Analysis of time-to-event for observational studies: Guidance to the use of intensity models.

Cox regression model STRATOS initiative censoring hazard function immortal time bias multistate model prediction survival analysis time-dependent covariates

Journal

Statistics in medicine
ISSN: 1097-0258
Titre abrégé: Stat Med
Pays: England
ID NLM: 8215016

Informations de publication

Date de publication:
15 01 2021
Historique:
received: 30 03 2020
revised: 04 09 2020
accepted: 04 09 2020
pubmed: 13 10 2020
medline: 22 6 2021
entrez: 12 10 2020
Statut: ppublish

Résumé

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.

Identifiants

pubmed: 33043497
doi: 10.1002/sim.8757
doi:

Types de publication

Journal Article Observational Study Research Support, Non-U.S. Gov't

Langues

eng

Sous-ensembles de citation

IM

Pagination

185-211

Subventions

Organisme : NCI NIH HHS
ID : P30 CA046592
Pays : United States

Informations de copyright

© 2020 John Wiley & Sons Ltd.

Références

Altman DG, De Stavola BL, Love SB, Stepniewska KA. Review of survival analyses published in cancer journals. Br J Cancer. 1995;72(2):511-518.
Sauerbrei W, Abrahamowicz M, Altman DG, le Cessie S, Carpenter J, STRATOS Initiative. STRengthening analytical thinking for observational studies: the STRATOS initiative. Stat Med. 2014;33(30):5413-5432. https://doi.org/10.1002/sim.6265.
Kessing LV, Søndergaard L, Forman JL, Andersen PK. Lithium treatment and risk of dementia. Arch Gen Psychiatry. 2008;65:1331-1335.
Suissa S. Immortal time bias in pharmacoepidemiology. Am J Epidemiol. 2007;167(4):492-499.
Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol. 1983;1(11):710-719.
Keiding N. Delayed entry. Encyclopedia of Biostatistics. Hoboken, NJ: John Wiley & Sons, Ltd; 2005.
Andersen PK, Geskus RB, Witte DT, Putter H. Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol. 2012;41(3):861-870.
Andersen PK, Borgan Ø, Gill RD, Keiding N. Statistical Models Based on Counting Processes. New York, NY: Springer; 1993.
Cook RJ, Lawless JF. The Statistical Analysis of Recurrent Events. New York, NY: Springer; 2007.
Cox DR. Regression models and life-tables. J Royal Stat Soc Ser B (Methodol). 1972;34(2):187-220.
Breslow NE. Covariance analysis of censored survival data. Biometrics. 1974;30:89-99.
Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. Hoboken, NJ: John Wiley & Sons, Inc; 2002.
Cox DR. Partial likelihood. Biometrika. 1975;62:269-276.
Andersen PK, Gill RD. Cox's regression model for counting processes: a large sample study. Ann Stat. 1982;10(4):1100-1120.
Clayton DG, Hills M. Statistical Models in Epidemiology. Oxford, UK: Oxford University Press; 1993.
Joly P, Commenges D, Letenneur L. A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia. Biometrics. 1998;54:185-194.
Royston P, Lambert PC. Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model. College Station, TX: Stata Press; 2011.
Aalen OO. A linear regression model for the analysis of life times. Stat Med. 1989;8(8):907-925. https://doi.org/10.1002/sim.4780080803.
Lin DY, Ying Z. Semiparametric analysis of the additive risk model. Biometrika. 1994;81(1):61-71. https://doi.org/10.1093/biomet/81.1.61.
Martinussen T, Scheike TH. Dynamic Regression Models for Survival Data. New York, NY: Springer; 2007.
Aalen O, Borgan Ø, Gjessing H. Survival and Event History Analysis: A Process Point of View. New York, NY: Springer; 2008.
Wei LJ. The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med. 1992;11:1871-1879.
Keiding N, Andersen PK, Klein JP. The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates. Stat Med. 1997;16(2):215-224. https://doi.org/10.1002/(SICI)1097-0258(19970130)16:2<215::AID-SIM481>3.0.CO;2-J.
Bycott P, Taylor JMG. A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazards model. Stat Med. 1998;17(18):2061-2077.
Andersen PK, Liestøl K. Attenuation caused by infrequently updated covariates in survival analysis. Biostatistics. 2003;4(4):633-649.
de Bruijne MH, le Cessie S, Kluin-Nelemans HC, van Houwelingen HC. On the use of Cox regression in the presence of an irregularly observed time-dependent covariate. Stat Med. 2001;20(24):3817-3829.
Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997;53:330-339.
Tsiatis AA, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Stat Sin. 2004;4(3):809-834.
Horwitz RI, Feinstein AR. The problem of “protopathic bias” in case-control studies. Am J Med. 1980;68(2):255-258.
Gasparrini A. Modeling exposure-lag-response associations with distributed lag non-linear models. Stat Med. 2014;33(5):881-899.
Sylvestre MP, Abrahamowicz M. Flexible modeling of the cumulative effects of time-dependent exposures on the hazard. Stat Med. 2009;28(27):3437-3453.
Therneau TM, Grambsch PM. Modeling Survival Data: Extending the Cox Model. New York, NY: Springer; 2000.
Lin DY, Wei LJ, Ying Z. Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika. 1993;80(3):557-572. https://doi.org/10.1093/biomet/80.3.557.
Abrahamowicz M, MacKenzie TA. Joint estimation of time-dependent and non-linear effects of continuous covariates on survival. Stat Med. 2007;26:392-408.
Wynant W, Abrahamowicz M. Impact of the model-building strategy on inference about nonlinear and time-dependent covariate effects in survival analysis. Stat Med. 2014;33(19):3318-3337. https://doi.org/10.1002/sim.6178.
Schmoor C, Schumacher M. Effects of covariate omission and categorization when analysing randomized trials with the Cox model. Stat Med. 1997;16(3):225-237.
Bretagnolle J, Huber-Carol C. Effects of omitting covariates in Cox's model for survival data. Scand J Stat. 1988;15:125-138.
Struthers CA, Kalbfleisch JD. Misspecified proportional hazards models. Biometrika. 1986;74(2):363-369.
Hernán MA. The hazards of hazard ratios. Epidemiology. 2010;21(1):13-15.
Aalen OO, Cook RJ, Røysland K. Does Cox analysis of a randomized survival study yield a causal treatment effect? Lifetime Data Anal. 2015;21(4):579-593.
Martinussen T, Vansteelandt S, Andersen PK. Subtleties in the interpretation of hazard ratios. Lifetime Data Anal. 2020;26:833-855. https://doi.org/10.1007/s10985-020-09501-5.
Crowley JJ, Hu M. Covariance analysis of heart transplant survival data. J Am Stat Assoc. 1977;72:27-36.
Clark DA, Stinson EB, Griepp RB, Schroeder JS, Shumway NE, Harrison DC. Cardiac transplantation in man. Ann Intern Med. 1971;75(1):15-21.
Redmond C, Fisher B, Wieand HS. The methodologic dilemma in retrospectively correlating the amount of chemotherapy received in adjuvant therapy protocols with disease-free survival. Cancer Treat Rep. 1983;67:519-526.
Bonadonna G, Valagussa P. Dose-response effect of adjuvant chemotherapy in breast cancer. N Engl J Med. 1981;304(1):10-15.
Van Houwelingen HC, Putter H. Comparison of stopped Cox regression with direct methods such as pseudo-values and binomial regression. Lifetime Data Anal. 2015;21(2):180-196.
Andersen PK, Perme MP. Pseudo-observations in survival analysis. Stat Methods Med Res. 2010;19(1):71-99.
Van Houwelingen HC. Dynamic prediction by landmarking in event history analysis. Scand J Stat. 2007;34(1):70-85.
Jewell NP, Nielsen JP. A framework for consistent prediction rules based on markers. Biometrika. 1993;80(1):153-164.
Suresh K, Taylor JMG, Spratt DE, Daignault S, Tsodikov A. Comparison of joint modeling and landmarking for dynamic prediction under an illness-death model. Biom J. 2017;59(6):1277-1300.
Keogh RH, Seaman SR, Barrett JK, Taylor-Robinson D, Szczesniak R. Dynamic prediction of survival in cystic fibrosis: a landmarking analysis using UK patient registry data. Epidemiology. 2019;30(1):29-37.
Rizopoulos D. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics. 2011;67(3):819-829.
Fine JP, Gray RJA. Proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc. 1999;94(446):496-509. https://doi.org/10.1080/01621459.1999.10474144.
Rubin DB. Causal inference using potential outcomes: design, modeling. Decis J Am Stat Assoc. 2005;100(469):322-331.
Goetghebeur E, le Cessie S, De Stavola B, Moodie E, Waernbaum I. Formulating causal questions and principled statistical answers. Statistics in Medicine. 2020. http://dx.doi.org/10.1002/sim.8741.
Hernán MA, Robins JM. Causal Inference: What If. Boca Raton, FL: Chapman & Hall/CRC Press; 2020.
Chen PY, Tsiatis AA. Causal inference on the difference of the restricted mean lifetime between two groups. Biometrics. 2001;57(4):1030-1038.
Daniel RM, Cousens S, De Stavola B, Kenward MG, Sterne J. Methods for dealing with time-dependent confounding. Stat Med. 2013;32(9):1584-1618.
Blinc A, Kozak M, Šabovič M, et al. Survival and event-free survival of patients with peripheral arterial disease undergoing prevention of cardiovascular disease. Int Angiol. 2017;35:216-227.
Blinc A, Kozak M, Šabovič M, et al. Prevention of ischemic events in patients with peripheral arterial disease - design, baseline characteristics and 2-year results an observational study. Int Angiol. 2011;30:555-566.
Puri P, Sanyal AJ. Nonalcoholic fatty liver disease: definitions, risk factors and workup. Clin Liver Dis. 2012;1:99-103.
Tapper EB, Loomba R. Nonalcoholic fatty liver disease, metabolic syndrome, and the fight that will define clinical practice for a generation of hepatologists. Hepatology. 2018;67:1657-1659.
Allen AM, Therneau TM, Larson JJ, Coward A, Somers VK, Kamath PS. Nonalcoholic fatty liver disease incidence and impact on metabolic burden and death: a 20 year community study. Hepatology. 2018;67:1726-1736.
St Sauver JL, Grossardt BR, Yawn BP, et al. Data resource profile: the Rochester epidemiology project (REP) medical records-linkage system. Int J Epidemiol. 2012;41(6):1614-1624. https://doi.org/10.1093/ije/dys195.
Van Houwelingen HC, Putter H. Dynamic Prediction in Clinical Survival Analysis. Boca Raton, FL: CRC Press; 2012.
Cook RJ, Lawless JF. Multistate Models for the Analysis of Life History Data. Boca Raton, FL: Chapman & Hall/CRC Press; 2018.
Hougaard P. Analysis of Multivariate Survival Data. New York, NY: Springer; 2000.
Perme MP, Stare J, Estève J. On estimation in relative survival. Biometrics. 2012;68(1):113-120.

Auteurs

Per Kragh Andersen (P)

Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark.

Maja Pohar Perme (M)

Department of Biostatistics and Medical Informatics, Medical faculty, University of Ljubljana, Ljubljana, Slovenia.

Hans C van Houwelingen (HC)

Department of Biomedical Data Sciences, Leiden University, Leiden, The Netherlands.

Richard J Cook (RJ)

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.

Pierre Joly (P)

Inserm, ISPED, Bordeaux Populations Health Research Center, University of Bordeaux, Bordeaux, France.

Torben Martinussen (T)

Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark.

Jeremy M G Taylor (JMG)

Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA.

Michal Abrahamowicz (M)

Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada.

Terry M Therneau (TM)

Division of Biomedical Statistics and Informatics, Mayo Clinic, Rochester, New York, USA.

Articles similaires

[Redispensing of expensive oral anticancer medicines: a practical application].

Lisanne N van Merendonk, Kübra Akgöl, Bastiaan Nuijen
1.00
Humans Antineoplastic Agents Administration, Oral Drug Costs Counterfeit Drugs

Smoking Cessation and Incident Cardiovascular Disease.

Jun Hwan Cho, Seung Yong Shin, Hoseob Kim et al.
1.00
Humans Male Smoking Cessation Cardiovascular Diseases Female
Humans United States Aged Cross-Sectional Studies Medicare Part C
1.00
Humans Yoga Low Back Pain Female Male

Classifications MeSH