On computing standard errors for marginal structural Cox models |
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Authors: | R Ayesha Ali M Adnan Ali Zhe Wei |
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Institution: | 1. Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada 2. Social Dynamics, Toronto, ON, Canada 3. Canada Post, Ottawa, ON, Canada
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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. |
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