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# Cumulative incidence difference vs Hazard Ratio

We ran a Population-Level-Estimation study and we are requested by the journal statistical reviewers to provide cumulative incidence differences at designated time points (6 months, 12 months, 18 months, 24 months…) instead of hazard ratios.

I was wondering if there is any package that we can use to generate cumulative incidence difference and display in Evidence Explorer? Thank you very much! @schuemie @edburn @Adam_Black

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Correct me if I’m wrong but I think cumulative incidence is what is calculated in the Atlas Incidence rates tab and by the CohortIncidence R package. You could use Atlas or the CohortIncidence package to compute crude incidence in each cohort and report the difference but I’m guessing that is not what the reviewers are asking for. It sounds like they want an adjusted measure of absolute risk difference instead of relative risk. Is this a correct interpretation of your question?

I’m not sure how to do this with Hades but Martijn or Ed might know.

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Thanks @Adam_Black Yes they want a PS-adjusted measure of absolute risk difference (which is the difference in cumulative incidence between 2 groups at 6 months, 12 months, 18 months, 24 months of follow-up) instead of relative risk (hazard ratio).

Ok, I had to do some lookup as to the IR diff and CI Diff (IR diff seems to refer to rate, while CI diff seems to refer to proportion of people (ie: per person, not per time). In either case, Atlas can’t help you here because you are going to want to do is calculate the incidence proportion and incidence rate between the PS-matched populations with Time-At-Risk of 6mo, 12mo, 18mo and 24mo. You could do this using the CohortIncidence package if you can extract the PS-matched subjects from each cohort, and do the analysis only on those two sub-cohorts. You’d then specify the 4 time at risk windows, and calculate the difference of rates/proportions.

If you are familiar with the output from Population Level Estimation pacakge, you might be able to get the answer you want by definign the 4 time at risk windows, and caculating each IR/IP by counting the distinct people with cases / distinct people or cases / total follow up time. You’ll need to ask someone more familiar with PLE package for specific instructions on how to configure the analysis to do that, but I believe you just need to specify the additional time at risks so you get the result for each time window.

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Please correct me if I’m wrong, but I believe that if we assume no competing risks, the cumulative incidence is equal to one minus the Kaplan Meier estimator? @wallislau : are you modeling competing risks? If not, you can easily derive the cumulative risk and risk differences from the KM plot.

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Thanks @schuemie you are right, the cumulative incidence is 1-KM estimator. I am aware that the KM estimator values and their confidence intervals are in the “kaplan_meier_dist” file after executing the PLE - we used negative control calibration for the CIs of hazard ratios, I wonder if we can calibrate the CIs of the absolute cumulative incidence difference too?

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