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

  2. 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)

  3. 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) })

  4. 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.

  5. 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

  6. funnel(mod)

  7. 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")

  8. Many funnel types

  9. 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

  10. What is Trim and Fill Doing? par(mfrow=c(1,2)) funnel(mod) funnel(trimfill(mod, side="right")) par(mfrow=c(1,1))

  11. What is Trim and Fill Doing?

  12. 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

  13. 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

  14. 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

  15. Influence: inf(mod)