title: Structural Nested Cumulative Failure Time Models to Estimate the Effects of Interventions.
abstract: In the presence of time-varying confounders affected by prior treatment, standard statistical methods for failure time analysis may be biased. Methods that correctly adjust for this type of covariate include the parametric g-formula, inverse probability weighted estimation of marginal structural Cox proportional hazards models, and g-estimation of structural nested accelerated failure time models. In this article, we propose a novel method to estimate the causal effect of a time-dependent treatment on failure in the presence of informative right-censoring and time-dependent confounders that may be affected by past treatment: g-estimation of structural nested cumulative failure time models (SNCFTMs). An SNCFTM considers the conditional effect of a final treatment at timemon the outcome at each later timekby modeling the ratio of two counterfactual cumulative risks at timekunder treatment regimes that differ only at timem. Inverse probability weights are used to adjust for informative censoring. We also present a procedure that, under certain "no-interaction" conditions, uses the g-estimates of the model parameters to calculate unconditional cumulative risks under nondynamic (static) treatment regimes. The procedure is illustrated with an example using data from a longitudinal cohort study, in which the "treatments" are healthy behaviors and the outcome is coronary heart disease.
authors.affiliation: Research Fellow in the Department of Epidemiology, Harvard School of Public Health, Boston, MA 02115.
authors.forename: Sally
authors.initials: S
authors.lastname: Picciotto
authors.affiliation: Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA 02115.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Hernán
authors.affiliation: Department of Epidemiology, Harvard School of Public Health, Boston, MA 02115.
authors.forename: John H
authors.initials: JH
authors.lastname: Page
authors.affiliation: Department of Epidemiology, Harvard School of Public Health, Boston, MA 02115.
authors.forename: Jessica G
authors.initials: JG
authors.lastname: Young
authors.affiliation: Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA 02115.
authors.forename: James M
authors.initials: JM
authors.lastname: Robins
keywords: Causal inference; Coronary heart disease; Epidemiology; G-estimation; Inverse probability weighting