  Stratifying factors, like age and gender, can modify the effect of treatments
and exposures on risk of a studied outcome. Several effect measures, including
the relative risk, hazard ratio, odds ratio, and risk difference, can be used
to measure this modification. It is known that choice of effect measure may
determine the presence and direction of effect-measure modification. We show
that considering the opposite outcome -- for example, recovery instead of death
-- may similarly influence effect-measure modification. In fact, if the
relative risk for the studied outcome and the relative risk for the opposite
outcome agree about the direction of effect-measure modification, then so will
the two cumulative hazard ratios, the risk difference, and the odds ratio. When
risks are randomly sampled from the uniform (0,1) distribution, the probability
of this happening is 5/6. Disagreement is probable enough that researchers
considering one relative risk should also consider the other and further
discussion if they disagree. (If possible, researchers should also report
estimated risks.) We provide examples through case studies on HCV, COVID-19,
and bankruptcy following melanoma treatment.
