title: On computing standard errors for marginal structural Cox models.
abstract: In recent decades, marginal structural models have gained popularity for proper adjustment of time-dependent confounders in longitudinal studies through time-dependent weighting. When the marginal model is a Cox model, using current standard statistical software packages was thought to be problematic because they were not developed to compute standard errors in the presence of time-dependent weights. We address this practical modelling issue by extending the standard calculations for Cox models with case weights to time-dependent weights and show that the coxph procedure in R can readily compute asymptotic robust standard errors. Through a simulation study, we show that the robust standard errors are rather conservative, though corresponding confidence intervals have good coverage. A second contribution of this paper is to introduce a Cox score bootstrap procedure to compute the standard errors. We show that this method is efficient and tends to outperform the non-parametric bootstrap in small samples.
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada, aali@uoguelph.ca.
authors.forename: R Ayesha
authors.initials: RA
authors.lastname: Ali
authors.forename: M Adnan
authors.initials: MA
authors.lastname: Ali
authors.forename: Zhe
authors.initials: Z
authors.lastname: Wei
mesh_terms: D003198:Computer Simulation; D016001:Confidence Intervals; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies / Q000379:methods*; D016016:Proportional Hazards Models