A comparison of time dependent Cox regression, pooled logistic regression and cross sectional pooling with simulations and an application to the Framingham Heart Study.
Typical survival studies follow individuals to an event and measure explanatory variables for that event, sometimes repeatedly over the course of follow up. The Cox regression model has been used widely in the analyses of time to diagnosis or death from disease. The associations between the survival outcome and time dependent measures may be biased unless they are modeled appropriately.



In this paper we explore the Time Dependent Cox Regression Model (TDCM), which quantifies the effect of repeated measures of covariates in the analysis of time to event data. This model is commonly used in biomedical research but sometimes does not explicitly adjust for the times at which time dependent explanatory variables are measured. This approach can yield different estimates of association compared to a model that adjusts for these times. In order to address the question of how different these estimates are from a statistical perspective, we compare the TDCM to Pooled Logistic Regression (PLR) and Cross Sectional Pooling (CSP), considering models that adjust and do not adjust for time in PLR and CSP.



In a series of simulations we found that time adjusted CSP provided identical results to the TDCM while the PLR showed larger parameter estimates compared to the time adjusted CSP and the TDCM in scenarios with high event rates. We also observed upwardly biased estimates in the unadjusted CSP and unadjusted PLR methods. The time adjusted PLR had a positive bias in the time dependent Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect, a subject level covariate, when compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered.



We conclude that survival analyses that explicitly account in the statistical model for the times at which time dependent covariates are measured provide more reliable estimates compared to unadjusted analyses. We present results from the Framingham Heart Study in which lipid measurements and myocardial infarction data events were collected over a period of 26 years.
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA. ngwaj@bu.edu.|Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe St, Baltimore, MD, 21205, USA. ngwaj@bu.edu.
Julius S
JS
Ngwa
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA.
Howard J
HJ
Cabral
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA.
Debbie M
DM
Cheng
Department of Biostatistics and Bioinformatics, Duke University, School of Medicine, 2400 Pratt St, 7021 North Pavilion, Durham, NC, 27705, USA.
Michael J
MJ
Pencina
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA.
David R
DR
Gagnon
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA.
Michael P
MP
LaValley
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA. adrienne@bu.edu.|National Heart, Lung, and Blood Institute's Framingham Heart Study, Framingham, MA, 01702, USA. adrienne@bu.edu.
L Adrienne
LA
Cupples
D015415:Biomarkers / Q000097:blood; D003430:Cross-Sectional Studies; D005260:Female; D006331:Heart Diseases / Q000097:blood / Q000401:mortality*; D006801:Humans; D016015:Logistic Models; D008137:Longitudinal Studies; D008297:Male; D016016:Proportional Hazards Models; D012307:Risk Factors; D016019:Survival Analysis; D014280:Triglycerides / Q000097:blood
D015415:Biomarkers; D014280:Triglycerides
Cross sectional pooling (CSP); Longitudinal and survival data; Pooled logistic regression (PLR); Time dependent covariate model (TDCM)