Inverse probability weighted estimation of risk under representative interventions in observational studies

Researchers are often interested in using observational data to estimate the effect on a health outcome of maintaining a continuous treatment within a pre-specified range over time; e.g. "always exercise at least 30 minutes per day". There may be many precise interventions that could achieve this range. In this paper we consider representative interventions. These are special cases of random dynamic interventions; interventions under which treatment at each time is assigned according to a random draw from a distribution that may depend on a subject's measured past. Estimators of risk under representative interventions on a time-varying treatment have previously been described based on g-estimation of structural nested cumulative failure time models. In this paper, we consider an alternative approach based on inverse probability weighting (IPW) of marginal structural models. In particular, we show that the risk under a representative intervention on a time-varying continuous treatment can be consistently estimated via computationally simple IPW methods traditionally used for deterministic static (i.e. "nonrandom" and "nondynamic") interventions for binary treatments. We present an application of IPW in this setting to estimate the 28-year risk of coronary heart disease under various representative interventions on lifestyle behaviors in the Nurses Health Study.