[R-meta] intercept-slope model & network meta-analysis

Dear
?List
,

?I have a datset containing 36 field plots experiments testing the effect
of several fungicides to control a soybean fungic disease.

?
This is how my raw ?data looks like
? ?
?
(36 independent studies - CRBDs)?:

  study      fungic   rep    Mod_A   Mod_B   sev yield
      1
?Check ?
     1    2High    1Low    55  2918
      1         Check
? ?
     2    2High    1Low    50  3468
      1
?
Check
? ?
   3    2High    1Low    45  1626
      1
?
Check
? ?
   4    2High    1Low    40  2921
      1
?        Trt_A

? ?
   1    2High    1Low    35  2414
      1
?
Trt_A
?

? ?
   2    2High    1Low    40  3104
      1
?
Trt_A
??

? ?
  3    2High    1Low    25  1878
      1
?
Trt_A
? ?
  4    2High    1Low    30  1952
      1
?
Trt_
?B

? ?
   1    2High    1Low    40  2708
      1
?
Trt_
?B

? ?
   2    2High    1Low    50  2475
?     ...?
     36

?
?At each study, ?a set of
fungic
?ides are the
treatments
? including a Check?
(different combinations across the studies, that?s why I adopted network MA)
,
?"?
rep
?"?
 are the blocks,
?"?
sev
?"?
 is the disease (%) and
?"?
yield
?"?
 is the grain mass.

?The moderator variables are study-specific characteristics, like disease
pressure (Mod_A) or Yield potential (Mod_B)?

I have two objectives:

1? estimate the intercept and slope of the relationship yield ~ sev and
test the inclusion of moderator variables (I?m not testing the effect of
the treatments in this case, I?m interested on the trends of yield ~ sev)
?.
I started using a
multivariate
?
Two-Stage Analysis
?
?
approach then
?, f
ollowing the tutorial ?(
http://www.metafor-project.org/doku.php/tips:two_stage_analysis#mixed-effects_model_approach
)
? ?
I moved to a multi-level
?
Mixed-Effects Models
? with very similiar results (but much more time-efficiency)?
?
I am trying this:

# Overall random intercept and slopes
m1  <- lmer(yield ~ sev + (sev|study), data=df)

# Including effect of moderators on the intercept and slopes
m2  <- lmer(yield ~ sev * mod
?_?
A+ (sev|study), data=df)

# Including effect of moderator A on the intercept
m3  <- lmer(yield ~ sev + mod
?_?
A+ (sev|study), data=df)

# Including effect of moderator A on the slope
m4  <- lmer(yield ~ sev : mod
?_?
A+ (sev|study), data=df)

# Including effect of moderator A on the slope and moderator B on the
intercept
m5  <- lmer(yield ~ sev : mod
?_?
A + mod
?_?
B + (sev|study), data=longs)

Question: do I need to include the moderator variables in random effects?
?Is it enough to use the AIC to test the goodness of fit of the models and
likelihood ratio of them to select the best model??

===============================

2? Then I do wanted to test the effect of treatments on yield, considering
mean differences to the untreated checks within each study.
So I performed a network meta-analysis, agreggating the data and estimating
the Mean Square Error from each study ANOVA
?:?

Aggregated data:

study     fungic
?  ?
yield
?_m?

?
?Mod_A
?
?   ?
?  Mod_B

? ?
MSE
?
1
?Check

? ?
2640
?     ? 2_High     1_Low
88931.95
    1
Trt_A

? ?
? ?
2733
?  ?
2_High
?   ?

1_Low
?    ?
88931.95
    1
?      Trt_B

?  ?
2858
?  ?
2_High
?   ?

1_Low
?   ?

88931.95

?...

?where yield_m is the within-study treatment mean and MSE is the
within-study mean square error from ANOVA ?

?The model I tried is:?

net_D <- rma.mv(yield
?_m?
, vi2,
                mods = ~ fungic
? * Mod_A?
,
                random = ~ fungic | study,
                struct= "UN", method="ML",
                data= df,
                control = list(optimizer="nlm"))

?anova(net_D, btt=9:14)  # to test the effect of moderators?

where vi2: vi = MSE / bk #Sampling variance for yi (bk = 4)

?My concern is if Am I going well with this model? ?or should I try to use
the raw data as well, considering the block effect?

Thanks for your help!

Juan
? Edwards

(Phd candidate at Plant disease epidemiology lab in Univ. Sao Paulo -
Brazil)