# [R-meta] Fwd: predicted intervals in metafor

Raynaud Armstrong r@yn@ud@@rm@trong @ending from gm@il@com
Fri Jun 8 19:03:16 CEST 2018

```---------- Forwarded message ----------
From: Raynaud Armstrong <raynaud.armstrong using gmail.com>
Date: Fri, Jun 8, 2018 at 1:02 PM
Subject: Re: [R-meta] predicted intervals in metafor
To: Michael Dewey <lists using dewey.myzen.co.uk>

Thanks Michael. *I got the following output for my meta-regression. My
heterogeneity statistics are all 0 - what does this mean?*

#meta-regression
> metareg <- rma (yi=cohen, vi=se_cohen, mods = ~ mean_age + year +
country, data=metav)
Warning message:
In rma(yi = cohen, vi = se_cohen, mods = ~mean_age + year + country,  :
Studies with NAs omitted from model fitting.
> metareg

Mixed-Effects Model (k = 7; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0 (SE = 0.1825)
tau (square root of estimated tau^2 value):             0
I^2 (residual heterogeneity / unaccounted variability): 0.00%
H^2 (unaccounted variability / sampling variability):   1.00
R^2 (amount of heterogeneity accounted for):            NA%

Test for Residual Heterogeneity:
QE(df = 3) = 0.3265, p-val = 0.9550

Test of Moderators (coefficient(s) 2:4):
QM(df = 3) = 1.6838, p-val = 0.6406

Model Results:

estimate       se     zval    pval     ci.lb     ci.ub
intrcpt      39.8696  65.5910   0.6079  0.5433  -88.6863  168.4255
mean_age      0.0456   0.0373   1.2223  0.2216   -0.0275    0.1187
year         -0.0203   0.0332  -0.6109  0.5413   -0.0852    0.0447
countryUSA   -0.1974   0.3959  -0.4987  0.6180   -0.9733    0.5785

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Ray

On Fri, Jun 8, 2018 at 7:02 AM, Michael Dewey <lists using dewey.myzen.co.uk>
wrote:

> Dear Ray
>
>
> http://www.metafor-project.org/doku.php/analyses
>
> You need examples for mixed effects but all the examples are worth
> examining as are the other pages found via the left navigation.
>
> Michael
>
>
> On 07/06/2018 18:41, Raynaud Armstrong wrote:
>
>> Dear Wolfgang,
>> Are there any good meta-regression tutorials or examples in R using
>> metafor
>> package?
>>
>> Thanks
>> Ray
>>
>> On Wed, Jun 6, 2018 at 5:02 AM, Viechtbauer, Wolfgang (SP) <
>> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>
>> Dear Rav,
>>>
>>> The default is REML.
>>>
>>> Checking whether the sampling distribution of the outcome measure is
>>> normal is not something that you can do in your observed data. Outcome
>>> measures typically used in meta-analysis all have, at least
>>> asymptotically,
>>> a normal sampling distribution. So, as long as your sample sizes are not
>>> too small, this is not something you typically have to worry about.
>>>
>>> As for the distribution of the true effects: In principle, this can be
>>> checked in the actual data, but this is difficult to do. One possible
>>> approach is to examine the distribution of the predicted random effects,
>>> which you can get with the ranef() function.
>>>
>>> Best,
>>> Wolfgang
>>>
>>> -----Original Message-----
>>> From: Raynaud Armstrong [mailto:raynaud.armstrong using gmail.com]
>>> Sent: Tuesday, 05 June, 2018 19:24
>>> To: r-sig-meta-analysis using r-project.org; Viechtbauer, Wolfgang (SP)
>>> Subject: Fwd: [R-meta] predicted intervals in metafor
>>>
>>> Dear Wolfgang,
>>> Sorry for not being clear. I was just wanting to know if I needed to
>>> check
>>> normality of my effect sizes collectively - which you have already
>>> answered. I would also like to know the default method in random effects
>>> meta-analysis in metafor - is it REML or DL?
>>>   How can we test the assumption that the sampling distributions are
>>> normal
>>> and that the underlying true effects are normal?
>>>
>>>
>>> Thanks
>>> RAv
>>>
>>> On Tue, Jun 5, 2018 at 12:48 PM, Viechtbauer, Wolfgang (SP) <
>>> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>> Dear Raynaud,
>>>
>>> Not sure what you mean by 'default method'. Do you mean the method for
>>> computing the prediction interval? By default, it is:
>>>
>>> mu-hat +/- 1.96 sqrt(SE(mu-hat)^2 + tau^2)
>>>
>>> where 'mu-hat' is the estimate of mu, SE(mu-hat) is the corresponding
>>> standard error, and tau^2 is the estimated amount of heterogeneity
>>> (between-study variance).
>>>
>>> When using the Knapp & Hartung method (argument: test="knha"), then
>>> instead of 1.96 (or rather qnorm(.975) to be exact), the equation uses
>>> the
>>> 97.5th percentile from a t-distribution with k-1 df (where k is the
>>> number
>>> of studies).
>>>
>>> As for the distribution of the effect sizes: The RE model does not assume
>>> that the collection of observed effects is normally distributed. It
>>> assumes
>>> that the sampling distributions are normal and that the underlying true
>>> effects are normal. However, that does not imply that the (marginal)
>>> distribution of the observed effects is normally distributed.
>>>
>>> Best,
>>> Wolfgang
>>>
>>> -----Original Message-----
>>> From: Raynaud Armstrong [mailto:raynaud.armstrong using gmail.com]
>>> Sent: Tuesday, 05 June, 2018 17:57
>>> To: r-sig-meta-analysis using r-project.org; Viechtbauer, Wolfgang (SP)
>>> Subject: Fwd: [R-meta] predicted intervals in metafor
>>>
>>> Hi everyone!
>>> I would like to know what is the default method in random effects
>>> meta-analysis in metafor.
>>> My effect size (cohen's d) is not normally distributed. Does that matter?
>>> Thanks
>>> RAv
>>> ---------- Forwarded message ----------
>>> From: Raynaud Armstrong <raynaud.armstrong using gmail.com>
>>> Date: Sat, Dec 16, 2017 at 6:34 AM
>>> Subject: Re: [R-meta] predicted intervals in metafor
>>> To: "Viechtbauer Wolfgang (SP)" <wolfgang.viechtbauer@
>>> maastrichtuniversity.nl>
>>>
>>> Perfect - it worked!
>>> Thanks
>>>
>>> On Fri, Dec 15, 2017 at 3:38 AM, Viechtbauer Wolfgang (SP) <
>>> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>> Dear Raynaud,
>>>
>>> Once you have the SMD values and corresponding sampling variances, the
>>> code is the same. Here is an example:
>>>
>>> library(metafor)
>>>
>>> dat <- get(data(dat.normand1999))
>>>
>>> ### calculate SMDs and corresponding sampling variances
>>> dat <- escalc(measure="SMD", m1i=m1i, sd1i=sd1i, n1i=n1i, m2i=m2i,
>>> sd2i=sd2i, n2i=n2i, data=dat)
>>> dat
>>>
>>> ### meta-analysis of SMD values using a random-effects model
>>> res <- rma(yi, vi, data=dat)
>>> res
>>>
>>> ### get prediction/credibility interval
>>> predict(res)
>>>
>>> If you have calculated the SMD values and variances yourself, you can
>>> skip
>>> the escalc() step and go straight to rma(). Adjust variables names as
>>> needed.
>>>
>>> Best,
>>> Wolfgang
>>>
>>> -----Original Message-----
>>> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
>>> bounces using r-project.org] On Behalf Of Raynaud Armstrong
>>> Sent: Friday, 15 December, 2017 1:37
>>> To: r-sig-meta-analysis using r-project.org
>>> Subject: [R-meta] predicted intervals in metafor
>>>
>>> Hi there,
>>> I would like to calculate predicted intervals in addition to my pooled
>>> estimate and CIs as I have plenty of between-study variation in my
>>> meta-analysis. I am using metafor package and my summary estimated is an
>>> effect size (SMD) and not odds ratios. The examples I have come across
>>> mainly focus on odds ratios and I wonder what to do for SMDs.
>>> I would appreciate if someone could suggest what function to use.
>>>
>>> Thank you,
>>> Raynaud
>>>
>>>
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>>
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>>
> --
> Michael
> http://www.dewey.myzen.co.uk/home.html
>

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