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

Viechtbauer Wolfgang (SP) wolfgang.viechtbauer at maastrichtuniversity.nl
Wed Aug 9 13:06:40 CEST 2017

```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). 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. 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?

Best,
Wolfgang

-----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 ~ 15m², however the grain weight was expressed in kg/10000 m² (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
```

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