# From observed event rates to event rate per anno and 5-year risk

**URL:** <https://discourse.datamethods.org/t/from-observed-event-rates-to-event-rate-per-anno-and-5-year-risk/5929>\
**Category:** meta-analysis\
**Created:** [August 30, 2022, 6:09am UTC](https://discourse.datamethods.org/t/from-observed-event-rates-to-event-rate-per-anno-and-5-year-risk/5929 "2022-08-30T06:09:35Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![a\_j](https://discourse.datamethods.org/letter_avatar_proxy/v4/letter/a/dfb087/32.png) [@a\_j](https://discourse.datamethods.org/u/a_j)\
**Post date:** [August 30, 2022, 6:09am UTC](https://discourse.datamethods.org/t/from-observed-event-rates-to-event-rate-per-anno-and-5-year-risk/5929/1 "2022-08-30T06:09:35Z")

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Dear all,

I try to figure out how the Cholesterol Treatment Trialists’ (CTT) Collaboration calculated their meta-analysis but I have some trouble to reproduce the results.

According to the Baseline characteristics table and Figure 1 of the paper (Lancet. 2010 Nov 13;376(9753):1670-81.):

- 21 trials comparing statin with control were analyzed

- the median follow-up was 4.8 years

- the number of events / patients in the control group was 8934 / 64 782

- the number of events / patients in the statin group was 7136/64 744

Dividing the number of events by the number of patients per group leads me to an event rate of 11.02% and 13.79% for the control and statin group, respectively.

Maybe it is naïve (assuming a continuous and linear relationship between event occurrence and time), but I then divided these rates by the median follow-up of 4.8, leading to event rates per anno of 2.87% and 2.30%, respectively.

However, the authors depicted per anno rates of 3.6% and 2.8%, respectively.

Moreover, the unweighted risk ratio calculated based on the above-mentioned numbers is 0.80 and not 0.78 as the depicted subtotal treatment effect in Figure 1.

Most likely, I am just naïve and my statistical calculations are wrong. Therefore, I would be happy to get some expert support/guidance here!

In the slide deck provided on the CCT website, the authors present the 5-year risk of an event. Is it possible to calculate this measure based on the published data (without individual patient data)?

I am looking forward to your replies.

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<div class="post-metadata">

**Author:** ![pmbrown](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/pmbrown/32/1382_2.png) [@pmbrown](https://discourse.datamethods.org/u/pmbrown)\
**Post date:** [August 31, 2022, 2:29pm UTC](https://discourse.datamethods.org/t/from-observed-event-rates-to-event-rate-per-anno-and-5-year-risk/5929/2 "2022-08-31T14:29:20Z")

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but you didn’t follow the equation given in their stats section, typical for meta-analysis: “log of the rate ratio per mmol/L (log RR) is calculated as _S/V_ with variance _1/V_ (and hence with 95% CI of _S/V±_1·96/√_V_), where _S_ is the sum over all trials of _d_ (_o–e_) and _V_ is the sum over all trials of _d2v_”. You can maybe find an online calculator that does the calculation. Although it can be difficult to reproduce exactly because of rounging error

[link to article](https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(10)61350-5/fulltext)