[R-meta] meta-analysis of ratios or ratios/ratios? can you help me ?

[Viechtbauer, Wolfgang (NP)]

Dear Martin,

I suspect you are not getting any responses as it is a bit difficult (at least for me) to follow your question. But if I understand your question correctly, then here are some thoughts:

It is not clear to me if the authors report mean(FINAL)/mean(BASAL) or if they report mean(FINAL/BASAL). In other words, do they report the ratio of the means of the mean of the (individual) ratios?

If it is the former, then mean(FINAL) / mean(BASAL) is the ratio of the means, which is a well-known effect size measure in meta-analysis (which is log transformed for the analysis). This measure is sometimes called the (log) response ratio. But to compute the sampling variance of log(mean(FINAL) / mean(BASAL)), one needs to known the means and SDs of the FINAL and BASAL values.

If it is the latter, then mean(FINAL/BASAL) is really just a mean and could be meta-analyzed as such (assuming that SD(FINAL/BASAL) or the corresponding standard error are reported). Note though that ratios such as FINAL/BASAL are not 'symmetric' around 1. For example, if FINAL/BASAL is 2 for one person and FINAL/BASAL is 0.5 for another person (which is really the same magnitude on such a ratio scale, but in opposite directions), then mean(FINAL/BASAL) is not 1, which is counter-intuitive.

As for the analysis approaches: You can do approach 1 using a multilevel/multivariate model with rma.mv().

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Martin Lobo via R-sig-meta-analysis
> Sent: Wednesday, January 10, 2024 14:07
> To: r-sig-meta-analysis using r-project.org
> Cc: Martin Lobo <mlobo4370 using hotmail.com>
> Subject: [R-meta] meta-analysis of ratios or ratios/ratios? can you help me ?
>
> Hello everyone.
>
> I'm going to expand the explanation to see if someone can help me. I want to
> investigate the changes in uCRP with a specific treatment vs placebo. The
> difficulty I have is that very few report this quantitative variable (uCRP). But
> I have found many papers that report the FINAL/BASAL relationship in both
> branches. From this data I came up with two strategies.
> 1- Analyze the FINAL/BASAL relationship in the two branches with their
> respective confidence intervals.
> 2- Analyze the ratio of ratios (FINAL/BASAL TREATMENT BRANCH / FINAL/BASAL
> PLACEBO BRANCH) in both branches with their respective confidence intervals.
>
> I can't find how to analyze option one with metagen, since I can only enter the
> TE and the seTE. I don't know if with this data the two branches could be
> analyzed directly in some way or directly with metafor.
>
> Although option 2 could be analyzed with metagen using OR or RR as effect
> measures, I would not know if it would be conceptually correct, since the data
> are the percentage changes of a continuous variable and not the proportion of
> binary events.
> I would appreciate help with this analysis.
>
> Have a great year everyone.
>
> Martin from argentina
>
> Lorenzo Martín Lobo MTSAC, FACC, FESC
> Especialista Jerarquizado en Cardiología
> Jefe de Dpto Enf. Cardiovasculares y Cardiometabolismo Hospital Militar Campo de
> Mayo.
> Jefe de Cardiología Hospital Militar Campo de Mayo
> Ex Jefe de Unidad Coronaria Hospital Militar Campo de Mayo
> Miembro Titular de la Sociedad Argentina de Cardiología
> Fellow American College of Cardiology
> Fellow European Society of Cardiology
> Ex Miembro del Area de Investigación de la SAC
> Ex Director del Consejo de Aterosclerosis y Trombosis de la SAC
> Miembro Asesor del Consejo de Aterosclerosis y Trombosis de la SAC
> Ex Director del Consejo de Epidemiología y Prevención Cardiovascular de la SAC
> Miembro Asesor del Consejo de Epidemiología y Prevención Cardiovascular de la
> SAC
> Experto en Lipidos de la Sociedad Argentina de Lipidos.
> Miembro de la Sociedad Argentina de Lipidos.
> Instructor de ACLS de la American Heart Association