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Distributional interaction: Interpretational problems when using incidence odds ratios to assess interaction

机译：分布交互：使用发生几率比来评估交互时的解释性问题

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It is well known that the incidence odds ratio approximates the risk ratio when the disease of interest is rare, but increasingly overestimates the risk ratio as the disease becomes more common. However when assessing interaction, incidence odds ratios may not approximate risk ratios even when the disease is rare. We use the term "distributional interaction" to refer to interaction that appears when using incidence odds ratios that does not appear, or appears to a lesser degree, when using risk ratios. The interpretational problems that arise from this discrepancy can have important implications in epidemiologic research. Therefore, quantification of the relationship between the interaction odds ratio and the interaction risk ratio is warranted. In this paper, we provide a formula to quantify the differences between incidence odds ratios and risk ratios when they are used to estimate effect modification on a multiplicative scale. Using this formula, we examine the conditions under which these two estimates diverge. Furthermore, we expand this discussion to the implications of using incidence odds ratios to assess effect modification on an additive scale. Finally, we illustrate how distributional interaction arises and the problems that it causes using an example from the literature. Whenever the risk of the outcome variable is non-negligible, distributional interaction is possible. This is true even when the disease is rare (e.g., disease risk is less than 5%). Therefore, when assessing interaction on either an additive or multiplicative scale, caution should be taken in interpreting interaction estimates based on incidence odds ratios.
机译：众所周知，当所关注的疾病罕见时，发病几率比接近风险比，但是随着疾病变得更加普遍，发病率比逐渐高估了风险比。但是，在评估相互作用时，即使这种疾病很少见，发生几率也可能无法接近风险率。我们使用术语“分布性交互作用”来指代使用风险比率时未出现的发生率或较小程度的出现率时出现的交互作用。这种差异引起的解释性问题可能对流行病学研究产生重要影响。因此，有必要对相互作用几率与相互作用风险比之间的关系进行量化。在本文中，我们提供了一个公式，用于量化当用几率比和风险比来估计乘数尺度上的效果修正时的差异。使用该公式，我们检查了这两个估计值出现差异的条件。此外，我们将讨论扩展到使用发生率比来评估累加标度上的效应修正的含义。最后，我们使用文献中的例子来说明分布相互作用是如何产生的，以及它引起的问题。只要结果变量的风险不可忽略，就可以进行分布交互。即使是罕见疾病（例如，疾病风险低于5％），也是如此。因此，在以加性或乘性尺度评估相互作用时，应谨慎考虑基于发生率比的相互作用估计。

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