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 time m on the outcome at each later time k by modeling the ratio of two counterfactual cumulative risks at time k under treatment regimes that differ only at time m. 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.

KEY WORDS:

• Causal inference
• Coronary heart disease
• Epidemiology
• G-estimation
• Inverse probability weighting

Acknowledgments

This research was funded by NIH grants R01 HL34594 and R01 HL080644. The authors thank Roger Logan for programming support, and JoAnn Manson, Frank Hu, and Walter Willett for helpful comments on the article.

Notes

^aThis variable is omitted from the model for R_m when R_m represents behavior consistent with an intervention on this risk factor.