  Observational studies are frequently used to estimate the effect of an
exposure or treatment on an outcome. To obtain an unbiased estimate of the
treatment effect, it is crucial to measure the exposure accurately. A common
type of exposure misclassification is recall bias, which occurs in
retrospective cohort studies when study subjects may inaccurately recall their
past exposure. Particularly challenging is differential recall bias in the
context of self-reported binary exposures, where the bias may be directional
rather than random , and its extent varies according to the outcomes
experienced. This paper makes several contributions: (1) it establishes bounds
for the average treatment effect (ATE) even when a validation study is not
available; (2) it proposes multiple estimation methods across various
strategies predicated on different assumptions; and (3) it suggests a
sensitivity analysis technique to assess the robustness of the causal
conclusion, incorporating insights from prior research. The effectiveness of
these methods is demonstrated through simulation studies that explore various
model misspecification scenarios. These approaches are then applied to
investigate the effect of childhood physical abuse on mental health in
adulthood.
