Latency estimation for chronic disease risk: a damped exponential weighting model
Open accessAbstract
Identifying the susceptible period when environmental factors affect disease risk is essential for understanding disease etiology. Most existing epidemiologic studies use oversimplified summaries of time-dependent exposures such as baseline or most current exposure, or the cumulative average of exposure over available follow-up periods. In this paper, we introduce a damped exponential weighting model for estimating optimal exposure weights for different time intervals. This model can accommodate flexible patterns of weights and can be fit using standard software. We applied the model to assess the latency of BMI and alcohol for post-menopausal breast cancer based on 30-year exposure history in the Nurses' Health Study. We have also performed a simulation study to assess the validity of the proposed hypothesis testing and estimation procedures in realistic conditions. We found that the type I error is close to 0.05; the bias in our parameter estimates is low and the coverage probability of interval estimates is close to 0.95. For ER+/PR+ breast cancer we found that recent BMI was a more important predictor of risk than more distant BMI; for ER-/PR- breast cancer, no latency was found and risk was characterized by cumulative high levels of BMI over a long period of time. For alcohol intake, we saw a strong positive association with cumulative intake for ER+/PR+ breast cancer; no significant association was found for cumulative intake or for any latency measure of risk for ER-/PR- breast cancer. Our results underscore the value of an easy-to-implement approach to latency analysis of exposure profiles for chronic disease.
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Exponential weighting has previously been used in both medical and non-medical error/risk analysis.
“exponential weighting has previously been used in both medical42–44 and non-medical45 46 error/risk analysis.”
From Clinical AI Scribes in primary care: accuracy, error severity and implications for clinical practice (2025) · cites this paper as [42]
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Cites
Willett, W. C. (1998) · doi:10.1093/acprof:oso/9780195122978.001.0001 · Cited by 4,541 · see citing works
Self-citationDistributed lag non‐linear models
Gasparrini, A., Armstrong, B., & Kenward, M. G. (2010) · Statistics in Medicine · doi:10.1002/sim.3940 · Cited by 2,481 · see citing works
Calle, E. E., Heath Jr., C. W., Coates, R. J., Liff, J. M., Franceschi, S., Talamini, R., Chantarakul, N., Koetsawang, S., Rachawat, D., Morabia, A., et al. (1997) · The Lancet · doi:10.1016/s0140-6736(97)08233-0 · Cited by 2,450 · see citing works
Body mass index, serum sex hormones, and breast cancer risk in postmenopausal women
Endogenous Hormones Breast Cancer Collaborative Group (2003) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/djg022 · Cited by 1,093 · see citing works
Hu, F. B., Stampfer, M. J., Rimm, E., Ascherio, A., Rosner, B. A., Spiegelman, D., & Willett, W. C. (1999) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a009849 · Cited by 1,085 · see citing works
Self-citationApplying Cox Regression to Competing Risks
Lunn, M., & McNeil, D. (1995) · Biometrics · doi:10.2307/2532940 · Cited by 1,017 · see citing works
A LIFE COURSE APPROACH TO CHRONIC DISEASE EPIDEMIOLOGY
Lynch, J. W., & Smith, G. D. (2005) · Annual Review of Public Health · doi:10.1146/annurev.publhealth.26.021304.144505 · Cited by 923 · see citing works
Modeling exposure–lag–response associations with distributed lag non‐linear models
Gasparrini, A. (2013) · Statistics in Medicine · doi:10.1002/sim.5963 · Cited by 839 · see citing works
TEST OF THE NATIONAL DEATH INDEX
Stampfer, M. J., Willett, W. C., Speizer, F. E., DYSERT, D. C., LIPNICK, R. J., ROSNER, B. A., & Hennekens, C. H. (1984) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a113804 · Cited by 791 · see citing works
Self-citationYuan, C., Spiegelman, D., Rimm, E. B., Rosner, B. A., Stampfer, M. J., Barnett, J. B., Chavarro, J. E., Subar, A. F., Sampson, L. K., & Willett, W. C. (2017) · American Journal of Epidemiology · doi:10.1093/aje/kww104 · Cited by 469 · see citing works
Self-citationBelanger, C. F., Hennekens, C. H., ROSNER, B. A., & Speizer, F. E. (1978) · AJN American Journal of Nursing · doi:10.2307/3462013 · Cited by 463 · cited 1× · see citing works
“The NHS was established in 1976 and included 121,700 US female registered nurses, aged 30–55 years [11].”
BackgroundSelf-citationMunsell, M. F., Sprague, B. L., Berry, D. A., Chisholm, G. B., & Trentham‐Dietz, A. (2013) · Epidemiologic Reviews · doi:10.1093/epirev/mxt010 · Cited by 384 · see citing works
Rothman, K. J. (1981) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a113189 · Cited by 264 · see citing works
Potential for Bias When Estimating Critical Windows for Air Pollution in Children’s Health
Wilson, A., Chiu, Y.-H. M., Hsu, H. L., Wright, R. O., Wright, R. J., & Coull, B. A. (2017) · American Journal of Epidemiology · doi:10.1093/aje/kwx184 · Cited by 243 · see citing works
Postmenopausal plasma sex hormone levels and breast cancer risk over 20 years of follow-up
Zhang, X., Tworoger, S. S., Eliassen, A. H., & Hankinson, S. E. (2013) · Breast Cancer Research and Treatment · doi:10.1007/s10549-012-2391-z · Cited by 190 · see citing works
Flexible modeling of the cumulative effects of time‐dependent exposures on the hazard
Sylvestre, M., & Abrahamowicz, M. (2009) · Statistics in Medicine · doi:10.1002/sim.3701 · Cited by 168 · see citing works
Trajectory of body shape across the lifespan and cancer risk
Song, M., Willett, W. C., Hu, F. B., Spiegelman, D. L., Must, A., Wu, K., Chan, A. T., & Giovannucci, E. L. (2015) · International Journal of Cancer · doi:10.1002/ijc.29981 · Cited by 142 · see citing works
Self-citationSong, M., Hu, F. B., Wu, K., Must, A., Chan, A. T., Willett, W. C., & Giovannucci, E. L. (2016) · BMJ · doi:10.1136/bmj.i2195 · Cited by 130 · see citing works
Self-citationWeight and weight changes in early adulthood and later breast cancer risk
ROSNER, B. A., Eliassen, A. H., Toriola, A. T., Chen, W. Y., Hankinson, S. E., Willett, W. C., Berkey, C. S., & Colditz, G. A. (2017) · International Journal of Cancer · doi:10.1002/ijc.30627 · Cited by 119 · see citing works
Self-citationTime Course of Risk Factors in Cancer Etiology and Progression
Wei, E. K., Wolin, K. Y., & Colditz, G. A. (2010) · Journal of Clinical Oncology · doi:10.1200/jco.2009.26.9324 · Cited by 97 · see citing works
Abrahamowicz, M., Bartlett, G., Tamblyn, R. M., & du Berger, R. (2006) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2005.01.021 · Cited by 88 · cited 1× · see citing works
“[8] proposed parametric models with an a priori defined weight function for inclusion of weighted exposures in Cox models.”
MethodAnalysis of Exposure‐Time‐Response Relationships Using a Spline Weight Function
Hauptmann, M., Wellmann, J., Lubin, J. H., Rosenberg, P. S., & Kreienbrock, L. (2000) · Biometrics · doi:10.1111/j.0006-341x.2000.01105.x · Cited by 71 · see citing works
Xiang, H., Stallones, L. F., & Keefe, T. J. (1999) · American Journal of Industrial Medicine · doi:10.1002/(sici)1097-0274(199903)35:3 · Cited by 69 · see citing works
ROSNER, B. A., Glynn, R. J., Tamimi, R. M., Chen, W. Y., Colditz, G. A., Willett, W. C., & Hankinson, S. E. (2013) · American Journal of Epidemiology · doi:10.1093/aje/kws457 · Cited by 68 · see citing works
Self-citationAttenuation caused by infrequently updated covariates in survival analysis
Andersen, P. K. (2003) · Biostatistics · doi:10.1093/biostatistics/4.4.633 · Cited by 64 · cited 1× · see citing works
“General issues of infrequently updated covariates are considered by Andersen and Liestel [21].”
BackgroundAssociations of early life and adulthood adiposity with risk of epithelial ovarian cancer
Huang, T., Tworoger, S. S., Willett, W. C., Stampfer, M. J., & ROSNER, B. A. (2018) · Annals of Oncology · doi:10.1093/annonc/mdy546 · Cited by 53 · see citing works
Self-citationJACKKNIFE BIAS REDUCTION FOR POLYCHOTOMOUS LOGISTIC REGRESSION
Bull, S. B., Greenwood, C. M. T., & Hauck, W. W. (1997) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19970315)16:5 · Cited by 22 · see citing works
Danieli, C., Cohen, S., Liu, A., Pilote, L., Guo, L., Beauchamp, M., Marelli, A. J., & Abrahamowicz, M. (2019) · American Journal of Epidemiology · doi:10.1093/aje/kwz114 · Cited by 22 · see citing works
Hierarchical Latency Models for Dose-Time-Response Associations
Richardson, D. B., MacLehose, R. F., Langholz, B. M., & Cole, S. R. (2011) · American Journal of Epidemiology · doi:10.1093/aje/kwq387 · Cited by 19 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [4]Langholz B, Thomas D, Xiang A, Stram D. Latency analysis in epidemiologic studies of occupational exposures: application to the Colorado Plateau uranium miner’s cohort. Am J Ind Med. 1999; 35(3): 246– 56. 9987557
- [7]Vacek PM. Assessing the effect of intensity when exposure varies over time. Stat Med. 1997; 16(5): 505– 513. 9089959
- [8]Abrahamowicz M, Bartlett G, Tamblyn R, duBerger R. Modelling cumulative dose and exposure duration provides insight regarding the associations between benzodiazepines and injuries. Journal of Clinical Epidemiology 2006; 59(4): 393– 403. 16549262
Cited by
Sorted by citations
Sohi, I., Rehm, J. T., Saab, M., Virmani, L., Franklin, A., Sánchez, G., Jhumi, M., Irshad, A., Shah, H., Correia, D. M., et al. (2024) · Alcoholism Clinical and Experimental Research · doi:10.1111/acer.15493 · Cited by 38 · see citing works
Insulinemic potential of diet and risk of total and subtypes of breast cancer among US females
Romanos-Nanclares, A., Tabung, F. K., Willett, W. C., ROSNER, B. A., Holmes, M. D., Chen, W. Y., Tamimi, R. M., & Eliassen, A. H. (2022) · American Journal of Clinical Nutrition · doi:10.1093/ajcn/nqac284 · Cited by 23 · see citing works
Self-citationClinical AI Scribes in primary care: accuracy, error severity and implications for clinical practice
Draper, T. C., Cox, T., Lamb-Riddell, K., Moretti, L. A., McCormick, J., Trowell, S., Kiely, J., & Luxton, R. (2025) · BMJ Digital Health & AI · doi:10.1136/bmjdhai-2025-000092 · Cited by 10 · see citing works
“Although exponential weighting is not commonly applied in medicine, 40 medical adverse effects are known to escalate exponentially in severity, 41 and exponential weighting has previously been used in both medical 42–44 and non-medical 45 46 error/risk analysis.”
Wang, T., Chai, B., Chen, W. Y., Holmes, M. D., Erdrich, J., Hu, F. B., ROSNER, B. A., Tamimi, R. M., Willett, W. C., Kang, J. H., et al. (2024) · International Journal of Cancer · doi:10.1002/ijc.34917 · Cited by 5 · see citing works
“33 To reduce screening and surveillance bias, we also repeated the main analyses by excluding participants who did not report breast cancer screening in the last cycle ( n = 15,120), adjusting for number of questionnaires returned, and applying an inverse probability weighted model 34 for screening…”
MethodSelf-citationLiao, W., Liu, X., Kang, N., Niu, M., Song, Y., Wang, L., Wei, D., Liu, P., Sun, C., Mao, Z., et al. (2022) · Frontiers in Public Health · doi:10.3389/fpubh.2022.792394 · Cited by 4 · see citing works
Deng, S., Guo, Z., He, S., & Sun, X. (2025) · PLoS ONE · doi:10.1371/journal.pone.0335467 · Cited by 4 · see citing works
“Methodolog-ically, causal mediation analysis (bootstrap = 1000) was introduced to analyse the pathway effects of “EPWV → frailty → physical dysfunction”, and dynamic risk models were used to quantify the cumulative effects of biomarkers over time [18,19].”
Peskoe, S. B., Zhang, N., Spiegelman, D. L., & Wang, M. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1682
“Analytical methods have been proposed to model and estimate the effects of exposures as functions of time (Thomas, 2009; Langholz et al., 1999; Finkelstein, 1991; Richardson et al., 2011a; Hauptmann et al., 2000; Sylvestre and Abrahamowicz, 2009; Zanobetti et al., 2000; Richardson et al., 2011b; Schwartz et al., 2008;…”
Chemical public health disasters
Vallero, D. A., & Letcher, T. M. (2023) · Elsevier eBooks · doi:10.1016/b978-0-443-18651-6.00021-4
ROSNER, B. A., & Kempen, J. H. (2026) · Ophthalmic Epidemiology · doi:10.1080/09286586.2026.2646230
“Confidence limits for λ can be obtained either by simulation from a bivariate normal distribution 12 or by obtaining exact confidence limits for the ratio of two correlated normal random variables (Hinckley 13 ).”
Self-citationThe Nurses' Health Studies: a half-century of discovery in women's health
Romanos-Nanclares, A., Willett, W. C., Chavarro, J. E., Hu, F. B., Stampfer, M. J., ROSNER, B. A., Kang, J. H., & Eliassen, A. H. (2026) · The Lancet Obstetrics Gynaecology & Women s Health · doi:10.1016/s3050-5038(26)00220-7
Self-citationGuo, F., Qian, Z., Wang, W., Wang, F., ROSNER, B. A., & Wang, M. (2026) · Statistics in Medicine · doi:10.1002/sim.70755
“𝑋 𝑤 is a weighted sum of the exposure history up to time .”
InfluentialSelf-citationJeong, E., Jeong, W., Oh, K. H., & Jun, J. K. (2026) · Journal of Medical Internet Research · doi:10.2196/91101
- Authors
- Michels, K., Song, M., Willett, W. C., & Rosner, B.
- Affiliations
- University of California, Los Angeles (US)
- Harvard University (US)
- Brigham and Women's Hospital (US)
- Corresponding author
- Rosner, Bernard
- Venue
- European Journal of Epidemiology
- Published
- 2020-07-30
- Volume
- 35
- Issue
- 9
- Pages
- 807-819
- ISSN
- 0393-2990 (ISSN-L)
- 1573-7284
- PMC
- PMC7530062
- OpenAlex
- W3045995061
- Cited by
- 12
- References
- 30
- Citations by year
- 2026: 4 · 2025: 2 · 2024: 2 · 2023: 2 · 2022: 2
- FWCI
- 0.71
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- European Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- American Cancer Society (MRSG-17-220-01 – NEC)
- National Institutes of Health (K99 CA215314, R00 CA215314, UM1 CA186107, P01 CA87969)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Health Sciences › Medicine › Oncology › Cancer Risks and Factors
- Physical Sciences › Environmental Science › Health, Toxicology and Mutagenesis › Health, Environment, Cognitive Aging
- Keywords
- latency estimation, time-varying exposure, postmenopausal breast cancer, body mass index, alcohol consumption, cumulative exposure, hormone receptor status, Nurses' Health Study, chronic disease risk
- MeSH terms
- Adult, Alcohol Drinking, Breast Neoplasms, Chronic Disease, Disease Susceptibility, Environmental Exposure, Female, Humans, Middle Aged, Receptors, Estrogen, Receptors, Progesterone, Research Design, Risk Factors, Time Factors, Body Mass Index, Proportional Hazards Models, Epidemiologic Studies, Postmenopause, Risk Assessment
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