How to Evaluate the Effects of Potential Bias in Meta-analysis in

R

Load, Prep, and Check

library(ggplot2)

library(metafor)

#load the data

marine <- read.csv("marine_meta_short.csv",

na.strings=c("NA", ".", ""))

#check variable types

summary(marine)

Calculating Effect Sizes by Hand#Log Ratio

marine$LR <- log(marine$Y_Poly) –

log(marine$Y_Avg_Mono)

marine$VLR <- with(marine, {

SD_Poly^2 / (N_Poly * Y_Poly^2) +

SD_Avg_Mono^2 / (N_Avg_Mono * Y_Avg_Mono^2)

})

Fit a Model (we’ll talk about this soon)

mod <- rma(LR, VLR, data=marine)

Warning message:

In rma(LR, VLR, data = marine) :

Studies with NAs omitted from model fitting.

What did we find?Random-Effects Model (k = 168; tau^2 estimator: REML)

…

Model Results:

estimate se zval pval ci.lb ci.ub

0.1324 0.0429 3.0851 0.0020 0.0483 0.2165 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

funnel(mod)

Many funnel types

funnel(mod, main="Standard Error")

funnel(mod, yaxis="vi", main="Sampling Variance")

funnel(mod, yaxis="seinv", main="Inverse Standard Error")

funnel(mod, yaxis="vinv", main="Inverse Sampling Variance")

Many funnel types

trimfill(mod, side="right")

Model Results:

estimate se zval pval ci.lb ci.ub 0.2957 0.0493 5.9994 <.0001 0.1991 0.3923 ***

---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

What is Trim and Fill Doing?

par(mfrow=c(1,2))

funnel(mod)

funnel(trimfill(mod, side="right"))

par(mfrow=c(1,1))

What is Trim and Fill Doing?

Fail-Safe: fsn(LR, VLR, data=marine)

Fail-safe N Calculation Using the Rosenthal Approach

Observed Significance Level: <.0001

Target Significance Level: 0.05

Fail-safe N: 12681

Other Types of Fail-Safe Numbers

> fsn(LR, VLR, data=marine, type="Rosenberg") #based on weighted analysis

Fail-safe N Calculation Using the Rosenberg Approach

Average Effect Size: 0.0384

Observed Significance Level: <.0001

Target Significance Level: 0.05

Fail-safe N: 3733

Other Types of Fail-Safe Numbers

> fsn(LR, VLR, data=marine, type="Orwin") #based on unweighted analysis and target effect size

Fail-safe N Calculation Using the Orwin Approach

Average Effect Size: 0.1091

Target Effect Size: 0.0546

Fail-safe N: 168

Influence: inf(mod)