Recommended calculation to determine box sizes of point estimates

[TACdeVries]

Dear Adayim/all,

Is there a recommended formula to determine the box sizes of the point estimates based on weights as used in meta-analytic models?

My best attempt so far is dividing the weight (in %) by 10 and taking the square root hereof. This results in values roughly between 0.5 and 1.5 and looks reasonable while still being proportional to the study weight. However, I don't want to give the wrong impression and would prefer a 'standard' method.

Does anyone know what the 'usual' formula is to determine the size? Or are there other suggestions to determine the box sizes based on weight?

Thanks,
Tim

[TACdeVries]

Dear all,

I noticed a line of code in another thread. That one seems to work well after a few minor tweak. Thus, what was used was:

x <- sqrt(1/sizes)
sizes <- x/max(x)

As I am using weights which are already inversely related to the SE, I got satisfying results by using the code below. As expected this resulted in box sizes being proportional to the study weight.

sqrt(weights(model))/max(sqrt(weights(model)))

Hopefully this code is also to someone else's liking.

Best,
Tim

[adayim]

Hi Tim,

Thank you for your advice. I attempted to compute a weight earlier, as you said, and I'm not sure whether I did it right. I am not an expert in meta-analysis. As a result, I deleted the weight calculating code. Another reason I'm doing so is that this package isn't only for meta-analysis. Some people may want to present the model coefficients, and this is the main reason for developing this package. They want to have different weighting methods. As a result, I have left it to the user to decide.

I have pinned this issue so others can check it out and provide some other suggestions.

Thank you very much for this.

[TACdeVries]

Thanks Adayim,

Looking forward to seeing suggestions of others. Maybe some are more experienced with the code underlying meta-analytic packages. I will try to contact a developer of one of the major meta-analysis packages to see if I can get a response.

[TACdeVries]

I've had contact with Prof. Wolfgang, developer of the Metafor package and his method is quite similar. However, he restricts the minimum to 0.5 and maximum size to 1.5.

In a nutshell:

plim <- c(0.5, 1.5)
wi <- sqrt(weights(model))
rng <- max(wi, na.rm=TRUE) - min(wi, na.rm=TRUE) 
psize <- (wi - min(wi, na.rm=TRUE)) / rng
psize <- (psize * (plim[2] - plim[1])) + plim[1]

The exact coding used in the metafor package: weblink

   ### set default point sizes (if not specified by user)

   if (is.null(psize)) {
      if (length(plim) < 2L)
         stop(mstyle$stop("Argument 'plim' must be of length 2 or 3."))
      wi <- sqrt(weights)
      if (!is.na(plim[1]) && !is.na(plim[2])) {
         rng <- max(wi, na.rm=TRUE) - min(wi, na.rm=TRUE)
         if (rng <= .Machine$double.eps^0.5) {
            psize <- rep(1, k)
         } else {
            psize <- (wi - min(wi, na.rm=TRUE)) / rng
            psize <- (psize * (plim[2] - plim[1])) + plim[1]
         }
      }
      if (is.na(plim[1]) && !is.na(plim[2])) {
         psize <- wi / max(wi, na.rm=TRUE) * plim[2]
         if (length(plim) == 3L)
            psize[psize <= plim[3]] <- plim[3]
      }
      if (!is.na(plim[1]) && is.na(plim[2])) {
         psize <- wi / min(wi, na.rm=TRUE) * plim[1]
         if (length(plim) == 3L)
            psize[psize >= plim[3]] <- plim[3]
      }
      if (all(is.na(psize)))
         psize <- rep(1, k)
   }

[adayim]

I am planning to keep this issue opened if it is OK with you. So others can see this. Thank you.