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Published in: Emerging Themes in Epidemiology 1/2013

Open Access 01-12-2013 | Research article

The impact of missing data on analyses of a time-dependent exposure in a longitudinal cohort: a simulation study

Authors: Amalia Karahalios, Laura Baglietto, Katherine J Lee, Dallas R English, John B Carlin, Julie A Simpson

Published in: Emerging Themes in Epidemiology | Issue 1/2013

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Abstract

Background

Missing data often cause problems in longitudinal cohort studies with repeated follow-up waves. Research in this area has focussed on analyses with missing data in repeated measures of the outcome, from which participants with missing exposure data are typically excluded. We performed a simulation study to compare complete-case analysis with Multiple imputation (MI) for dealing with missing data in an analysis of the association of waist circumference, measured at two waves, and the risk of colorectal cancer (a completely observed outcome).

Methods

We generated 1,000 datasets of 41,476 individuals with values of waist circumference at waves 1 and 2 and times to the events of colorectal cancer and death to resemble the distributions of the data from the Melbourne Collaborative Cohort Study. Three proportions of missing data (15, 30 and 50%) were imposed on waist circumference at wave 2 using three missing data mechanisms: Missing Completely at Random (MCAR), and a realistic and a more extreme covariate-dependent Missing at Random (MAR) scenarios. We assessed the impact of missing data on two epidemiological analyses: 1) the association between change in waist circumference between waves 1 and 2 and the risk of colorectal cancer, adjusted for waist circumference at wave 1; and 2) the association between waist circumference at wave 2 and the risk of colorectal cancer, not adjusted for waist circumference at wave 1.

Results

We observed very little bias for complete-case analysis or MI under all missing data scenarios, and the resulting coverage of interval estimates was near the nominal 95% level. MI showed gains in precision when waist circumference was included as a strong auxiliary variable in the imputation model.

Conclusions

This simulation study, based on data from a longitudinal cohort study, demonstrates that there is little gain in performing MI compared to a complete-case analysis in the presence of up to 50% missing data for the exposure of interest when the data are MCAR, or missing dependent on covariates. MI will result in some gain in precision if a strong auxiliary variable that is not in the analysis model is included in the imputation model.
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Literature
1.
go back to reference Karahalios A, Baglietto L, English D, Simpson J: A review of reporting missing data in cohort studies with repeated assessment of exposure measures. BMC Med Res Methodol. 2012, 12: 96. 10.1186/1471-2288-12-96PubMedCentralCrossRefPubMed Karahalios A, Baglietto L, English D, Simpson J: A review of reporting missing data in cohort studies with repeated assessment of exposure measures. BMC Med Res Methodol. 2012, 12: 96. 10.1186/1471-2288-12-96PubMedCentralCrossRefPubMed
2.
go back to reference Eekhout I, de Boer RM, Twisk JWR, de Vet HCW, Heymans MW: Missing data: a systematic review of how they are reported and handled. Epidemiology. 2012, 23 (5): 729-732. 10.1097/EDE.0b013e3182576cdbCrossRefPubMed Eekhout I, de Boer RM, Twisk JWR, de Vet HCW, Heymans MW: Missing data: a systematic review of how they are reported and handled. Epidemiology. 2012, 23 (5): 729-732. 10.1097/EDE.0b013e3182576cdbCrossRefPubMed
3.
go back to reference Marshall A, Altman DG, Royston P, Holder RL: Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study. BMC Med Res Methodol. 2010, 10: 7. 10.1186/1471-2288-10-7PubMedCentralCrossRefPubMed Marshall A, Altman DG, Royston P, Holder RL: Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study. BMC Med Res Methodol. 2010, 10: 7. 10.1186/1471-2288-10-7PubMedCentralCrossRefPubMed
4.
go back to reference White IR, Carlin JB: Bias and efficiency of multiple imputation compared with complete-case analysis for missing covariate values. Stat Med. 2010, 29 (28): 2920-31. 10.1002/sim.3944CrossRefPubMed White IR, Carlin JB: Bias and efficiency of multiple imputation compared with complete-case analysis for missing covariate values. Stat Med. 2010, 29 (28): 2920-31. 10.1002/sim.3944CrossRefPubMed
5.
go back to reference van der Heijden GJMG, Donders ART, Stijnen T, Moons KGM: Imputation of missing values is superior to complete case analysis and the missing-indicator method in multivariable diagnostic research: a clinical example. J Clin Epidemiol. 2006, 59 (10): 1102-1109. 10.1016/j.jclinepi.2006.01.015CrossRefPubMed van der Heijden GJMG, Donders ART, Stijnen T, Moons KGM: Imputation of missing values is superior to complete case analysis and the missing-indicator method in multivariable diagnostic research: a clinical example. J Clin Epidemiol. 2006, 59 (10): 1102-1109. 10.1016/j.jclinepi.2006.01.015CrossRefPubMed
6.
go back to reference Vach W, Blettner M: Biased estimation of the odds ratio in case-control studies due to the use of ad hoc methods of correcting for missing values for confounding variables. Am J Epidemiol. 1991, 134 (8): 895-907.PubMed Vach W, Blettner M: Biased estimation of the odds ratio in case-control studies due to the use of ad hoc methods of correcting for missing values for confounding variables. Am J Epidemiol. 1991, 134 (8): 895-907.PubMed
7.
go back to reference SAS Insitute Inc: SAS OnlineDoc, Version 8. Cary, NC: SAS Institute, Inc.; 2000. SAS Insitute Inc: SAS OnlineDoc, Version 8. Cary, NC: SAS Institute, Inc.; 2000.
8.
go back to reference StataCorp: Stata statistical software: Release 11. College Station, TX: StataCorp LP; 2009. StataCorp: Stata statistical software: Release 11. College Station, TX: StataCorp LP; 2009.
9.
go back to reference Little RJA, Rubin DB: Statistical analysis with missing data (2nd edition). New York: J Wiley & Sons; 2002. Little RJA, Rubin DB: Statistical analysis with missing data (2nd edition). New York: J Wiley & Sons; 2002.
10.
go back to reference Demissie S, LaValley MP, Horton NJ, Glynn RJ, Cupples LA: Bias due to missing exposure data using complete-case analysis in the proportional hazards regression model. Stat Med. 2003, 22 (4): 545-557. 10.1002/sim.1340CrossRefPubMed Demissie S, LaValley MP, Horton NJ, Glynn RJ, Cupples LA: Bias due to missing exposure data using complete-case analysis in the proportional hazards regression model. Stat Med. 2003, 22 (4): 545-557. 10.1002/sim.1340CrossRefPubMed
11.
go back to reference Knol MJ, Janssen KJM, Donders ART, Egberts ACG, Heerdink ER, Grobbee DE, Moons KGM, Geerlings MI: Unpredictable bias when using the missing indicator method or complete case analysis for missing confounder values: an empirical example. J Clin Epidemiol. 2010, 63 (7): 728-736. 10.1016/j.jclinepi.2009.08.028CrossRefPubMed Knol MJ, Janssen KJM, Donders ART, Egberts ACG, Heerdink ER, Grobbee DE, Moons KGM, Geerlings MI: Unpredictable bias when using the missing indicator method or complete case analysis for missing confounder values: an empirical example. J Clin Epidemiol. 2010, 63 (7): 728-736. 10.1016/j.jclinepi.2009.08.028CrossRefPubMed
12.
go back to reference Moons KGM, Donders RART, Stijnen T, Harrell FEJr: Using the outcome for imputation of missing predictor values was preferred. J Clin Epidemiol. 2006, 59 (10): 1092-1101. 10.1016/j.jclinepi.2006.01.009CrossRefPubMed Moons KGM, Donders RART, Stijnen T, Harrell FEJr: Using the outcome for imputation of missing predictor values was preferred. J Clin Epidemiol. 2006, 59 (10): 1092-1101. 10.1016/j.jclinepi.2006.01.009CrossRefPubMed
13.
go back to reference Peyre H, Leplège A, Coste J: Missing data methods for dealing with missing items in quality of life questionnaires. A comparison by simulation of personal mean score, full information maximum likelihood, multiple imputation, and hot deck techniques applied to the SF-36 in the French 2003 decennial health survey. Qual Life Res. 2011, 20 (2): 287-300. 10.1007/s11136-010-9740-3CrossRefPubMed Peyre H, Leplège A, Coste J: Missing data methods for dealing with missing items in quality of life questionnaires. A comparison by simulation of personal mean score, full information maximum likelihood, multiple imputation, and hot deck techniques applied to the SF-36 in the French 2003 decennial health survey. Qual Life Res. 2011, 20 (2): 287-300. 10.1007/s11136-010-9740-3CrossRefPubMed
14.
go back to reference Touloumi G, Babiker AG, Pocock SJ, Darbyshire JH: Impact of missing data due to drop-outs on estimators for rates of change in longitudinal studies: a simulation study. Stat Med. 2001, 20 (24): 3715-3728. 10.1002/sim.1114CrossRefPubMed Touloumi G, Babiker AG, Pocock SJ, Darbyshire JH: Impact of missing data due to drop-outs on estimators for rates of change in longitudinal studies: a simulation study. Stat Med. 2001, 20 (24): 3715-3728. 10.1002/sim.1114CrossRefPubMed
15.
go back to reference Janssen KJM, Donders ART, Harrell FE Jr, Vergouwe Y, Chen Q, Grobbee DE, Moons KGM: Missing covariate data in medical research: to impute is better than to ignore. J Clin Epidemiol. 2010, 63 (7): 721-727. 10.1016/j.jclinepi.2009.12.008CrossRefPubMed Janssen KJM, Donders ART, Harrell FE Jr, Vergouwe Y, Chen Q, Grobbee DE, Moons KGM: Missing covariate data in medical research: to impute is better than to ignore. J Clin Epidemiol. 2010, 63 (7): 721-727. 10.1016/j.jclinepi.2009.12.008CrossRefPubMed
16.
go back to reference Ambler G, Omar RZ, Royston P: A comparison of imputation techniques for handling missing predictor values in a risk model with a binary outcome. Stat Methods Med Res. 2007, 16 (3): 277-298. 10.1177/0962280206074466CrossRefPubMed Ambler G, Omar RZ, Royston P: A comparison of imputation techniques for handling missing predictor values in a risk model with a binary outcome. Stat Methods Med Res. 2007, 16 (3): 277-298. 10.1177/0962280206074466CrossRefPubMed
17.
go back to reference Rajan KB, Leurgans SE: Joint modeling of missing data due to non-participation and death in longitudinal aging studies. Stat Med. 2010, 29 (21): 2260-2268. 10.1002/sim.4010PubMedCentralCrossRefPubMed Rajan KB, Leurgans SE: Joint modeling of missing data due to non-participation and death in longitudinal aging studies. Stat Med. 2010, 29 (21): 2260-2268. 10.1002/sim.4010PubMedCentralCrossRefPubMed
18.
go back to reference Shardell M, Miller RR: Weighted estimating equations for longitudinal studies with death and non-monotone missing time-dependent covariates and outcomes. Stat Med. 2008, 27 (7): 1008-1025. 10.1002/sim.2964PubMedCentralCrossRefPubMed Shardell M, Miller RR: Weighted estimating equations for longitudinal studies with death and non-monotone missing time-dependent covariates and outcomes. Stat Med. 2008, 27 (7): 1008-1025. 10.1002/sim.2964PubMedCentralCrossRefPubMed
19.
go back to reference Giles GG, English DR: The Melbourne Collaborative Cohort Study. IARC Sci Publ. 2002, 156: 69-70.PubMed Giles GG, English DR: The Melbourne Collaborative Cohort Study. IARC Sci Publ. 2002, 156: 69-70.PubMed
20.
go back to reference Frezza EE, Wachtel MS, Chiriva-Internati M: Influence of obesity on the risk of developing colon cancer. Gut. 2006, 55 (2): 285-291. 10.1136/gut.2005.073163PubMedCentralCrossRefPubMed Frezza EE, Wachtel MS, Chiriva-Internati M: Influence of obesity on the risk of developing colon cancer. Gut. 2006, 55 (2): 285-291. 10.1136/gut.2005.073163PubMedCentralCrossRefPubMed
21.
go back to reference MacInnis R, English D, Hopper J, Haydon A, Gertig D, Giles G: Body size and composition and colon cancer risk in men. Cancer Epidemiol Biomarkers Prev. 2004, 13 (4): 553.PubMed MacInnis R, English D, Hopper J, Haydon A, Gertig D, Giles G: Body size and composition and colon cancer risk in men. Cancer Epidemiol Biomarkers Prev. 2004, 13 (4): 553.PubMed
22.
go back to reference MacInnis R, English D, Hopper J, Gertig D, Haydon A, Giles G: Body size and composition and colon cancer risk in women. Int J Cancer. 2006, 118 (6): 1496-1500. 10.1002/ijc.21508CrossRefPubMed MacInnis R, English D, Hopper J, Gertig D, Haydon A, Giles G: Body size and composition and colon cancer risk in women. Int J Cancer. 2006, 118 (6): 1496-1500. 10.1002/ijc.21508CrossRefPubMed
23.
go back to reference MacInnis R, English D, Haydon A, Hopper J, Gertig D, Giles G: Body size and composition and risk of rectal cancer (Australia). Cancer Causes Control. 2006, 17 (10): 1291-1297. 10.1007/s10552-006-0074-yCrossRefPubMed MacInnis R, English D, Haydon A, Hopper J, Gertig D, Giles G: Body size and composition and risk of rectal cancer (Australia). Cancer Causes Control. 2006, 17 (10): 1291-1297. 10.1007/s10552-006-0074-yCrossRefPubMed
24.
go back to reference Rapp K, Klenk J, Ulmer H, Concin H, Diem G, Oberaigner W, Schroeder J: Weight change and cancer risk in a cohort of more than 65, 000 adults in Austria. Ann Oncol. 2008, 19 (4): 641-648.CrossRefPubMed Rapp K, Klenk J, Ulmer H, Concin H, Diem G, Oberaigner W, Schroeder J: Weight change and cancer risk in a cohort of more than 65, 000 adults in Austria. Ann Oncol. 2008, 19 (4): 641-648.CrossRefPubMed
25.
go back to reference Thygesen LC, Grønbaek M, Johansen C, Fuchs CS, Willett WC, Giovannucci E: Prospective weight change and colon cancer risk in male US health professionals. Int J Cancer. 2008, 123 (5): 1160-1165. 10.1002/ijc.23612PubMedCentralCrossRefPubMed Thygesen LC, Grønbaek M, Johansen C, Fuchs CS, Willett WC, Giovannucci E: Prospective weight change and colon cancer risk in male US health professionals. Int J Cancer. 2008, 123 (5): 1160-1165. 10.1002/ijc.23612PubMedCentralCrossRefPubMed
26.
go back to reference Lohman T, Roche A, Martorell R (Eds): Anthropometric standardization reference manual. Champaign IL: Kinetics Books; 1988. Lohman T, Roche A, Martorell R (Eds): Anthropometric standardization reference manual. Champaign IL: Kinetics Books; 1988.
27.
go back to reference Burton A, Altman DG, Royston P, Holder RL: The design of simulation studies in medical statistics. Stat Med. 2006, 25 (24): 4279-4292. 10.1002/sim.2673CrossRefPubMed Burton A, Altman DG, Royston P, Holder RL: The design of simulation studies in medical statistics. Stat Med. 2006, 25 (24): 4279-4292. 10.1002/sim.2673CrossRefPubMed
28.
go back to reference Tannenbaum S, Holford N, Lee H, Peck C, Mould D: Simulation of correlated continuous and categorical variables using a single multivariate distribution. J Pharmacokinet Pharmacodyn. 2006, 33 (6): 773-794. 10.1007/s10928-006-9033-1CrossRefPubMed Tannenbaum S, Holford N, Lee H, Peck C, Mould D: Simulation of correlated continuous and categorical variables using a single multivariate distribution. J Pharmacokinet Pharmacodyn. 2006, 33 (6): 773-794. 10.1007/s10928-006-9033-1CrossRefPubMed
29.
go back to reference Bender R, Augustin T, Blettner M: Generating survival times to simulate Cox proportional hazards models. Stat Med. 2005, 24 (11): 1713-1723. 10.1002/sim.2059CrossRefPubMed Bender R, Augustin T, Blettner M: Generating survival times to simulate Cox proportional hazards models. Stat Med. 2005, 24 (11): 1713-1723. 10.1002/sim.2059CrossRefPubMed
30.
go back to reference Little RJ: Modeling the drop-out mechanism in repeated-measures studies. J Am Stat Assoc. 1995, 90 (431): 1112-1121. 10.1080/01621459.1995.10476615.CrossRef Little RJ: Modeling the drop-out mechanism in repeated-measures studies. J Am Stat Assoc. 1995, 90 (431): 1112-1121. 10.1080/01621459.1995.10476615.CrossRef
31.
go back to reference Schafer J, Olsen M: Multiple imputation for multivariate missing-data problems: a data analyst’s perspective. Multivariate Behav Res. 1998, 33 (4): 545-571. 10.1207/s15327906mbr3304_5.CrossRef Schafer J, Olsen M: Multiple imputation for multivariate missing-data problems: a data analyst’s perspective. Multivariate Behav Res. 1998, 33 (4): 545-571. 10.1207/s15327906mbr3304_5.CrossRef
33.
go back to reference Rubin D: Multiple imputation for nonresponse in surveys. New York: J Wiley & Sons; 1987.CrossRef Rubin D: Multiple imputation for nonresponse in surveys. New York: J Wiley & Sons; 1987.CrossRef
34.
go back to reference Sterne J, White I, Carlin J, Spratt M, Royston P, Kenward M, Wood A, Carpenter J: Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls. BMJ. 2009, 338: b2393. 10.1136/bmj.b2393PubMedCentralCrossRefPubMed Sterne J, White I, Carlin J, Spratt M, Royston P, Kenward M, Wood A, Carpenter J: Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls. BMJ. 2009, 338: b2393. 10.1136/bmj.b2393PubMedCentralCrossRefPubMed
35.
go back to reference Jelicić H, Phelps E, Lerner RM: Why missing data matter in the longitudinal study of adolescent development: using the 4-H Study to understand the uses of different missing data methods. J Youth Adolesc. 2010, 39 (7): 816-835. 10.1007/s10964-010-9542-5CrossRefPubMed Jelicić H, Phelps E, Lerner RM: Why missing data matter in the longitudinal study of adolescent development: using the 4-H Study to understand the uses of different missing data methods. J Youth Adolesc. 2010, 39 (7): 816-835. 10.1007/s10964-010-9542-5CrossRefPubMed
36.
go back to reference Xu Q, Paik MC, Rundek T, Elkind MSV, Sacco RL: Reweighting estimators for Cox regression with missing covariate data: analysis of insulin resistance and risk of stroke in the Northern Manhattan Study. Stat Med. 2011, 30 (28): 3328-3340. 10.1002/sim.4380PubMedCentralCrossRefPubMed Xu Q, Paik MC, Rundek T, Elkind MSV, Sacco RL: Reweighting estimators for Cox regression with missing covariate data: analysis of insulin resistance and risk of stroke in the Northern Manhattan Study. Stat Med. 2011, 30 (28): 3328-3340. 10.1002/sim.4380PubMedCentralCrossRefPubMed
37.
go back to reference Bassett JK, Severi G, English DR, Baglietto L, Krishnan K, Hopper JL, Giles GG: Body size, weight change, and risk of colon cancer. Cancer Epidemiol Biomarkers Prev. 2010, 19 (11): 2978-2986. 10.1158/1055-9965.EPI-10-0543CrossRefPubMed Bassett JK, Severi G, English DR, Baglietto L, Krishnan K, Hopper JL, Giles GG: Body size, weight change, and risk of colon cancer. Cancer Epidemiol Biomarkers Prev. 2010, 19 (11): 2978-2986. 10.1158/1055-9965.EPI-10-0543CrossRefPubMed
38.
go back to reference Laake I, Thune I, Selmer R, Tretli S, Slattery ML, Veierød MB: A prospective study of body mass index, weight change, and risk of cancer in the proximal and distal colon. Cancer Epidemiol Biomarkers Prev. 2010, 19 (6): 1511-1522. 10.1158/1055-9965.EPI-09-0813CrossRefPubMed Laake I, Thune I, Selmer R, Tretli S, Slattery ML, Veierød MB: A prospective study of body mass index, weight change, and risk of cancer in the proximal and distal colon. Cancer Epidemiol Biomarkers Prev. 2010, 19 (6): 1511-1522. 10.1158/1055-9965.EPI-09-0813CrossRefPubMed
39.
go back to reference Donders ART, van der Heijden GJMG, Stijnen T, Moons KGM: Review: a gentle introduction to imputation of missing values. J Clin Epidemiol. 2006, 59 (10): 1087-1091. 10.1016/j.jclinepi.2006.01.014CrossRefPubMed Donders ART, van der Heijden GJMG, Stijnen T, Moons KGM: Review: a gentle introduction to imputation of missing values. J Clin Epidemiol. 2006, 59 (10): 1087-1091. 10.1016/j.jclinepi.2006.01.014CrossRefPubMed
40.
go back to reference Lee KJ, Carlin JB: Multiple imputation for missing data: fully conditional specification versus multivariate normal imputation. Am J Epidemiol. 2010, 171 (5): 624-632. 10.1093/aje/kwp425CrossRefPubMed Lee KJ, Carlin JB: Multiple imputation for missing data: fully conditional specification versus multivariate normal imputation. Am J Epidemiol. 2010, 171 (5): 624-632. 10.1093/aje/kwp425CrossRefPubMed
41.
go back to reference Liu J, Gelman A, Hill J, Su YS: On the stationary distribution of iterative imputations. 2010, arXiv preprint arXiv:1012.2902. Liu J, Gelman A, Hill J, Su YS: On the stationary distribution of iterative imputations. 2010, arXiv preprint arXiv:1012.2902.
42.
go back to reference Graham J: Using modern missing data methods with auxiliary variables to mitigate the effects of attrition on statistical power. Missing data: analysis and design. New York: Springer; 2012, 253-275.CrossRef Graham J: Using modern missing data methods with auxiliary variables to mitigate the effects of attrition on statistical power. Missing data: analysis and design. New York: Springer; 2012, 253-275.CrossRef
43.
44.
go back to reference R Development Core Team: R: A language and environment for statistical computing. Software. Vienna, Austria: R Foundation for Statistical Computing; 2004. R Development Core Team: R: A language and environment for statistical computing. Software. Vienna, Austria: R Foundation for Statistical Computing; 2004.
45.
go back to reference IBM Corp: IBM SPSS statistics for windows. 2012, Version 21.0, Armonk, NY. IBM Corp: IBM SPSS statistics for windows. 2012, Version 21.0, Armonk, NY.
46.
go back to reference Mackinnon A: The use and reporting of multiple imputation in medical research - a review. J Intern Med. 2010, 268 (6): 586-593. 10.1111/j.1365-2796.2010.02274.xCrossRefPubMed Mackinnon A: The use and reporting of multiple imputation in medical research - a review. J Intern Med. 2010, 268 (6): 586-593. 10.1111/j.1365-2796.2010.02274.xCrossRefPubMed
47.
go back to reference Schafer JL, Graham JW: Missing data: our view of the state of the art. Psychol Methods. 2002, 7 (2): 147-177.CrossRefPubMed Schafer JL, Graham JW: Missing data: our view of the state of the art. Psychol Methods. 2002, 7 (2): 147-177.CrossRefPubMed
48.
go back to reference Schafer J: Assumptions. Analysis of incomplete multivariate data. New York: Chapman and Hall; 1997.CrossRef Schafer J: Assumptions. Analysis of incomplete multivariate data. New York: Chapman and Hall; 1997.CrossRef
49.
go back to reference Bradshaw PT, Ibrahim JG, Gammon MD: A Bayesian proportional hazards regression model with non-ignorably missing time-varying covariates. Stat Med. 2010, 29 (29): 3017-3029. 10.1002/sim.4076PubMedCentralCrossRefPubMed Bradshaw PT, Ibrahim JG, Gammon MD: A Bayesian proportional hazards regression model with non-ignorably missing time-varying covariates. Stat Med. 2010, 29 (29): 3017-3029. 10.1002/sim.4076PubMedCentralCrossRefPubMed
Metadata
Title
The impact of missing data on analyses of a time-dependent exposure in a longitudinal cohort: a simulation study
Authors
Amalia Karahalios
Laura Baglietto
Katherine J Lee
Dallas R English
John B Carlin
Julie A Simpson
Publication date
01-12-2013
Publisher
BioMed Central
Published in
Emerging Themes in Epidemiology / Issue 1/2013
Electronic ISSN: 1742-7622
DOI
https://doi.org/10.1186/1742-7622-10-6

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