The Validity and Efficiency of Hypothesis Testing in Observational Studies with Time-Varying Exposures

The fundamental obstacle of observational studies is that of unmeasured confounding.  If all potential confounders are measured within the data, and treatment occurs at but a single time-point, conventional regression adjustment methods provide consistent estimates and allow for valid hypothesis testing in a relatively straightforward manner.  In situations for which treatment occurs at several successive timepoints, as in many longitudinal studies, another type of confounding is also problematic: even if all confounders are known and measured in the data, time-dependent confounding may bias estimates and invalidate testing due to collider-stratification.  While ``causal inference methods'' can adequately adjust for time-dependent confounding, these methods require strong and unverifiable assumptions.  Alternatively, instrumental variable analysis can be used.  By means of a simple illustrative scenario and simulation studies, this paper sheds light on the issues involved when considering the relative merits of these two approaches for the purpose of hypothesis testing in the presence of time-dependent confounding.