH, FSH, and TESTO were risk factors of POAG and/or significantly associated with POAG progression.Conclusion: A decreased E2 level is a POAG risk factor and is associated with VF progression in women with POAG, especially in premenopausal subjects. Additionally, other sex hormones (PROG, LH, FSH, and TESTO) might also play a role in POAG pathogenesis.

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Variation in estrogen-related genes and cross-sectional and longitudinal blood pressure in the Framingham Heart Study

Journal of Hypertension ◽

10.1097/01.hjh.0000188728.66183.92 ◽

2005 ◽

Vol 23 (12) ◽

pp. 2193-2200 ◽

Cited By ~ 64

Author(s):

Inga Peter ◽

Amanda M Shearman ◽

Deborah R Zucker ◽

Christopher H Schmid ◽

Serkalem Demissie ◽

...

Keyword(s):

Blood Pressure ◽

Framingham Heart Study ◽

Cross Sectional ◽

Heart Study

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Revisiting methods for modeling longitudinal and survival data: Framingham Heart Study

BMC Medical Research Methodology ◽

10.1186/s12874-021-01207-y ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Julius S. Ngwa ◽

Howard J. Cabral ◽

Debbie M. Cheng ◽

David R. Gagnon ◽

Michael P. LaValley ◽

...

Keyword(s):

Maximum Likelihood ◽

Longitudinal Data ◽

Survival Data ◽

Framingham Heart Study ◽

Time Dependent ◽

Time To Event ◽

Longitudinal Measure ◽

Heart Study ◽

Longitudinal And Survival Data ◽

Joint Method

Abstract Background Statistical methods for modeling longitudinal and time-to-event data has received much attention in medical research and is becoming increasingly useful. In clinical studies, such as cancer and AIDS, longitudinal biomarkers are used to monitor disease progression and to predict survival. These longitudinal measures are often missing at failure times and may be prone to measurement errors. More importantly, time-dependent survival models that include the raw longitudinal measurements may lead to biased results. In previous studies these two types of data are frequently analyzed separately where a mixed effects model is used for the longitudinal data and a survival model is applied to the event outcome. Methods In this paper we compare joint maximum likelihood methods, a two-step approach and a time dependent covariate method that link longitudinal data to survival data with emphasis on using longitudinal measures to predict survival. We apply a Bayesian semi-parametric joint method and maximum likelihood joint method that maximizes the joint likelihood of the time-to-event and longitudinal measures. We also implement the Two-Step approach, which estimates random effects separately, and a classic Time Dependent Covariate Model. We use simulation studies to assess bias, accuracy, and coverage probabilities for the estimates of the link parameter that connects the longitudinal measures to survival times. Results Simulation results demonstrate that the Two-Step approach performed best at estimating the link parameter when variability in the longitudinal measure is low but is somewhat biased downwards when the variability is high. Bayesian semi-parametric and maximum likelihood joint methods yield higher link parameter estimates with low and high variability in the longitudinal measure. The Time Dependent Covariate method resulted in consistent underestimation of the link parameter. We illustrate these methods using data from the Framingham Heart Study in which lipid measurements and Myocardial Infarction data were collected over a period of 26 years. Conclusions Traditional methods for modeling longitudinal and survival data, such as the time dependent covariate method, that use the observed longitudinal data, tend to provide downwardly biased estimates. The two-step approach and joint models provide better estimates, although a comparison of these methods may depend on the underlying residual variance.

Download Full-text