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. 2020 Jun 29;190(1):142–149. doi: 10.1093/aje/kwaa122

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© The Author(s) 2020. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

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Graphical depiction of identification using the prior event rate ratio (PERR) and the prior event rate difference (PERD). Observed incidence rates, denoted by circles for the control group and triangles for the treated group (connected by solid lines to highlight the change between the pretreatment and the posttreatment periods), are identical in both panels. The observed incidence rate in the control group increased from 27.24 in the pretreatment period to 30.41 in the posttreatment period. A) On the multiplicative scale, that is an increase by a factor of 1.12. Using PERR, the counterfactual posttreatment rate in the treated group is estimated to be the observed pretreatment rate, 62.07, increased by the same factor: (dashed lines highlight the change between the pretreatment rate and the counterfactual posttreatment rate). B) On the additive scale, the increase in the control group is 3.17. Using PERD, the counterfactual posttreatment rate in the treated group is estimated to be the observed pretreatment rate, 62.07, increased by 3.17, that is . All rates are expressed as events per 1,000 person-years. Data for this illustration is from Table 4 in Othman et al. (5).

Inline graphic — Graphical depiction of identification using the prior event rate ratio (PERR) and the prior event rate difference (PERD). Observed incidence rates, denoted by circles for the control group and triangles for the treated group (connected by solid lines to highlight the change between the pretreatment and the posttreatment periods), are identical in both panels. The observed incidence rate in the control group increased from 27.24 in the pretreatment period to 30.41 in the posttreatment period. A) On the multiplicative scale, that is an increase by a factor of 1.12. Using PERR, the counterfactual posttreatment rate in the treated group is estimated to be the observed pretreatment rate, 62.07, increased by the same factor: (dashed lines highlight the change between the pretreatment rate and the counterfactual posttreatment rate). B) On the additive scale, the increase in the control group is 3.17. Using PERD, the counterfactual posttreatment rate in the treated group is estimated to be the observed pretreatment rate, 62.07, increased by 3.17, that is . All rates are expressed as events per 1,000 person-years. Data for this illustration is from Table 4 in Othman et al. (5).