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I'm very new to the metafor package and wanted to check my interpretation of the model output, specifically in regards to calculating relative risks and confidence intervals.

I've used the rma.mv() function for a meta-analysis of incidence rates of tuberculosis in prisons. Incidence rates were extracted for each study identified by systematic review, with some studies reporting multiple rates for different years or locations. (Therefore 'cohorts' are nested within 'studies'.)

Here's an example of the data:

study_id cohort_id n_diagnosed person_years who_region passive_active
   131       354        77      14298.00       a        1Passive
    93       120        5       277150.00      a        1Passive
    93       121        14      277150.00      a        1Passive
    93       122        15      277150.00      a        1Passive
    136       382        2      2000.00        Africa   2Active
    136       383        7      2000.00        Africa   2Active
    187       516        16     100000.00      Africa   3Not Specified
    187       517        2      100000.00      S.E Asia 3Not Specified

I've used the following to calculate the incidence rates and variances:

pd_ec <- escalc(
   measure = 'IR',
   xi = data_cohort_incidence$number_diagnosed,
   ti = data_cohort_incidence$person_years
)

And here is a multivariate model stratifying by whether the WHO region and whether the data was actively or passively collected.

m0 <- rma.mv(pd_ec$y, pd_ec$v, method='REML', mods = ~ who_region_mod + passive_active,
        random= ~ 1 | study_id,
        tdist=TRUE,
        data=data_cohort_incidence)

I get this output:enter image description here

My understanding is that estimates indicate the incidence rate per person year, with the incidence rate of, for example, Africa being equal to the intercept summed with the estimate for the African Region (-.0028+.0167 = .0139). (https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/subgroup-analyses-in-three-level-models.html) Is this interpretation correct? Is the incidence rate for active screening equal to the intercept + Active (-.0028+.0080) = .0052)?

Relative risks would be obtained by dividing the rates for each region or screening type by the intercept? And how would one calculate the 95% Confidence Intervals for relative risk? Thanks in advance!

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