  Objective: Recently Doi et al. argued that risk ratios should be replaced
with odds ratios in clinical research. We disagreed, and empirically documented
the lack of portability of odds ratios, while Doi et al. defended their
position. In this response we highlight important errors in their position.
  Study Design and Setting: We counter Doi et al.'s arguments by further
examining the correlations of odds ratios, and risk ratios, with baseline risks
in 20,198 meta-analyses from the Cochrane Database of Systematic Reviews.
  Results: Doi et al.'s claim that odds ratios are portable is invalid because
1) their reasoning is circular: they assume a model under which the odds ratio
is constant and show that under such a model the odds ratio is portable; 2) the
method they advocate to convert odds ratios to risk ratios is biased; 3) their
empirical example is readily-refuted by counter-examples of meta-analyses in
which the risk ratio is portable but the odds ratio isn't; and 4) they fail to
consider the causal determinants of meta-analytic inclusion criteria: Doi et
al. mistakenly claim that variation in odds ratios with different baseline
risks in meta-analyses is due to collider bias. Empirical comparison between
the correlations of odds ratios, and risk ratios, with baseline risks show that
the portability of odds ratios and risk ratios varies across settings.
  Conclusion: The suggestion to replace risk ratios with odds ratios is based
on circular reasoning and a confusion of mathematical and empirical results. It
is especially misleading for meta-analyses and clinical guidance. Neither the
odds ratio nor the risk ratio is universally portable. To address this lack of
portability, we reinforce our suggestion to report variation in effect measures
conditioning on modifying factors such as baseline risk; understanding such
variation is essential to patient-centered practice.
