[R-meta] question on scatter plot of estimates (Fisher's Z) against the standard error
Gabriel Cotlier
g@b|k|m01 @end|ng |rom gm@||@com
Tue Nov 7 10:47:37 CET 2023
Dear Greta and colleagues:
Probably, I think I found the solution to reproduce outside the metafor
package the funnel plot without funnel background and with :
yaxis="seinv" for the inverse of the standard errors
I got the same results as in the funnel plot from the metafor package using
the inverse of the square root of the variance (not of the standard
deviation) as 1/SE, that would be:
Inv_SE <- 1/sqrt(vi_data), where vi is the variance data.
## Greta example using metafore function funenel()
ri <- c(0.5, 0.6, 0.7, 0.8, 0.9)
ni <- c(100,110,150,200,250)
dat <-escalc(measure = "ZCOR", ri = ri, ni = ni)
funnel_all <- rma.mv(yi, vi, data=dat)
png(file = "funnel_Greta_example.png",
width = 250,
height = 200,
res = 600,
units = "mm")
f1 <- funnel(funnel_all,
back = "white",
# shade = "white",
yaxis = "seinv",
level = 0,
# ylim = c(1, 5),
refline=0,
main="my plot",
ylab = "Presicion (1/SE)",
xlim = c(0.53,1.5))
# shade = c("white", "gray55", "gray75"),
# refline = 0)
# bg = "grey")
# legend = TRUE)
#grid(NULL, NULL,lwd = 1.6)
abline(h=c(9.849, 11.316,12.783, 14.249, 15.716 ), col="grey", lwd=1, lty=3)
abline(v=1, col="blue", lwd=2)
abline(v=c( 0.6, 0.8, 1, 1.2, 1.4), col="grey", lwd=1, lty=3)
dev.off()
##
## Variance : from general model extracted
vi_data <-funnel_all$vi
## Estimates : from general model extracted estimates
yi_data <-funnel_all$yi[1:5]
## square root of the variance
SE_5 <- 1/sqrt(vi_data)
# estimates
E <-funnel_all$yi
N<-dat$ni
## construct data frame
df <- data.frame (Estimates = c(E), Standsrd_Error = c(SE_5))
View(df)
library(ggplot2)
###################################### MY PLOT
###################################
## Scatter plot
scaleFUN <- function(x) sprintf("%.2f", x)
p<- ggplot(df, aes(x=Estimates, y=Standsrd_Error)) +
geom_point(aes(size = Estimates), alpha=0.7, color="#2568E6")+
scale_size_area() +
labs(x = "Fisher's z",
y = "Standard Error (SE)")+
theme(plot.title = element_text(hjust = 0.5))+
# theme(plot.margin = unit(2 ,8, 8, 2), "cm"))+
scale_y_continuous(n.breaks = 12,labels=scaleFUN)+
scale_x_continuous(n.breaks = 12,labels=scaleFUN)+
geom_vline(xintercept = 0)+
theme(axis.text.y = element_text(size = 15))+
theme(axis.text.x = element_text(size = 15))+
theme(axis.title.y = element_text(size = 15))+
theme(axis.title.x = element_text(size = 15))+
ggtitle( "Fisher's z vs. Standard Error")+
theme(plot.title = element_text(size = 17, face = "bold"))+
theme(legend.text = element_text(size = 15))
p
png(filename = "myExample.png", width = 28, height = 18 ,units = "cm" ,
res =100 )
print(p)
[image: image.png]
On Tue, Nov 7, 2023 at 9:49 AM Gabriel Cotlier <gabiklm01 using gmail.com> wrote:
> Hello all,
> According to:
> https://www.metafor-project.org/doku.php/plots:funnel_plot_variations I
> think it could be the argument:
>
>
> -
>
> yaxis="seinv" for the inverse of the standard errors
>
> Is what gives the 1/SE for each element in the vector of effect sizes in
> the x-axis.
>
> How can I "stand alone"—that would be outside the metafore package or not
> using the funnel function—to plot the same scatterplot of effect sizes
> (x-axis) against 1/SE (y-axis) in communion and a simple R scatter
> plot—without the funnel background—and afterwards use it to further cluster
> by coloring or using shapes ("pch") the effect sizes according to different
> categorical variables in the data frame?
>
> Thanks a lot for your help.
> Kind regards,
> Gabriel
>
>
>
> On Tue, Nov 7, 2023 at 9:13 AM Gabriel Cotlier <gabiklm01 using gmail.com>
> wrote:
>
>> Dear Greta and colleges,
>>
>> As can be seen below, Greta has provided a nice solution to a problem I
>> could not solve before, which is to have as an output of metafor's package
>> function funnel() for plotting the funnel plot without the background of
>> the funnel itself, which I very slightly modified as follows:
>>
>> ###################
>> ##
>> ##. CODE FUNNEL
>> ##
>> ###################
>>
>> ## data
>> ri <- c(0.5, 0.6, 0.7, 0.8, 0.9)
>> ni <- c(100,110,150,200,250)
>> dat <-escalc(measure = "ZCOR", ri = ri, ni = ni)
>>
>> ## model
>> funnel_all <- rma.mv(yi, vi, data=dat)
>>
>> ## get max and min values for plot
>> #funnel_all$yi
>> #min(funnel_all$yi)
>> #max(funnel_all$yi)
>>
>> ## funnel plot
>> f1 <- funnel(funnel_all,
>> back = "white",
>> # shade = "white",
>> yaxis = "seinv",
>> level = 0,
>> # ylim = c(1, 5),
>> refline=0,
>> main="my plot",
>> ylab = "Presicion (1/SE)",
>> xlim = c(0.53,1.5))
>> # shade = c("white", "gray55", "gray75"),
>> # refline = 0)
>> # bg = "grey")
>> # legend = TRUE)
>> #grid(NULL, NULL,lwd = 1.6)
>> abline(h=c(9.849, 11.316, 12.783, 14.249, 15.716 ), col="grey", lwd=1,
>> lty=3)
>> abline(v=1, col="blue", lwd=2)
>> abline(v=c( 0.6, 0.8, 1, 1.2, 1.4), col="grey", lwd=1, lty=3)
>>
>>
>> This has been a very efficient solution for my problem of getting exactly
>> the same funnel plot as the result of the metafore package
>> function funnel() without the funnel as a background. However, now I am
>> facing the challenge of having plotted the same funnel plot as the
>> output from the metafor's funnel() function without the background but
>> without the option of clustering by coloring or giving different point
>> shapes to the effect szes (points in the funnel plot) according to a
>> categorical in my data frame. I assume—probably wrongly—that for this task
>> I would have to reproduce the same funnel plot as is output from the funnel
>> plot function in the metafore package without the funnel background, as in
>> the code above, and use my data frame with the categorical variables to
>> color the points or give them different shapes and sizes using the
>> categorical variables in my data frame. Now the funnel plot function plots
>> in the x-axis the effect sizes, something I can easily get from my data
>> frame, but in the y-axis it uses 1/standad error (or 1 / SD). The
>> problem is that, as far as I understand, the standard error (SE)
>> corresponds to the standard deviation, or the R function sd() which gives
>> one value per input vector. Therefore, for some reason, plotting the effect
>> sizes (a vector class numeric) in the x-axis and 1/sd(effect_sizes) will
>> give me a number, not a vector of the same length as the effect sizes.
>>
>> *Therefore, how could one reproduce the same funnel plot as in the
>> metafore function (without the funnel background, just a scatterplot)
>> with an x-axis composed of the vector of effect sizes and a y-axis with
>> another vector corresponding to 1/stands error (1/SE) of each element in
>> the x-axis--If 1/SE is is equal to 1/sd(efect_sizes) which is a scaler and
>> not a vector ?*
>>
>> I think maybe this could be achieved somehow by giving, in the y-axis, a
>> kind of *"element-wise 1/SE"* to each element in the x-axis; that would
>> be an value corresponding to 1/SE to each of the elements in the vector of
>> effect sizes in the x-axis. Could this be the idea behind the funnel plot
>> function with 1/SE on the y-axis?
>>
>> If so, can this be somehow achieved following the example provided by
>> Greta below?
>>
>> ri <- c(0.5, 0.6, 0.7, 0.8, 0.9)
>> ni <- c(100,110,150,200,250)
>> dat <-escalc(measure = "ZCOR", ri = ri, ni = ni)
>>
>> Thanks a lot for your help and guidance.
>> Kind regards,
>> Gabriel
>>
>> On Fri, Jul 21, 2023 at 9:28 AM Gabriel Cotlier <gabiklm01 using gmail.com>
>> wrote:
>>
>>> Dear Greta,
>>>
>>> Thank you very much.
>>> The code you provided for the funnel plot is exactly what I was looking
>>> for.
>>>
>>> I just changed my refline to zero and adjusted the xlim to the interval
>>> [-4 6], so it is exactly the same as the metafor::funnel plot but without
>>> all the background, keeping only the scattering of the points.
>>>
>>> Thanks a lot again.
>>> Kind regards,
>>> Gabriel
>>>
>>>
>>>
>>> On Thu, Jul 20, 2023 at 11:21 PM Dr. Gerta Rücker <
>>> gerta.ruecker using uniklinik-freiburg.de> wrote:
>>>
>>>> Dear Gabriel,
>>>>
>>>> Both plots are correct and equivalent (though I like the metafor plot
>>>> much more). If it is only to get rid of the confidence region, why don't
>>>> you use the funnel() function of metafor and suppress all elements you
>>>> don't want?
>>>> For example, try (object funnel_all taken from your R code, fictitious
>>>> data coming from me, as you did not provide them!)
>>>>
>>>> ri <- c(0.5, 0.6, 0.7, 0.8, 0.9)
>>>> ni <- c(100,110,150,200,250)
>>>> dat <-escalc(measure = "ZCOR", ri = ri, ni = ni)
>>>>
>>>> funnel_all <- rma.mv(yi, vi, data=dat)
>>>> funnel(funnel_all, back = "white", shade = "white", level = 0, xlim =
>>>> c(0.5,1.6), refline = 2)
>>>>
>>>> The xlim argument is used to fix the x-axis range, while putting the
>>>> refline outside the visible region (simply a trick, I couldn't find an
>>>> argument to determine the refline's color). You may also change the y-axis
>>>> range, e.g.,
>>>>
>>>> funnel(funnel_all, back = "white", shade = "white", level = 0, xlim =
>>>> c(0.5,1.6), refline = 2, ylim = c(0.06, 0.105))
>>>>
>>>> if you think this makes sense. With respect to the inverted axis, see
>>>> Michael's post.
>>>>
>>>> Best,
>>>> Gerta
>>>>
>>>>
>>>>
>>>> UNIVERSITÄTSKLINIKUM FREIBURG
>>>> Institute for Medical Biometry and Statistics
>>>>
>>>> Dr. Gerta Rücker
>>>> Guest Scientist
>>>>
>>>> Stefan-Meier-Straße 26 · 79104 Freiburg
>>>> gerta.ruecker using uniklinik-freiburg.de
>>>>
>>>>
>>>> https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker
>>>>
>>>>
>>>> -----Ursprüngliche Nachricht-----
>>>> Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org>
>>>> Im Auftrag von Gabriel Cotlier via R-sig-meta-analysis
>>>> Gesendet: Donnerstag, 20. Juli 2023 16:28
>>>> An: Michael Dewey <lists using dewey.myzen.co.uk>
>>>> Cc: Gabriel Cotlier <gabiklm01 using gmail.com>; R Special Interest Group
>>>> for Meta-Analysis <r-sig-meta-analysis using r-project.org>
>>>> Betreff: Re: [R-meta] question on scatter plot of estimates (Fisher's
>>>> Z) against the standard error
>>>>
>>>> Dear Michael,
>>>> Here is the code below:
>>>> Thanks a lot.
>>>> Kind regards,
>>>> Gabriel
>>>>
>>>> ## Transformation of Pearson's Product-moment correlation coefficient
>>>> (r)
>>>> to Fisher's Z
>>>> dat <-escalc(measure = "ZCOR",
>>>> ri = ri,
>>>> ni = ni,
>>>> data = dat)
>>>>
>>>> ##
>>>> funnel_all <- rma.mv(yi,
>>>> vi,
>>>> # mods = ~ Type,
>>>> random = ~ 1 | Article / Sample_ID,
>>>> data=dat)
>>>>
>>>> funnel_all
>>>> ## funnel plot form metafor
>>>> funnel(funnel_all)
>>>>
>>>> ## Variance : from general model extracted
>>>> vi_data <-funnel_all$vi
>>>>
>>>> ## Estimates : from general model extracted estimates
>>>> yi_data <-funnel_all$yi[1:150]
>>>>
>>>> ## calculate standard error SE: square root of the variance
>>>> SE<- sqrt(vi_data)
>>>>
>>>> # estimates
>>>> E <-funnel_all$yi
>>>>
>>>> ## construct data frame
>>>> df <- data.frame (Estimates = c(E), Standsrd_Error = c(SE))
>>>> View(df)
>>>> library(ggplot2)
>>>> ## Scatter plot
>>>> scaleFUN <- function(x) sprintf("%.2f", x)
>>>> p<- ggplot(df, aes(x=Estimates, y=Standsrd_Error)) +
>>>> geom_point(aes(size = Estimates), alpha=0.7, color="#2568E6")+
>>>> scale_size_area() +
>>>> labs(x = "Fisher's z",
>>>> y = "Standard Error (SE)")+
>>>> theme(plot.title = element_text(hjust = 0.5))+
>>>> # theme(plot.margin = unit(2 ,8, 8, 2), "cm"))+
>>>> scale_y_continuous(n.breaks = 12,labels=scaleFUN)+
>>>> scale_x_continuous(n.breaks = 12,labels=scaleFUN)+
>>>> geom_vline(xintercept = 0)+
>>>> theme(axis.text.y = element_text(size = 15))+
>>>> theme(axis.text.x = element_text(size = 15))+
>>>> theme(axis.title.y = element_text(size = 15))+
>>>> theme(axis.title.x = element_text(size = 15))+
>>>> ggtitle( "Fisher's z vs. Standard Error")+
>>>> theme(plot.title = element_text(size = 17, face = "bold"))+
>>>> theme(legend.text = element_text(size = 15))
>>>> p
>>>> png(filename = "myplot.png", width = 28, height = 18 ,units = "cm" ,
>>>> res
>>>> =100 )
>>>> print(p)
>>>> dev.off()
>>>>
>>>>
>>>>
>>>> On Thu, Jul 20, 2023 at 4:51 PM Michael Dewey <lists using dewey.myzen.co.uk>
>>>> wrote:
>>>>
>>>> > Dear Gabriel
>>>> >
>>>> > Comments in-line
>>>> >
>>>> > On 20/07/2023 05:55, Gabriel Cotlier wrote:
>>>> > > Dear Michael,
>>>> > >
>>>> > > I think you are completely right, in the fact, the plot I am
>>>> producing
>>>> > > is indeed valid for the purpose for which I want to use it, meaning
>>>> it
>>>> > > is representative of the relationship I want to show. Therefore, I
>>>> > > assume that the plot I am getting, is supposed to be sufficient.
>>>> > >
>>>> > > However, I receive from the function metafore:: funnel (model), for
>>>> a
>>>> > > model without modierators, a very nice representation of the
>>>> scarring of
>>>> > > the observed outcomes or the estimates (x axis), as a function of
>>>> the SE
>>>> > > (e.i., square root of the sampling variance, SE assumef to have a
>>>> pseudo
>>>> > > confidence interval region drawn around each of its values). While,
>>>> when
>>>> > > I plot by myself
>>>> > > x = observed outcomes
>>>> > > y = square root of the sampling variance,
>>>> > >
>>>> > > Then the plot shows that:
>>>> > > a. the scattering of the points appears upside down with respect
>>>> to the
>>>> > > output of the function metafore:: funnel (model),
>>>> >
>>>> > I have already answered that one in a previous post. It is just the
>>>> > convention
>>>> >
>>>> > > b. the scale of the y axis, instead of having a defined top at zero
>>>> and
>>>> > > from there values are represented downwards, the scale is different.
>>>> > >
>>>> >
>>>> > Without your code it is hard to tell but I suspect you are not
>>>> plotting
>>>> > what you think you are. Are you plotting the inverse of the se?
>>>> >
>>>> > Michael
>>>> >
>>>> > >
>>>> > > Anyways, I started thinking that in any case, such a difference in
>>>> the
>>>> > > plot I am doing by myself is not necessarily wrong, but is just a
>>>> > > different way of representing the data. Just the scattering of the
>>>> > > points in one case looks like the upside down scattering of the
>>>> other.
>>>> > > And I assume this is because maybe the function metafore::funnel()
>>>> > > applies some operation on the square root of the mean (y axis) that
>>>> I
>>>> > > presume is the calculation of the aforementioned pseudo confidence
>>>> > > interval for each value, but I am not sure.
>>>> > >
>>>> > > Thanks a lot for your response.
>>>> > > Kind regards,
>>>> > > Gabriel
>>>> > >
>>>> > > On Wed, Jul 19, 2023 at 7:20 PM Michael Dewey <
>>>> lists using dewey.myzen.co.uk
>>>> > > <mailto:lists using dewey.myzen.co.uk>> wrote:
>>>> > >
>>>> > > I am sorry Gabriel but I do not understand why the plot you say
>>>> you
>>>> > > produced fails to do what you say you want.
>>>> > >
>>>> > > Michael
>>>> > >
>>>> > > On 19/07/2023 10:59, Gabriel Cotlier wrote:
>>>> > > > Hello Michael,
>>>> > > > Thank you very much for your response.
>>>> > > > I just would like to show that the of data set I have has
>>>> high
>>>> > > > uncertainty given that no possible pattern is observable or
>>>> > > detectable
>>>> > > > and no order is possible to visulize in the scattering,
>>>> > > > I thought that a plot with x axis = fisher's z observed
>>>> > > > outcomes (estimates) and y axis = standard error or any
>>>> > > other measure of
>>>> > > > uncertainty could at least visually demostrate that
>>>> assumption.
>>>> > > > If such a lack of pattern or high uncertainty in the data
>>>> set can
>>>> > > also
>>>> > > > be demonstrated numerically, even better.
>>>> > > > Kind regards,
>>>> > > > Gabriel
>>>> > > >
>>>> > > > On Wed, Jul 19, 2023 at 12:29 PM Michael Dewey
>>>> > > <lists using dewey.myzen.co.uk <mailto:lists using dewey.myzen.co.uk>
>>>> > > > <mailto:lists using dewey.myzen.co.uk
>>>> > > <mailto:lists using dewey.myzen.co.uk>>> wrote:
>>>> > > >
>>>> > > > Dear Gabriel
>>>> > > >
>>>> > > > I am not realy sure what you are trying to do but one
>>>> point
>>>> > which
>>>> > > > occurs
>>>> > > > to me is that forest plots are conventional plotted with
>>>> small
>>>> > > > values of
>>>> > > > standard error at the top.
>>>> > > >
>>>> > > > Michael
>>>> > > >
>>>> > > > On 19/07/2023 06:07, Gabriel Cotlier via
>>>> R-sig-meta-analysis
>>>> > > wrote:
>>>> > > > > Dear all,
>>>> > > > >
>>>> > > > > I have already posted this question with no response.
>>>> > > > > Maybe this time I am luckier and someone with more
>>>> > > knowledge than
>>>> > > > me in the
>>>> > > > > Metafor package can answer me.
>>>> > > > >
>>>> > > > > In a nutshell, what I would like is to be able to
>>>> produce a
>>>> > > > scatter plot of
>>>> > > > > the observed oucomes or the estimates, in my case
>>>> Fisher's
>>>> > > z for
>>>> > > > the x axis
>>>> > > > > and the standard error in the y axis, with the
>>>> standard
>>>> > error
>>>> > > > (SE) the
>>>> > > > > same as it appears when running the funnel() function
>>>> for a
>>>> > > > funnel plot
>>>> > > > > with the model (without moderators) as the input
>>>> argument.
>>>> > > > Actually, it is
>>>> > > > > a funnel plot without the background of the funnel
>>>> > > distribution
>>>> > > > but just
>>>> > > > > the scatter of points, that is suppressing the funnel
>>>> > > distribution on
>>>> > > > > the background.
>>>> > > > >
>>>> > > > > I tried to do so in agreement with the definition of
>>>> SE
>>>> > > used for
>>>> > > > the funnel
>>>> > > > > plot in the package Vignette published at Journal of
>>>> > > Scientific
>>>> > > > software in
>>>> > > > > page 26:
>>>> > > > >
>>>> > > > > "*For models without moderators, the figure shows the
>>>> > observed
>>>> > > > outcomes on
>>>> > > > > the horizontal axis against their corresponding
>>>> standard
>>>> > > errors
>>>> > > > (i.e., the
>>>> > > > > square root of the sampling variances) on the vertical
>>>> > axis. A
>>>> > > > vertical
>>>> > > > > line indicates the **estimate based on the model. A
>>>> pseudo
>>>> > > confidence
>>>> > > > > interval region is drawn around this value with bounds
>>>> > > equal to
>>>> > > > ±1.96 · SE,
>>>> > > > > where SE is the standard error value from the vertical
>>>> > axis.*"
>>>> > > > >
>>>> > > > >
>>>> > > > > I tried to reproduce the vertical axis (y) using the
>>>> > > square root
>>>> > > > of the
>>>> > > > > sampling variable, but the result was an upside down
>>>> > > scaling of the
>>>> > > > > observed outcomes or estimates on a different y scale
>>>> for
>>>> > > the x
>>>> > > > ticks. The
>>>> > > > > plot seems to have similarities with the funnel plot
>>>> from
>>>> > the
>>>> > > > funnel()
>>>> > > > > function, but it is not exactly the same without the
>>>> > > background
>>>> > > > of the
>>>> > > > > funnel distribution graphic. Maybe the problem could
>>>> be
>>>> > > that in the
>>>> > > > > funnel() function, contrary to my simple attempt to
>>>> > imitate it
>>>> > > > with the
>>>> > > > > square root of the sampling variable, the pseudo
>>>> confidence
>>>> > > > interval is
>>>> > > > > estimated for each value? Could this be the reason?
>>>> > > > >
>>>> > > > >
>>>> > > > > If so, how could I reproduce the funnel () function
>>>> plot
>>>> > > without
>>>> > > > the funnel
>>>> > > > > distribution graphic in the background and just the
>>>> > > scattering of the
>>>> > > > > points using the same pseudo-confidence interval?
>>>> > > > >
>>>> > > > >
>>>> > > > > Thanks a lot for your help and assistance.
>>>> > > > >
>>>> > > > > Kind regards,
>>>> > > > >
>>>> > > > > Gabriel
>>>> > > > >
>>>> > > > > [[alternative HTML version deleted]]
>>>> > > > >
>>>> > > > > _______________________________________________
>>>> > > > > R-sig-meta-analysis mailing list @
>>>> > > > R-sig-meta-analysis using r-project.org
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>>>> > > > >
>>>> > > >
>>>> > > > --
>>>> > > > Michael
>>>> > > > http://www.dewey.myzen.co.uk/home.html
>>>> > > <http://www.dewey.myzen.co.uk/home.html>
>>>> > > > <http://www.dewey.myzen.co.uk/home.html
>>>> > > <http://www.dewey.myzen.co.uk/home.html>>
>>>> > > >
>>>> > > >
>>>> > > >
>>>> > > <
>>>> >
>>>> http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient
>>>> > <
>>>> >
>>>> http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient
>>>> >>
>>>> > Virus-free.www.avg.com <http://Virus-free.www.avg.com> <
>>>> >
>>>> http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient
>>>> > <
>>>> >
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>>>> > >>
>>>> > > >
>>>> > > > <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>>>> > >
>>>> > > --
>>>> > > Michael
>>>> > > http://www.dewey.myzen.co.uk/home.html
>>>> > > <http://www.dewey.myzen.co.uk/home.html>
>>>> > >
>>>> >
>>>> > --
>>>> > Michael
>>>> > http://www.dewey.myzen.co.uk/home.html
>>>> >
>>>>
>>>> [[alternative HTML version deleted]]
>>>>
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