metaprop in R: same results for random effects, fixed effects and prediction interval [closed]

Question

I am using the metaprop function in R to obtain estimates for a fixed effects model, a random effects model and a prediction interval.

I've done this many times, without any issues, but I'm puzzled by a result I recently arrived at.

The code I'm using is:

    metaprop(df1$r, df1$n, df1$A, method.ci="WS", sm="PLOGIT", method.tau="ML", prediction=TRUE, level.predict=0.95, method="GLMM")

I'm getting the same proportion and same confidence interval, to 4 decimal places, for each of the fixed effects and random effects. The prediction interval also matched the confidence intervals for both models.

Is this just a coincidence or is something going wrong? The heterogeneity statistics could explain it, as I'm aware that the difference between RE and FE is the presence of between-study variation being taken into account for RE models. The heterogeneity results are:

 Quantifying heterogeneity:
    tau^2 = 0; H = 1.00; I^2 = 0.0%

 Test of heterogeneity:
     Q d.f.  p-value             Test
  8.11   12   0.7767        Wald-type
 19.39   12   0.0795 Likelihood-Ratio

Although the individual proportions and interval are generally relatively similar, they aren't all the same, so should the between-study variance really be zero?

Any help with this would be appreciated. I feel that the results are correct, but a better explanation would be welcome.

Answer 1

The value of $I^2 = \frac{Q - \mathrm{df}}{Q}$. If $Q < \mathrm{df}$ then this would be negative so it is conventional to truncate it at zero. This is not specific to analysis of proportions or indeed to the specific choice of software you have made.