title: Evaluating Additive Interaction Using Survival Percentiles.
abstract: Evaluation of statistical interaction in time-to-event analysis is usually limited to the study of multiplicative interaction, via inclusion of a product term in a Cox proportional-hazard model. Measures of additive interaction are available but seldom used. All measures of interaction in survival analysis, whether additive or multiplicative, are in the metric of hazard, usually assuming that the interaction between two predictors of interest is constant during the follow-up period. We introduce a measure to evaluate additive interaction in survival analysis in the metric of time. This measure can be calculated by evaluating survival percentiles, defined as the time points by which different subpopulations reach the same incidence proportion. Using this approach, the probability of the outcome is fixed and the time variable is estimated. We also show that by using a regression model for the evaluation of conditional survival percentiles, including a product term between the two exposures in the model, interaction is evaluated as a deviation from additivity of the effects. In the simple case of two binary exposures, the product term is interpreted as excess/decrease in survival time (i.e., years, months, days) due to the presence of both exposures. This measure of interaction is dependent on the fraction of events being considered, thus allowing evaluation of how interaction changes during the observed follow-up. Evaluation of interaction in the context of survival percentiles allows deriving a measure of additive interaction without assuming a constant effect over time, overcoming two main limitations of commonly used approaches.
authors.affiliation: From the aUnit of Biostatistics, and bUnit of Nutritional Epidemiology, Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
authors.forename: Andrea
authors.initials: A
authors.lastname: Bellavia
authors.forename: Matteo
authors.initials: M
authors.lastname: Bottai
authors.forename: Nicola
authors.initials: N
authors.lastname: Orsini
mesh_terms: D015340:Epidemiologic Research Design; D006801:Humans; D053208:Kaplan-Meier Estimate; D011336:Probability; D016016:Proportional Hazards Models; D013223:Statistics as Topic; D016019:Survival Analysis
references.citation: Epidemiology. 2007 Nov;18(6):805-35
references.pmid: 18049195
references.citation: Am J Epidemiol. 2015 Aug 1;182(3):271-7
references.pmid: 26093508
references.citation: Epidemiology. 2009 Mar;20(2):161-6
references.pmid: 19034025
references.citation: Biometrics. 2010 Mar;66(1):105-14
references.pmid: 19459836
references.citation: Biom J. 2010 Aug;52(4):487-503
references.pmid: 20680972
references.citation: Eur J Epidemiol. 2011 Jun;26(6):433-8
references.pmid: 21344323
references.citation: Eur J Epidemiol. 2011 Jul;26(7):557-61
references.pmid: 21519893
references.citation: Am J Epidemiol. 2001 May 15;153(10):1016-20
references.pmid: 11384958
references.citation: Hum Mol Genet. 2002 Oct 1;11(20):2463-8
references.pmid: 12351582
references.citation: Am J Epidemiol. 2003 Aug 1;158(3):251-8
references.pmid: 12882947
references.citation: Am J Epidemiol. 1974 Jun;99(6):385-8
references.pmid: 4841816
references.citation: Am J Epidemiol. 1976 Dec;104(6):587-92
references.pmid: 998606
references.citation: Am J Epidemiol. 1980 Oct;112(4):465-6
references.pmid: 7424894
references.citation: Am J Epidemiol. 1980 Oct;112(4):467-70
references.pmid: 7424895
references.citation: Int J Epidemiol. 1981 Dec;10(4):383-7
references.pmid: 7327838
references.citation: Stat Med. 1983 Apr-Jun;2(2):243-51
references.pmid: 6359318
references.citation: J Clin Epidemiol. 1991;44(3):221-32
references.pmid: 1999681
references.citation: Environ Health Perspect. 1993 Dec;101 Suppl 4:59-66
references.pmid: 8206043
references.citation: Lifetime Data Anal. 2006 Dec;12(4):407-19
references.pmid: 17053975
references.citation: Ann Epidemiol. 2007 Mar;17(3):227-36
references.pmid: 17320789
references.citation: Epidemiology. 2011 Sep;22(5):713-7
references.pmid: 21558856
references.citation: Int J Epidemiol. 2012 Apr;41(2):514-20
references.pmid: 22253321
references.citation: Epidemiology. 2012 Sep;23(5):770-1
references.pmid: 22872120
references.citation: Epidemiology. 2012 Sep;23(5):733-7
references.pmid: 22732385
references.citation: Epidemiology. 2015 Mar;26(2):e17-8
references.pmid: 25643112
references.citation: Int J Biostat. 2009;5(1):Article 28
references.pmid: 26204606
references.citation: Epidemiology. 2009 Jan;20(1):14-7
references.pmid: 19234397