  Standard measures of effect, including the risk ratio, the odds ratio, and
the risk difference, are associated with a number of well-described
shortcomings, and no consensus exists about the conditions under which
investigators should choose one effect measure over another. In this paper, we
introduce a new framework for reasoning about choice of effect measure by
linking two separate versions of the risk ratio to a counterfactual causal
model. In our approach, effects are defined in terms of "counterfactual outcome
state transition parameters", that is, the proportion of those individuals who
would not have been a case by the end of follow-up if untreated, who would have
responded to treatment by becoming a case; and the proportion of those
individuals who would have become a case by the end of follow-up if untreated
who would have responded to treatment by not becoming a case. Although
counterfactual outcome state transition parameters are generally not identified
from the data without strong monotonicity assumptions, we show that when they
stay constant between populations, there are important implications for model
specification, meta-analysis, and research generalization.
