[R-meta] network meta-analysis - include block (within-study) level

I think I now have a general understanding of your data structure and what
you are doing. Some final thoughts:

1) If you include block as an effect in the ANOVAs, you must include block
in whatever model you are going to fit afterwards. In particular, by
including block as an effect in the ANOVAs, you are removing that source of
variability from the residual variance. But the variance of a raw yield
value is sigma^2_block + sigma^2_resid. By using the MSE for the variance,
the sampling variance will only reflect sigma^2_resid, so you need to
account for the block level variance in whatever model you fit afterwards.

2) Using
??
MSE/n (with n = 4/5) only makes sense if you are averaging within blocks
(which you seem to be doing at the end). But even that is only approximate.
Multiple yield values within the same block are correlated sigma^2_block /
(sigma^2_block + sigma^2_resid) -- but MSE/n assumes independence.

3) Below, you end up constructing a dataset with yield values averaged
within blocks. Now I don't understand the original question anymore,
because in such a dataset, one cannot include block as another random
effect. Also, see 1) -- in such a dataset, you cannot account for the block
level variance.

I still think you may want to analyze your data (not aggregated in any
way) with a mixed-effects model directly, allowing for trial and block
level variance (plus residual variance). In this case, you are making
things more difficult by trying to do a two-stage analysis.

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com

-----Original Message-----
From: Juan Pablo Edwards Molina [mailto:edwardsmolina at gmail.com]
Sent: Wednesday, August 09, 2017 19:47
To: Viechtbauer Wolfgang (SP)
Cc: r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] network meta-analysis - include block (within-study)
level

| ?Okay, so let me see if I understand. What you are showing below are
actually the raw data from trial 3. And you have more trials of
| that type (either with 4 or 5 blocks and treatments may differ slightly
across trials, but all trials have 'Check'). So now you want to
| meta-analyze those yield values, including 'treatment' as the predictor
of interest (and accounting for the nested structure of the
| data).

Exactly Wolfgang, this is a sample of the treatments sets

table(dat$trt, dat$study)

??
Trials------->          1  2  3  4 11 13 14 38 39 41 42 60 62 63 65 66

AA_CHECK           1  1  1  1   1   1   1   1   1   1   1   1   1   1   1
  1
AZ_BF                 0  0  0  0   0   0   0   1   1   1   1   1   1   1
1   1
CZM                    1  1  1  1   1   1   1   1   1   1   1   0   0   0
  0   0
EPO_FLUX_PYRA   1  1  1  1   1   1   1   1   1   1   1   1   1   1   1   1
FLUX_PYRA          0  0  0  0   1   1   1   1   1   1   1   1   1   1   1
  1
MZB                    0  0  0  0   0   0   0   1   1   1   1   1   1   1
  1   1
PROT_TRIF           1  1  1  1   1   1   1   1   1   1   1   1   1   1   1
  1

Te diferent sets of treatments was  the reason to led me to think about a
network meta-analysis.

?vi2 = MSE/n # multivariate approach for Sampling variance of yield (n=4
or 5)

dat$fungic <- relevel(factor(yield_dat$fungic), ref="AA_CHECK")

?In order to do so, you need a variance of the yield values. Obviously,
you do not have a variance per row, since each row is a single measurement.
So, you fitted some ANOVA model to these data (per trial) in order to
obtain the MSE and then want to use that as the variance for all yield
values from that trial.

yes, I used the treatment means within the trials and that MSE as trial
variance?.

But what is 'n' in V_yield/n (i.e., MSE/n)? Seems to me that MSE *is* the
variance you want. For example:

??
??
dat <- read.table(header=TRUE, text = "
trt     trial   bk    yield
Check   3       1     2493
Check   3       2     2173
Check   3       3     2628
Check   3       4     2168
Fox     3       1     3194
Fox     3       2     2363
Fox     3       3     2887
Fox     3       4     3278
NTX     3       1     2988
NTX     3       2     2361
NTX     3       3     2341
NTX     3       4     3218")

res <- lm(yield ~ trt + factor(bk), data=dat)
summary(res)
??
sigma(res)^2 ### error variance

### or treating 'bk' as random, but this yields the same results

library(nlme)
res <- lme(yield ~ trt, random = ~ 1 | bk, data=dat)
summary(res)
sigma(res)^2 ### error variance

Using aov() would require restructuring the data, but will also yield the
same results.

But if you are doing all of that anyway, why not just analyze ALL of the
data that way, adding trial as another random effect?

?Yes I did that ?for each treatment so final data set was:

??
    trial  year   bk           trt                yield
??
  MSE    vi2
1       1 2012   4    AA_CHECK          2640
??
88931.9   22233
2       1 2012   4    CZM_CM_TEBU    2337   88931.9   22233
3       1 2012   4    CZM                   2733   88931.9   22233
4       1 2012   4    CZM+LS             2238   88931.9   22233
5       1 2012   4    EPO_FLUX_PYRA  2858   88931.9   22233
6       1 2012   4    EPO_FLUX_PYRA  3103   88931.9   22233

?Can I analyze it as mixed model even with the different sets of
treatments??

Many thanks?!
Juan

-----Original Message-----
From: Juan Pablo Edwards Molina [mailto:edwardsmolina at gmail.com]
Sent: Wednesday, August 09, 2017 02:41
To: Viechtbauer Wolfgang (SP)
Cc: r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] network meta-analysis - include block (within-study)
level

Please do not consider my last reply!!
I mixed everything (because I am also estimating slopes and intercepts
with the same data set...)

I'm performing a network meta-analysis to estimate the treatments yield
difference with the untreated check.

this is my data structure,

?trt     trial   bk    yield
Check   3       1     2493
Check   3       2     2173
Check   3       3     2628
Check   3       4     2168
Fox     3       1     3194
Fox     3       2     2363
Fox     3       3     2887
Fox     3       4     3278
NTX     3       1     2988
NTX     3       2     2361
NTX     3       3     2341
NTX     3       4     3218

yield = plot grain yield at crop maturity (single value). Actually, plots
were ~ 15m?, however the grain weight was expressed in kg/10000 m? (1ha). ?
bk = are the blcoks within each trial (4 or 5).
trt = fungicide tratments to reduce a soybean disease.

I estimated yield difference (with the check) by setting Check as
reference level in the following model:

?net1 <- rma.mv(yield_mean, vi2, mods = ~ treatment, random = ~
treatment| trial,
                         method="ML", struct="UN", data=df)

?where yield_mean is the vector of treatments yield means and vi2 is the
vector of sampling variances obtained by:

vi2 <- V_yield/n  (for each trial)

(V_yield = MSE from anova)

?Since I have the raw full dataset,  I wonder if the correct would be to
include a block? random effect.

Sorry again...

Juan
? Edwards?

On Wed, Aug 9, 2017 at 6:34 AM, Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
So is 'y' is the mean treatment yield here? Also, is that really the
average of multiple measurements (e.g., if there is subsampling)? Or is 'y'
just the single measurement (yield) for that particular block and
treatment? I still do not quite understand what kind of data you have.
Also, what is 'x'?

Best,
Wolfgang

-----Original Message-----
From: Juan Pablo Edwards Molina [mailto:edwardsmolina at gmail.com]
Sent: Tuesday, August 08, 2017 23:26
To: Viechtbauer Wolfgang (SP)
Cc: r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] network meta-analysis - include block (within-study)
level

Pretty close to that structure ?you say?:  I have ?several treatments at
each block (balanced experiments), actually different set of treatments
across the k-trials (all trials have the untreated Check)

This are a few lines of trial 3:
?
trt    trial bk  x    y
Check  3     1   40   2493
Check  3     2   45   2173
Check  3     3   40   2628
Check  3     4   40   2168
Fox    3     1   35   3194
Fox    3     2   30   2363
Fox    3     3   35   2887
Fox    3     4   30   3278
NTX    3     1   40   2988
NTX    3     2   35   2361
NTX    3     3   35   2341
NTX    3     4   35   3218
?
|? Also, do you have the raw mean and variance (or SD) and sample size for
each row of the dataset? It seems like you are first fitting some kind of
ANOVA within each study, but | that might actually complicate things.

Yes, I have the raw full dataset so I ?have the observation level ?values
to calculate SD, means..?

Several authors from the Phytopathology area use ANOVA MSE :

??
"...The within-study variance (V) for IND or DON for these fungicide
trials is the residual variance (mean square error) from an analysis of
variance (ANOVA) of the effects of treatment on disease or toxin. Where the
original data were available, this variance was calculated directly from an
ANOVA..."

http://apsjournals.apsnet.org/doi/abs/10.1094/PHYTO-97-2-0211

Juan

On Tue, Aug 8, 2017 at 6:03 PM, Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Dear Juan,

Could you show a bit of the data (structure)? In particular, does each
block contain two treatments, so that the structure looks something like
this?

trial block treatment mean
--------------------------
1     1     1         ...
1     1     2         ...
1     2     1         ...
1     2     2         ...
2     1     1         ...
2     1     2         ...
2     2     1         ...
2     2     2         ...
2     3     1         ...
2     3     2         ...
...
??
Also, do you have the raw mean and variance (or SD) and sample size for
each row of the dataset? It seems like you are first fitting some kind of
ANOVA within each study, but that might actually complicate things.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
bounces at r-project.org] On Behalf Of Juan Pablo Edwards Molina
Sent: Tuesday, August 08, 2017 22:09
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] network meta-analysis - include block (within-study)
level

Dear list,

I have a dataset containing crop field randomized block design experiments
with observations at plot level (experimental unit), and I want to estimate
the treatments grain yield difference relative to a untreated check.
??
net1 <- rma.mv(yield, vi2, mods = ~ treatment, random = ~ treatment|
trial,
                         method="ML", struct="UN", data=df)
??
where yield is the vector of mean treatments yield for vi2 is the vector of
sampling variances obtained by:

vi2 <- V_yield/n  (for each trial)

(V_yield = MSE from anova)

Do I need to include the block in the model? or using the experiment
treatments means will obtain the same results? I suppose something like:

net2 <- rma.mv(yield, vi2, mods = ~ treatment, random = ~ treatment|
block|
trial,
                         method="ML", struct="UN", data=df)

If the latter would be a better approach, how do I include the sampling
variance?

Thanks in advance,

Juan Edwards