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Re: msg for Statalist: "Which input for standard error in metaregression"

From   Paul Millar <[email protected]>
To   [email protected]
Subject   Re: msg for Statalist: "Which input for standard error in metaregression"
Date   Tue, 05 Jan 2010 18:20:16 -0700

An alternative would be to use PRE (proportional reduction in errors). This is R2 in OLS, but is available for most models. This simply calculates the improvement in prediction offered by
the model.  The command is -pre- after the model (post-estimation).

- Paul
At 10:05 AM 05/01/2010, you wrote:
Dear Maurizio:

On Mon, Jan 4, 2010 at 4:15 PM, Maurizio La Rocca <[email protected]> wrote:

> Using vwls I did not find the AdjR2. I've seen the using the command regress
> and then aweight the coefficients are equal with different se. Is it
> possible to consider that AdjR2?

I don't think there's a useful "adjusted R-squared" statistic for the
fixed-effect model fitted by -vwls- as fixed-effect meta-regression
assumes that the covariates explain all of the between-study variance,
which seems to imply that such a statistic should be 100%. This
assumption seems does not seem reasonable however, and i'm not alone
in thinking that fixed-effect meta-regression should not be used. To
quote Julian Higgins and Simon Thompson:

"It is not reasonable to assume that all of the heterogeneity is
explained, and the possibility of 'residual heterogeneity' must be
acknowledged in the statistical analysis. The appropriate analysis is
therefore 'random effects' rather than 'fixed effect'
-- S. G. Thompson and J. P. T. Higgins. How should meta-regression
analyses be undertaken and interpreted? Stat Med 21 (11):1559-1573,

"We demonstrate in particular that fixed effect meta-regression is
likely to produce seriously misleading results in the presence of
heterogeneity." <>
-- Julian P. T. Higgins and Simon G. Thompson. Controlling the risk of
spurious findings from meta-regression. Stat Med 23 (11):1663-1682,
2004. <>

Using -regress- with [aweight=1/se^2] results in a model with a
multiplicative overdispersion parameter rather than the more usual
additive component of variance. Thompson & Higgins 2002 briefly
discuss the former and explain why they prefer the latter. There's
more on the comparison between the two in a paper by Simon Thompson &
Stephen Sharp from 3 years earlier
<>, the
abstract of which includes,"We conclude that methods which allow for
an additive component of residual heterogeneity should be used."

> In general, what do you suggest to show in a paper as general statistics
> (provided as output of metareg)?

I'd suggest reporting the values of tau-squared both with and without
covariates, and comparing them by reporting the adjusted R-squared
figure as the "percentage of between-study variance explained" or
"proportion of heterogeneity explained". (That's in addition to
reporting the coefficients and standard errors and/or p-values for
each covariate.)  In medical applications it has become common to
report values of I-squared, following this BMJ paper in 2003
<>, but this may not be so
common in your field and has attracted some debate recently


Roger Harbord

> --------------------------------------------------
> From: "Roger Harbord" <[email protected]>
> Sent: Monday, January 04, 2010 10:40 AM
> To: <[email protected]>; "Maurizio La Rocca"
> <[email protected]>
> Cc: <[email protected]>
> Subject: Re: msg for Statalist: "Which input for standard error in
> metaregression"
>> Dear Maurizio:
>> On Mon, Jan 4, 2010 at 8:41 AM, Maurizio La Rocca <[email protected]>
>> wrote:
>>> I have a crucial doubt about the weights to use in a meta-regression.
>>> For fixed-effect I have to use this Stata command: vwls Y(effect size)
>>> DummyX1 DummyX2. Sd(StandardErrorEffectSize)
>>> For fixed-effect I have to use this Stata command, using reml- residual
>>> maximum likelihood - as option: metareg Y(effect size) DummyX1 DummyX2,
>>> wsse(StandardErrorEffectSize) bsest(reml)
>>> My doubt concerns the weight.
>>> If I compute a variance-weighted least squared regression do I have to
>>> input
>>> in the stata command the Standard Error of the Effect Size or the
>>> inverted
>>> squared standard error?
>>> End running a metareg (random-effect), is it correct, in this case, the
>>> use
>>> of the Standard Error of the Effect Size?
>> You have the command syntax right: -vwls- and -metareg- take the
>> standard error as argument to the sd() and wsse() options
>> respectively. (Note that Stata is case-sensitive so it may object if
>> you type "Sd" rather than "sd".)
>>> Moreover, I have a second doubt.
>>> Please, does anybody of you know how to compute R^2 after a
>>> variance-weighted least squared regression? Is it possible to compute it?
>> The current version of -metareg- includes in the output an "adjusted
>> R-squared" value that is computed as the percentage reduction in the
>> (residual) between-study variance when covariates are fitted (compared
>> to the random-effects meta-analysis model with no covariates). To
>> install the latest version of -metareg- type "findit metareg" in Stata
>> and click on the link labelled "sbe23_1", which is currently the fifth
>> item down (at least in Stata 11 with the latest updates installed). Or
>> if that doesn't work for you, try "net sj 8-4 sbe23_1". For further
>> discussion of the updated version of -metareg- see:
>> Harbord RM, Higgins JPT. Meta-regression in Stata. Stata Journal 2008;
>> 8(4):493-519. <>
>> Regards,
>> Roger.

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