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BMC Medical Research Methodology
Published in: BMC Medical Research Methodology 1/2016

Open Access 01-12-2016 | Research article

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

Authors: Julius S. Ngwa, Howard J. Cabral, Debbie M. Cheng, Michael J. Pencina, David R. Gagnon, Michael P. LaValley, L. Adrienne Cupples

Published in: BMC Medical Research Methodology | Issue 1/2016

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Abstract

Background

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.

Methods

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.

Results

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.

Conclusions

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.
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Literature
1.
Fisher LD, Lin DY. Time dependent covariates in the Cox proportional-hazards regression model. Annu Rev Public Health. 1999;20(1):145–57.CrossRefPubMed
2.
Cox DR, & Oakes D. Analysis of survival data (Vol. 21). London: CRC Press; 1984.
3.
Therneau TM, Grambsch PM. Modeling survival data: extending the Cox model. Berlin: Springer Science & Business Media; 2000.
4.
Cox DR. Regression models and life-tables. J R Stat Soc Ser B (Methodological). 1972;187–220.
5.
Cupples LA, D'Agostino RB, Anderson K, Kannel WB. Comparison of baseline and repeated measure covariate techniques in the Framingham Heart Study. Stat Med. 1988;7(1–2):205–18.CrossRefPubMed
6.
D'Agostino RB, Lee ML, Belanger AJ, Cupples LA, Anderson K, Kannel WB. Relation of pooled logistic regression to time dependent Cox regression analysis: The Framingham Heart Study. Stat Med. 1990;9(12):1501–15.CrossRefPubMed
7.
Pepe MS, Cai J. Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates. J Am Stat Assoc. 1993;88(423):811–20.CrossRef
8.
Prentice RL, Gloeckler LA. Regression analysis of grouped survival data with application to breast cancer data. Biometrics. 1978;34:57–67.CrossRefPubMed
9.
10.
Green MS, Symons MJ. A comparison of the logistic risk function and the proportional hazards model in prospective epidemiologic studies. J Chron Dis. 1983;36(10):715–23.CrossRefPubMed
11.
Ingram DD, Kleinman JC. Empirical comparisons of proportional hazards and logistic regression models. Stat Med. 1989;8(5):525–38.CrossRefPubMed
12.
Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data (Vol. 360). New York: John Wiley & Sons; 2011.
13.
Wu M, Ware JH. On the use of repeated measurements in regression analysis with dichotomous responses. Biometrics. 1979;35:513–21.CrossRefPubMed
14.
Wu L. Mixed effects models for complex data. London: CRC Press; 2010.
15.
Efron B. Logistic regression, survival analysis, and the Kaplan-Meier curve. J Am Stat Assoc. 1988;83(402):414–25.CrossRef
16.
Allison PD. Survival analysis using SAS: a practical guide. Cary NC: Sas Institute; 2010.
17.
Singer JD, Willett JB. Applied longitudinal data analysis: Modeling change and event occurrence. Oxford: Oxford university press; 2003.
18.
Burton A, Altman DG, Royston P, Holder RL. The design of simulation studies in medical statistics. Stat Med. 2006;25(24):4279–92.CrossRefPubMed
19.
De Miguel-Yanes JM, Shrader P, Pencina MJ, Fox CS, Manning AK, Grant RW, Meigs JB. Genetic risk reclassification for type 2 diabetes by age below or above 50 years using 40 type 2 diabetes risk single nucleotide polymorphisms. Diabetes Care. 2011;34(1):121–5.CrossRefPubMed
20.
Meigs JB, Shrader P, Sullivan LM, McAteer JB, Fox CS, Dupuis J, Cupples LA. Genotype score in addition to common risk factors for prediction of type 2 diabetes. N Engl J Med. 2008;359(21):2208–19.CrossRefPubMedPubMedCentral
21.
Fox CS, Pencina MJ, Meigs JB, Vasan RS, Levitzky YS, D’Agostino RB. Trends in the Incidence of Type 2 diabetes mellitus from the 1970s to the 1990s The Framingham Heart Study. Circulation. 2006;113(25):2914–8.CrossRefPubMed
22.
Ficociello LH, Perkins BA, Silva KH, Finkelstein DM, Ignatowska-Switalska H, Gaciong Z, Cupples LA, Aschengrau A, Warram JH, Krolewski AS. Determinants of progression from microalbuminuria to proteinuria in patients who have type 1 diabetes and are treated with angiotensin-converting enzyme inhibitors. Clin J Am Soc Nephrol. 2007;2(3):461–9.CrossRefPubMed
23.
Marshall LM, Spiegelman D, Barbieri RL, Goldman MB, Manson JE, Colditz GA, Hunter DJ. Variation in the incidence of uterine leiomyoma among premenopausal women by age and race. Obstet Gynecol. 1997;90(6):967–73.CrossRefPubMed
24.
Solomon DH, Karlson EW, Rimm EB, Cannuscio CC, Mandl LA, Manson JE, Curhan GC. Cardiovascular morbidity and mortality in women diagnosed with rheumatoid arthritis. Circulation. 2003;107(9):1303–13.CrossRefPubMed
25.
Schnabel RB, Sullivan LM, Levy D, Pencina MJ, Massaro JM, D'Agostino RB, Kannel WB. Development of a risk score for atrial fibrillation (Framingham Heart Study): a community-based cohort study. Lancet. 2009;373(9665):739–45.CrossRefPubMedPubMedCentral
26.
Magnani JW, Moser CB, Murabito JM, Nelson KP, Fontes JD, Lubitz SA, Benjamin EJ. Age of natural menopause and atrial fibrillation: The Framingham Heart Study. Am Heart J. 2012;163(4):729–34.CrossRefPubMedPubMedCentral
27.
Rienstra M, Lyass A, Murabito JM, Magnani JW, Lubitz SA, Massaro JM, Benjamin EJ. Reciprocal relations between physical disability, subjective health, and atrial fibrillation: The Framingham Heart Study. Am Heart J. 2013;166(1):171–8.CrossRefPubMedPubMedCentral
28.
D'Agostino RB. Beyond baseline data: the use of time-varying covariates. J Hypertens. 2008;26(4):639–40.CrossRefPubMed
Metadata
Title
A comparison of time dependent Cox regression, pooled logistic regression and cross sectional pooling with simulations and an application to the Framingham Heart Study
Authors
Julius S. Ngwa
Howard J. Cabral
Debbie M. Cheng
Michael J. Pencina
David R. Gagnon
Michael P. LaValley
L. Adrienne Cupples
Publication date
01-12-2016
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2016
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/s12874-016-0248-6

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