Abstract:
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Standard methods for estimating survival under time-varying treatments fail to account for bias that may occur when time-varying covariates exist that 1) confound the treatment-event relationship and 2) are affected by prior treatment. Initial work to address this bias resulted in the classic singly-robust estimators, which require the treatment model (inverse probability weighting (IPW)) or the potential outcome model (g-formula, g-estimation) to be correctly specified to achieve consistency. Doubly-robust estimators were then developed to provide inference that is robust to misspecification of either the treatment or potential outcome model (e.g. targeted maximum likelihood estimation (TMLE)). In theory, TMLE is more consistent and precise than singly-robust estimators, but at a substantial computational cost. Here, we apply IPW, g-formula, and TMLE to estimate a 5-year survival curve under 2 hypothetical static treatment strategies; we do so in simulated data and in a large cohort of HIV-positive patients. We compare the bias and variance of each estimator in simulated data, and provide recommendations for investigators interested in implementing these methods in large datasets.
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