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Published in: BMC Medical Research Methodology 1/2010

Open Access 01-12-2010 | Research article

Semi-parametric risk prediction models for recurrent cardiovascular events in the LIPID study

Authors: Jisheng Cui, Andrew Forbes, Adrienne Kirby, Ian Marschner, John Simes, David Hunt, Malcolm West, Andrew Tonkin

Published in: BMC Medical Research Methodology | Issue 1/2010

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Abstract

Background

Traditional methods for analyzing clinical and epidemiological cohort study data have been focused on the first occurrence of a health outcome. However, in many situations, recurrent event data are frequently observed. It is inefficient to use methods for the analysis of first events to analyse recurrent event data.

Methods

We applied several semi-parametric proportional hazards models to analyze the risk of recurrent myocardial infarction (MI) events based on data from a very large randomized placebo-controlled trial of cholesterol-lowering drug. The backward selection procedure was used to select the significant risk factors in a model. The best fitting model was selected using the log-likelihood ratio test, Akaike Information and Bayesian Information Criteria.

Results

A total of 8557 persons were included in the LIPID study. Risk factors such as age, smoking status, total cholesterol and high density lipoprotein cholesterol levels, qualifying event for the acute coronary syndrome, revascularization, history of stroke or diabetes, angina grade and treatment with pravastatin were significant for development of both first and subsequent MI events. No significant difference was found for the effects of these risk factors between the first and subsequent MI events. The significant risk factors selected in this study were the same as those selected by the parametric conditional frailty model. Estimates of the relative risks and 95% confidence intervals were also similar between these two methods.

Conclusions

Our study shows the usefulness and convenience of the semi-parametric proportional hazards models for the analysis of recurrent event data, especially in estimation of regression coefficients and cumulative risks.
Appendix
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Literature
1.
go back to reference Nelson W: Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications. 2003, Philadelphia: American Statistical AssociationCrossRef Nelson W: Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications. 2003, Philadelphia: American Statistical AssociationCrossRef
2.
go back to reference Cook R, Lawless J: The statistical analysis of recurrent events. 2007, New York: Springer Cook R, Lawless J: The statistical analysis of recurrent events. 2007, New York: Springer
3.
go back to reference Hobson RW, Weiss DG, Fields WS, Goldstone J, Moore WS, Towne JB, Wright CB: Efficacy of carotid endarterectomy for asymptomatic carotid stenosis. The Veterans Affairs Cooperative Study Group. New England Journal of Medicine. 1993, 328 (4): 221-227. 10.1056/NEJM199301283280401.CrossRefPubMed Hobson RW, Weiss DG, Fields WS, Goldstone J, Moore WS, Towne JB, Wright CB: Efficacy of carotid endarterectomy for asymptomatic carotid stenosis. The Veterans Affairs Cooperative Study Group. New England Journal of Medicine. 1993, 328 (4): 221-227. 10.1056/NEJM199301283280401.CrossRefPubMed
4.
go back to reference Li Q, Lagakos S: Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event. Statistics in Medicine. 1997, 16: 925-940. 10.1002/(SICI)1097-0258(19970430)16:8<925::AID-SIM545>3.0.CO;2-2.CrossRefPubMed Li Q, Lagakos S: Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event. Statistics in Medicine. 1997, 16: 925-940. 10.1002/(SICI)1097-0258(19970430)16:8<925::AID-SIM545>3.0.CO;2-2.CrossRefPubMed
5.
go back to reference Cox D: Regression models and life-tables. Journal of the Royal Statistical Society, Series B. 1972, 34: 187-220. Cox D: Regression models and life-tables. Journal of the Royal Statistical Society, Series B. 1972, 34: 187-220.
6.
go back to reference Wei L, Glidden D: An overview of statistical methods for multiple failure time data in clinical trials. Statistics in Medicine. 1997, 16: 833-839. 10.1002/(SICI)1097-0258(19970430)16:8<833::AID-SIM538>3.0.CO;2-2.CrossRefPubMed Wei L, Glidden D: An overview of statistical methods for multiple failure time data in clinical trials. Statistics in Medicine. 1997, 16: 833-839. 10.1002/(SICI)1097-0258(19970430)16:8<833::AID-SIM538>3.0.CO;2-2.CrossRefPubMed
7.
go back to reference Hougaard P: Analysis of Multivariate Survival Data. 2000, New York: Springer-VerlagCrossRef Hougaard P: Analysis of Multivariate Survival Data. 2000, New York: Springer-VerlagCrossRef
8.
go back to reference Therneau T, Grambsch P: Modeling Survival Data Extending the Cox Model. 2000, New York: Springer-VerlagCrossRef Therneau T, Grambsch P: Modeling Survival Data Extending the Cox Model. 2000, New York: Springer-VerlagCrossRef
9.
go back to reference Cook R, Lawless J: Analysis of repeated events. Statistical Methods in Medical Research. 2002, 11: 141-166. 10.1191/0962280202sm278ra.CrossRefPubMed Cook R, Lawless J: Analysis of repeated events. Statistical Methods in Medical Research. 2002, 11: 141-166. 10.1191/0962280202sm278ra.CrossRefPubMed
10.
go back to reference Cui JS, Forbes A, Kirby A, Marschner I, Simes J, West M, Tonkin A: Parametric conditional frailty models for recurrent cardiovascular events in the lipid study. Clinical Trials. 2008, 5 (6): 565-574. 10.1177/1740774508098464.CrossRefPubMed Cui JS, Forbes A, Kirby A, Marschner I, Simes J, West M, Tonkin A: Parametric conditional frailty models for recurrent cardiovascular events in the lipid study. Clinical Trials. 2008, 5 (6): 565-574. 10.1177/1740774508098464.CrossRefPubMed
11.
go back to reference Prentice R, Williams B, Peterson A: On the regression analysis of multivariate failure time data. Biometrika. 1981, 68: 373-379. 10.1093/biomet/68.2.373.CrossRef Prentice R, Williams B, Peterson A: On the regression analysis of multivariate failure time data. Biometrika. 1981, 68: 373-379. 10.1093/biomet/68.2.373.CrossRef
12.
go back to reference Andersen P, Gill R: Cox's regression model for counting process: a large sample study. Annals of Statistics. 1982, 10: 1100-1120. 10.1214/aos/1176345976.CrossRef Andersen P, Gill R: Cox's regression model for counting process: a large sample study. Annals of Statistics. 1982, 10: 1100-1120. 10.1214/aos/1176345976.CrossRef
13.
go back to reference Wei L, Lin D, Weissfeld L: Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association. 1989, 84: 1065-1073. 10.2307/2290084.CrossRef Wei L, Lin D, Weissfeld L: Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association. 1989, 84: 1065-1073. 10.2307/2290084.CrossRef
14.
go back to reference Lin D: Cox regression analysis of multivariate failure time data: the marginal approach. Statistics in Medicine. 1994, 13: 2233-2247. 10.1002/sim.4780132105.CrossRefPubMed Lin D: Cox regression analysis of multivariate failure time data: the marginal approach. Statistics in Medicine. 1994, 13: 2233-2247. 10.1002/sim.4780132105.CrossRefPubMed
15.
go back to reference Pepe M, Cai J: Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates. Journal of the American Statistical Association. 1993, 88: 811-820. 10.2307/2290770.CrossRef Pepe M, Cai J: Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates. Journal of the American Statistical Association. 1993, 88: 811-820. 10.2307/2290770.CrossRef
16.
go back to reference Lawless J, Nadeau J: Some simple robust methods for the analysis of recurrent events. Technometrics. 1995, 37: 18-68. 10.2307/1269617.CrossRef Lawless J, Nadeau J: Some simple robust methods for the analysis of recurrent events. Technometrics. 1995, 37: 18-68. 10.2307/1269617.CrossRef
17.
go back to reference Glidden D, Vittinghoff E: Modelling clustered survival data from multicentre clinical trials. Statistics in Medicine. 2004, 23: 369-388. 10.1002/sim.1599.CrossRefPubMed Glidden D, Vittinghoff E: Modelling clustered survival data from multicentre clinical trials. Statistics in Medicine. 2004, 23: 369-388. 10.1002/sim.1599.CrossRefPubMed
18.
go back to reference Wang M-C, Chang S-H: Nonparametric estimation of a recurrent survival function. Journal of the American Statistical Association. 1999, 94: 146-153. 10.2307/2669690.CrossRefPubMedPubMedCentral Wang M-C, Chang S-H: Nonparametric estimation of a recurrent survival function. Journal of the American Statistical Association. 1999, 94: 146-153. 10.2307/2669690.CrossRefPubMedPubMedCentral
19.
go back to reference Pena E, Strawderman R, Hollander M: Nonparametric estimation with recurrent event data. Journal of the American Statistical Association. 2001, 96: 1299-1315. 10.1198/016214501753381922.CrossRef Pena E, Strawderman R, Hollander M: Nonparametric estimation with recurrent event data. Journal of the American Statistical Association. 2001, 96: 1299-1315. 10.1198/016214501753381922.CrossRef
20.
go back to reference Pena E, Slate E, Gonzalez J: Semiparametric inference for a general class of models for recurrent events. Journal of Statistical Planning and Inference. 2007, 137: 1727-1747. 10.1016/j.jspi.2006.05.004.CrossRefPubMedPubMedCentral Pena E, Slate E, Gonzalez J: Semiparametric inference for a general class of models for recurrent events. Journal of Statistical Planning and Inference. 2007, 137: 1727-1747. 10.1016/j.jspi.2006.05.004.CrossRefPubMedPubMedCentral
21.
go back to reference Metcalfe C, Thompson S: Wei, Lin and Weissfeld's marginal analysis of multivariate failure time data: should it be applied to a recurrent events outcome?. Statistical Methods in Medical Research. 2007, 16: 103-122. 10.1177/0962280206071926.CrossRefPubMed Metcalfe C, Thompson S: Wei, Lin and Weissfeld's marginal analysis of multivariate failure time data: should it be applied to a recurrent events outcome?. Statistical Methods in Medical Research. 2007, 16: 103-122. 10.1177/0962280206071926.CrossRefPubMed
22.
go back to reference The Lipid Study Group: Design features and baseline characteristics of the LIPID (Long-Term Intervention with Pravastatin in Ischemic Disease) Study: a randomized trial in patients with previous acute myocardial infarction and/or unstable angina pectoris. American Journal of Cardiology. 1995, 76: 474-479. 10.1016/S0002-9149(99)80133-7.CrossRef The Lipid Study Group: Design features and baseline characteristics of the LIPID (Long-Term Intervention with Pravastatin in Ischemic Disease) Study: a randomized trial in patients with previous acute myocardial infarction and/or unstable angina pectoris. American Journal of Cardiology. 1995, 76: 474-479. 10.1016/S0002-9149(99)80133-7.CrossRef
23.
go back to reference The Lipid Study Group: The Lipid Study Group. Prevention of cardiovascular events and death with pravastatin in patients with coronary heart disease and a broad range of initial cholesterol levels. New England Journal of Medicine. 1998, 339: 1349-1357. 10.1056/NEJM199811053391902.CrossRef The Lipid Study Group: The Lipid Study Group. Prevention of cardiovascular events and death with pravastatin in patients with coronary heart disease and a broad range of initial cholesterol levels. New England Journal of Medicine. 1998, 339: 1349-1357. 10.1056/NEJM199811053391902.CrossRef
24.
go back to reference Marschner I, Colquhoun D, Simes R, Glasziou P, Harris P, Singh B, Friedlander D, White H, Thompson P, Tonkin A: Long-term risk stratification for survivors of acute coronary syndromes. Results from the Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) Study. Journal of the American College of Cardiology. 2001, 38: 56-63. 10.1016/S0735-1097(01)01360-2.CrossRefPubMed Marschner I, Colquhoun D, Simes R, Glasziou P, Harris P, Singh B, Friedlander D, White H, Thompson P, Tonkin A: Long-term risk stratification for survivors of acute coronary syndromes. Results from the Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) Study. Journal of the American College of Cardiology. 2001, 38: 56-63. 10.1016/S0735-1097(01)01360-2.CrossRefPubMed
25.
go back to reference American Heart Association Medical/Scientific Statement: Revisions to classification of functional capacity and objective assessment of patients with diseases of the heart. Circulation. 1994, 90 (1): 644-645. American Heart Association Medical/Scientific Statement: Revisions to classification of functional capacity and objective assessment of patients with diseases of the heart. Circulation. 1994, 90 (1): 644-645.
26.
go back to reference Campeau L: Letter: Grading of angina pectoris. Circulation. 1976, 54 (3): 522-523.PubMed Campeau L: Letter: Grading of angina pectoris. Circulation. 1976, 54 (3): 522-523.PubMed
27.
go back to reference Cox D: Partial likelihood. Biometrika. 1975, 62: 269-276. 10.1093/biomet/62.2.269.CrossRef Cox D: Partial likelihood. Biometrika. 1975, 62: 269-276. 10.1093/biomet/62.2.269.CrossRef
28.
go back to reference Lin D, Wei L: The robust inference for the Cox proportional hazards model. Journal of the American Statistical Association. 1989, 84: 1074-1178. 10.2307/2290085.CrossRef Lin D, Wei L: The robust inference for the Cox proportional hazards model. Journal of the American Statistical Association. 1989, 84: 1074-1178. 10.2307/2290085.CrossRef
29.
go back to reference Huber P: The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. 1967, Berkeley: University of California Press, 1: Huber P: The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. 1967, Berkeley: University of California Press, 1:
30.
go back to reference White H: A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica. 1980, 48: 817-830. 10.2307/1912934.CrossRef White H: A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica. 1980, 48: 817-830. 10.2307/1912934.CrossRef
31.
go back to reference Kalbfleisch J, Prentice R: Statistical Analysis of Failure time Data. 2002, New York: John Wiley & Sons, 2CrossRef Kalbfleisch J, Prentice R: Statistical Analysis of Failure time Data. 2002, New York: John Wiley & Sons, 2CrossRef
32.
go back to reference Stata Corporation: Stata Statistical Software: Release 10. 2007, College Station: Stata Corporation Stata Corporation: Stata Statistical Software: Release 10. 2007, College Station: Stata Corporation
33.
go back to reference Hollis S, Campbell F: What is meant by intention to treat analysis? Survey of published randomised controlled trials. British Medical Journal. 1999, 319: 670-674.CrossRefPubMedPubMedCentral Hollis S, Campbell F: What is meant by intention to treat analysis? Survey of published randomised controlled trials. British Medical Journal. 1999, 319: 670-674.CrossRefPubMedPubMedCentral
34.
go back to reference Harrell FJ: Regression modelling strategies. 2001, New York: Springer-VerlageCrossRef Harrell FJ: Regression modelling strategies. 2001, New York: Springer-VerlageCrossRef
35.
go back to reference Mahe C, Chevret S: Estimation of the treatment effect in a clinical trial when recurrent events define the endpoints. Statistics in Medicine. 1999, 18: 1821-1829. 10.1002/(SICI)1097-0258(19990730)18:14<1821::AID-SIM219>3.0.CO;2-O.CrossRefPubMed Mahe C, Chevret S: Estimation of the treatment effect in a clinical trial when recurrent events define the endpoints. Statistics in Medicine. 1999, 18: 1821-1829. 10.1002/(SICI)1097-0258(19990730)18:14<1821::AID-SIM219>3.0.CO;2-O.CrossRefPubMed
36.
go back to reference Ghosh D: Methods for analysis of multiple events in the presence of death. Control Clin Trials. 2000, 21: 115-126. 10.1016/S0197-2456(00)00043-X.CrossRefPubMed Ghosh D: Methods for analysis of multiple events in the presence of death. Control Clin Trials. 2000, 21: 115-126. 10.1016/S0197-2456(00)00043-X.CrossRefPubMed
37.
go back to reference Barai U, Teoh N: Multiple statistics for multiple events, with application to repeated infections in the growth factor studies. Stat Med. 1997, 16: 941-949. 10.1002/(SICI)1097-0258(19970430)16:8<941::AID-SIM546>3.0.CO;2-9.CrossRefPubMed Barai U, Teoh N: Multiple statistics for multiple events, with application to repeated infections in the growth factor studies. Stat Med. 1997, 16: 941-949. 10.1002/(SICI)1097-0258(19970430)16:8<941::AID-SIM546>3.0.CO;2-9.CrossRefPubMed
38.
go back to reference Cook R, Lawless J: Marginal analysis of recurrent events and a terminating event. Statistics in Medicine. 1997, 16: 911-924. 10.1002/(SICI)1097-0258(19970430)16:8<911::AID-SIM544>3.0.CO;2-I.CrossRefPubMed Cook R, Lawless J: Marginal analysis of recurrent events and a terminating event. Statistics in Medicine. 1997, 16: 911-924. 10.1002/(SICI)1097-0258(19970430)16:8<911::AID-SIM544>3.0.CO;2-I.CrossRefPubMed
39.
go back to reference Kelly P, Lim L: Survival analysis for recurrent event data: an application to childhood infectious diseases. Statistics in Medicine. 2000, 19: 13-33. 10.1002/(SICI)1097-0258(20000115)19:1<13::AID-SIM279>3.0.CO;2-5.CrossRefPubMed Kelly P, Lim L: Survival analysis for recurrent event data: an application to childhood infectious diseases. Statistics in Medicine. 2000, 19: 13-33. 10.1002/(SICI)1097-0258(20000115)19:1<13::AID-SIM279>3.0.CO;2-5.CrossRefPubMed
40.
go back to reference Sacks FM, Tonkin AM, Shepherd J, Braunwald E, Cobbe S, Hawkins CM, Keech A, Packard C, Simes J, Byington R, et al: Effect of pravastatin on coronary disease events in subgroups defined by coronary risk factors: the Prospective Pravastatin Pooling Project. Circulation. 2000, 102 (16): 1893-1900.CrossRefPubMed Sacks FM, Tonkin AM, Shepherd J, Braunwald E, Cobbe S, Hawkins CM, Keech A, Packard C, Simes J, Byington R, et al: Effect of pravastatin on coronary disease events in subgroups defined by coronary risk factors: the Prospective Pravastatin Pooling Project. Circulation. 2000, 102 (16): 1893-1900.CrossRefPubMed
41.
go back to reference Ridker PM, Buring JE, Rifai N, Cook NR: Development and validation of improved algorithms for the assessment of global cardiovascular risk in women: the Reynolds Risk Score. Journal of the American Medical Association. 2007, 297: 611-619. 10.1001/jama.297.6.611.CrossRefPubMed Ridker PM, Buring JE, Rifai N, Cook NR: Development and validation of improved algorithms for the assessment of global cardiovascular risk in women: the Reynolds Risk Score. Journal of the American Medical Association. 2007, 297: 611-619. 10.1001/jama.297.6.611.CrossRefPubMed
42.
go back to reference Ishikawa J, Tamura Y, Hoshide S, Eguchi K, Ishikawa S, Shimada K, Kario K: Low-grade inflammation is a risk factor for clinical stroke events in addition to silent cerebral infarcts in Japanese older hypertensives: the Jichi Medical School ABPM Study, wave 1. Stroke. 2007, 38: 911-917. 10.1161/01.STR.0000258115.46765.f1.CrossRefPubMed Ishikawa J, Tamura Y, Hoshide S, Eguchi K, Ishikawa S, Shimada K, Kario K: Low-grade inflammation is a risk factor for clinical stroke events in addition to silent cerebral infarcts in Japanese older hypertensives: the Jichi Medical School ABPM Study, wave 1. Stroke. 2007, 38: 911-917. 10.1161/01.STR.0000258115.46765.f1.CrossRefPubMed
43.
go back to reference Ghosh D, Lin D: Nonparametric analysis of recurrent events and death. Biometrics. 2000, 56: 554-562. 10.1111/j.0006-341X.2000.00554.x.CrossRefPubMed Ghosh D, Lin D: Nonparametric analysis of recurrent events and death. Biometrics. 2000, 56: 554-562. 10.1111/j.0006-341X.2000.00554.x.CrossRefPubMed
44.
go back to reference Wang M, Qin J, Chiang C: Analyzing recurrent event data with informative censoring. Journal of the American Statistical Association. 2001, 96: 1057-1065. 10.1198/016214501753209031.CrossRef Wang M, Qin J, Chiang C: Analyzing recurrent event data with informative censoring. Journal of the American Statistical Association. 2001, 96: 1057-1065. 10.1198/016214501753209031.CrossRef
45.
go back to reference Liu L, Wolfe R, Huang X: Shared frailty models for recurrent events and a terminal event. Biometrics. 2004, 60: 747-756. 10.1111/j.0006-341X.2004.00225.x.CrossRefPubMed Liu L, Wolfe R, Huang X: Shared frailty models for recurrent events and a terminal event. Biometrics. 2004, 60: 747-756. 10.1111/j.0006-341X.2004.00225.x.CrossRefPubMed
Metadata
Title
Semi-parametric risk prediction models for recurrent cardiovascular events in the LIPID study
Authors
Jisheng Cui
Andrew Forbes
Adrienne Kirby
Ian Marschner
John Simes
David Hunt
Malcolm West
Andrew Tonkin
Publication date
01-12-2010
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2010
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-10-27

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