[R-meta] Mean effects and standard deviation using metafor and netmeta for calculating probability

[Emerson M. Del Ponte]

Dear All,

I am comparing estimates by arm-based network model (metafor) vs a
contrast-based (netmeta) network meta-analysis. I am estimating the mean
difference (in crop yield) between each treatment (nine fungicides) and a
control (no fungicide).

In metafor, modelling the treatment means, and  keeping the control as
intercept, I directly obtain the absolute gain (effect-size of interest) in
yield for each fungicide relative to the control. Of course, I get the mean
difference directly when using netmeta in a network that shows
consistency. Interestingly,
the results were VERY similar using the arm- and contrast-based approaches,
in the two different package, for most fungicides. CI's were a bit shorter
in netmeta.

For one of the treatments:

netmeta
D =  528.28 kg/ha (438 - 617)

metafor
D =  525.95 kg/ha (427 - 624)

The problem I have is that I don't get the same tau^2 using both
approaches. Maybe I do not know how/where to get them. I have been using
these estimates of D in a cost-benefit analysis, to estimate the
probability of certain effect-size outcome under scenario of fungicide
costs and crop prices. For such, I need the D in yield and the standard
deviation from the meta-analysis. In metafor (the current approach used in
my papers) I take the square root of tau^2 for each treatment. For the nine
fungicides, they are quite close, ranging from 350,000 to 590,000.

For the D above:

netmeta:
tau^2 = 72,743 (I found only a single variance for the network )

metafor:
tau^2 = 561,233

The probability values I obtain are very sensitive to this difference in
standard deviations.

Does anyone know if I am doing right? or where to get (in both models) the
correct standard deviation for using in the calculation of the
probability?  See below a description of the probability from two papers -
the first using meta-analytic estimates, and the other in a  primary study:

"....The estimated between-study variance ( σˆ 2 ) from the meta-analyses
can be used to estimate the probability of the yield response to fungicide
in a new randomly selected study—done in the same manner as the studies
considered in this analysis—being lower (or higher) than some constant (C).
This probability is estimated as p = φ[(C –D )/ σˆ ], where φ(•) is the
cumulative standard-normal function and σˆ is the estimated between-study
standard deviation" "

"The probability, PD, that a fungicide treatment resulted in a yield
difference larger than a specified value (∆yD) (and thus, the probability
that the treatment resulted in a net return larger than D) was calculated
from the observed yield difference between treated and nontreated plots (
yf − yc ) and the observed standard deviation in yield, s,"

I can further share outputs of the analysis if needed.

Thanks,

Emerson




Prof. Emerson M. Del Ponte
Departamento de Fitopatologia
Universidade Federal de Viçosa
Viçosa, MG - Brasil
+55 (31) 3899-1103
Twitter: @edelponte

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