[R-meta] standard error in predictive nonlinear meta-regression model

[Philipp Doebler]

I would suggest you use the multivariate Delta method:

https://en.wikipedia.org/wiki/Delta_method#Multivariate_delta_method

You will have to compute some partial derivatives, which is not complicated
in your case if you have ever done it before.

Be warned though that, sometimes the Delta method approximations do not
perform well (and can underestimate the standard error). An alternative
would be to bootstrap the meta-analysis.

-Philipp


On Thu, Jan 18, 2018 at 6:07 PM, Cesar Terrer Moreno <cesar.terrer at me.com>
wrote:

> I am using a nonlinear meta-regression of the form y ~ p1 * exp(-p2*A),
> with the following coefficients:
>
>      estimate     se  zval    pval
> p1     5.5447 4.2592 1.302 0.19298
> p2     0.3856 0.0835 4.616 0.00000
> tau2   0.0000     NA    NA      NA
>
> I want to use this model to predict the effect size (in %) of a treatment,
> influenced by the variable A. Let's assume, for example, this is the
> effectiveness of a cancer treatment at a certain age A. For example, when
> A= 9, effect size is ~19%:
>
> make_pct <- function(x) (exp(x) - 1) * 100
> > make_pct(5.5447 * exp (-0.3856 * 9))
> [1] 18.82309
>
> The problem is that now I don't know how to calculate the standard error
> at e.g. A=9 using this model. I am sure this is very basic but I don't have
> any experience in this particular matter. Thanks
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>
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-- 
Prof. Dr. Philipp Doebler
Technische Universität Dortmund
Fakultät Statistik
Vogelpothsweg 87
44227 Dortmund

Tel.: +49 231-755 8259
Fax: +49 231-755 3918
doebler at statistik.tu-dortmund.de
www.statistik.tu-dortmund.de/1261.html


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