It is routinely argued that, unlike standard regression-based estimates, inverse probability weighted (IPW) estimates of the parameters of a correctly specified Cox marginal structural model (MSM) may remain unbiased in the presence of a time-varying confounder affected by prior treatment. Previously proposed methods for simulating from a known Cox MSM lack knowledge of the law of the observed outcome conditional on the measured past. Although unbiased IPW estimation does not require this knowledge, standard regression-based estimates rely on correct specification of this law. Thus, in typical high-dimensional settings, such simulation methods cannot isolate bias due to complex time-varying confounding as it may be conflated with bias due to misspecification of the outcome regression model. In this paper, we describe an approach to Cox MSM data generation that allows for a comparison of the bias of IPW estimates versus that of standard regression-based estimates in the complete absence of model misspecification. This approach involves simulating data from a standard parametrization of the likelihood and solving for the underlying Cox MSM. We prove that solutions exist and computations are tractable under many data-generating mechanisms. We show analytically and confirm in simulations that, in the absence of model misspecification, the bias of standard regression-based estimates for the parameters of a Cox MSM is indeed a function of the coefficients in observed data models quantifying the presence of a time-varying confounder affected by prior treatment. We discuss limitations of this approach including that implied by the 'g-null paradox'.
Simulation from a known Cox MSM using standard parametric models for the g-formula.