[R-meta] Question regarding metarate calling the Poisson model for meta-analysis

[Viechtbauer, Wolfgang (NP)]

Dear Roel,

Since you addressed this post to me directly -- just to let you know, I am unlikely to provide an answer to these questions. I would have to spend a few hours thinking about those (these are good but tricky questions), which is not something I can do at this moment. Maybe somebody else is willing to take a stab at answering them.

Best,
Wolfgang

>-----Original Message-----
>From: Willems, R.P.J. (Roel) [mailto:r.willems using amsterdamumc.nl]
>Sent: Monday, 30 May, 2022 18:14
>To: 'r-sig-meta-analysis using r-project.org'; Viechtbauer, Wolfgang (NP)
>Subject: RE: Question regarding metarate calling the Poisson model for meta-
>analysis
>
>Dear Prof. Viechtbauer,
>
>We have made excellent progress with the statistical analyses using the mixed-
>effects meta-regression model. Again, many thanks for your advice! We would very
>much appreciate if you could share your perspective on the interpretation of the
>pooled cumulative incidences using this approach.
>
>The studies analyzed provide cumulative incidence proportions from very different
>time points; for instance, at 30 days, while another provides the incidence at 90
>days or 12 months, etc. Given the definition of cumulative incidence: 'the
>proportion of a fixed population that becomes diseased in a stated period of
>time' specifying the time dimension is key for correct interpretation. How should
>we interpret the overall estimate of the model, which itself already accounts for
>the study differences in terms of follow-up time. To which time period do the
>overall incidence estimates relate?
>
>Do we need to transform the overall estimates of the different study subgroups
>that we calculated using these meta-regression models? For example, in order to
>create some sort of 'standardized' 'at 30-day' overall estimates that would
>facilitate comparison of the estimates from the different subgroup analyses? Or
>would it be better to refrain from using cumulative incidences and calculate the
>'approximate' no. of patient-days for all studies, and then meta-analyze the
>studies by setting them all to the same denominator - in terms of incidence rate
>per no. of patient days.
>
>Best,
>Roel
>
>R.P.J. Willems MD
>Medical Microbiology and Infection Prevention AII | Location AMC |
>L1-247 | Meibergdreef 9, 1105 HZ Amsterdam
>E: r.willems using amsterdamumc.nl
>www.amsterdamumc.nl | www.vumc.nl | www.amc.nl
>
>-----Oorspronkelijk bericht-----
>Van: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
>Verzonden: donderdag 24 maart 2022 12:49
>Aan: Willems, R.P.J. (Roel) <r.willems using amsterdamumc.nl>; 'r-sig-meta-analysis using r-
>project.org' <r-sig-meta-analysis using r-project.org>
>Onderwerp: RE: Question regarding metarate calling the Poisson model for meta-
>analysis
>
>Dear Roel,
>
>If you are looking at cumulative proportions, then I would personally just use a
>binomial/logistic model. If studies differ in terms of the time periods (e.g.,
>one study provides the cumulative proportion at 30 days while another at 90
>days), then this could be accounted for via a moderator in a logistic mixed-
>effects meta-regression model. rma.glmm() with measure="PLO" can do this.
>
>If you have multiple proportions for the same group of individuals at various
>follow-up timepoints, then things get more tricky. First of all, when you say
>"cumulative proportion at 30 days, at 90 days", do you mean that the first
>proportion is for number of cases between 0-30 days and the second proportion is
>for the number of cases (among the non-cases left over after 30 days) between 30-
>90 days? Or do you mean that the first proportion is for the number of cases
>between 0-30 days and the second proportion is for the number of cases between 0-
>90 days?
>
>In any case (pun intended), these proportions are not independent of each other.
>Some relevant articles:
>
>Trikalinos, T. A. & Olkin, I. (2012). Meta-analysis of effect sizes reported at
>multiple time points: A multivariate approach. Clinical Trials, 9(5), 610-620.
>https://eur04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.11
>77%2F1740774512453218&data=04%7C01%7Cr.willems%40amsterdamumc.nl%7C70ce522404
>b34722d25308da0d8c60a3%7C68dfab1a11bb4cc6beb528d756984fb6%7C0%7C0%7C6378371938073
>07577%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWw
>iLCJXVCI6Mn0%3D%7C3000&sdata=kFUD4%2BdxJW5IaTf0LpKyMrif0oLM4PWY7kWzWw7fplw%3D
>&reserved=0
>
>Trikalinos, T. A. & Olkin, I. (2008). A method for the meta-analysis of mutually
>exclusive binary outcomes. Statistics in Medicine, 27(21), 4279-4300.
>https://eur04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.10
>02%2Fsim.3299&data=04%7C01%7Cr.willems%40amsterdamumc.nl%7C70ce522404b34722d2
>5308da0d8c60a3%7C68dfab1a11bb4cc6beb528d756984fb6%7C0%7C0%7C637837193807307577%7C
>Unknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI
>6Mn0%3D%7C3000&sdata=D3zDqjjn9FvQw0ZX3Ka8RLM22Y1XJZvbL3GxdsNbDHA%3D&reser
>ved=0
>
>You will find this dataset and the corresponding analysis here:
>
>https://eur04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwviechtb.github
>.io%2Fmetadat%2Freference%2Fdat.fine1993.html&data=04%7C01%7Cr.willems%40amst
>erdamumc.nl%7C70ce522404b34722d25308da0d8c60a3%7C68dfab1a11bb4cc6beb528d756984fb6
>%7C0%7C0%7C637837193807307577%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjo
>iV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=vH4a1mYcRUMfxnYyA9VMGQ7Y
>Vr4QjLrSIppMxfeOlbs%3D&reserved=0
>
>This is actually a slightly more complex case where the outcome is the (log) odds
>ratio contrasting two conditions. The same principle applies for single groups,
>except that the outcome would then just me the log odds for individual groups.
>Note that a 'normal' model is used in this analysis, not a logistic mixed-effects
>model (for the latter, you would need the raw data).
>
>Best,
>Wolfgang