---

title: "How to perform a meta-analysis with R: a practical tutorial"

author: "Sara Balduzzi, Gerta Rücker, Guido Schwarzer"

output:

rmarkdown::pdf_document:

number_sections: false

rmarkdown::html_vignette:

toc: false

number_sections: false

bibliography: references.bib

vignette: >

%\VignetteIndexEntry{meta: How to perform a meta-analysis with R: a practical tutorial}

%\VignetteEngine{knitr::rmarkdown}

%\VignetteEncoding{UTF-8}

---

```{r, include = FALSE}

knitr::opts_chunk$set(

collapse = TRUE,

comment = "#>",

message = TRUE,

warning = FALSE

)

options(knitr.kable.NA = ".")

load("mmiss_limit.rda")

```

This vignette provides up-to-date commands for the analyses in "How to

perform a meta-analysis with R: a practical tutorial", *Evid Based

Ment Health* [@Bald:Ruec:Schw:how:2019].

## Install R packages

```{r, eval = FALSE}

install.packages(c("meta", "metasens"))

```

## Make R packages available

```{r}

library(meta)

```

```{r, eval = FALSE}

library(metasens)

```

Note, a similar message would be printed for R package

**metasens**. However, this vignette does not actually load

**metasens** as it might not be installed in addition to **meta**.

## Default settings for R session

Print results with two significant digits and use Paule-Mandel

estimator for between-study variance.

```{r}

settings.meta(digits = 2, method.tau = "PM")

```

Note, in the publication, argument 'method.tau' was used in R function

*metabin()*. Here, we set the Paule-Mandel method as the default for

any meta-analysis conducted in the current R session.

## Import the dataset

```{r}

joy = read.csv("Joy2006.txt")

# Add new variable: miss

joy$miss = ifelse((joy$drop.h + joy$drop.p) == 0,

"Without missing data", "With missing data")

head(joy)

str(joy)

```

## Section 'Fixed effect and random effects meta-analysis'

```{r}

m.publ = metabin(resp.h, resp.h + fail.h, resp.p, resp.p + fail.p,

data = joy, studlab = paste0(author, " (", year, ")"),

label.e = "Haloperidol", label.c = "Placebo",

label.left = "Favours placebo", label.right = "Favours haloperidol")

```

Print results of meta-analysis (Figure 1).

```{r}

summary(m.publ)

```

Same printout (result not shown)

```{r, eval = FALSE}

print(summary(m.publ))

```

Create Figure 2 (file 'figure2.pdf').

```{r}

forest(m.publ, sortvar = year, prediction = TRUE,

digits.pval.Q = 3,

file = "figure2.pdf", width = 10)

```

```{r, echo = FALSE, out.width = "95%"}

knitr::include_graphics("figure2.pdf")

```

## Section 'Assessing the impact of missing outcome data'

### Subgroup analysis of studies with and without missing data

```{r}

m.publ.sub = update(m.publ, subgroup = miss, print.subgroup.name = FALSE)

m.publ.sub

```

Create Figure 3 (file 'figure3.pdf').

```{r}

forest(m.publ.sub, sortvar = year,

xlim = c(0.1, 100), at = c(0.1, 0.3, 1, 3, 10, 30, 100),

digits.pval.Q = 3, test.subgroup.common = FALSE,

label.test.subgroup.random = "Test for subgroup differences:",

file = "figure3.pdf", width = 10)

```

```{r, echo = FALSE, out.width = "95%"}

knitr::include_graphics("figure3.pdf")

```

### Use imputation methods

```{r, eval = FALSE}

# Impute as no events (ICA-0) - default

mmiss.0 = metamiss(m.publ, drop.h, drop.p)

# Impute as events (ICA-1)

mmiss.1 = metamiss(m.publ, drop.h, drop.p, method = "1")

# Observed risk in control group (ICA-pc)

mmiss.pc = metamiss(m.publ, drop.h, drop.p, method = "pc")

# Observed risk in experimental group (ICA-pe)

mmiss.pe = metamiss(m.publ, drop.h, drop.p, method = "pe")

# Observed group-specific risks (ICA-p)

mmiss.p = metamiss(m.publ, drop.h, drop.p, method = "p")

# Best-case scenario (ICA-b)

mmiss.b = metamiss(m.publ, drop.h, drop.p, method = "b", small.values = "bad")

# Worst-case scenario (ICA-w)

mmiss.w = metamiss(m.publ, drop.h, drop.p, method = "w", small.values = "bad")

# Gamble-Hollis method

mmiss.gh = metamiss(m.publ, drop.h, drop.p, method = "GH")

# IMOR.e = 2 and IMOR.c = 2 (same as available case analysis)

mmiss.imor2 = metamiss(m.publ, drop.h, drop.p, method = "IMOR", IMOR.e = 2)

# IMOR.e = 0.5 and IMOR.c = 0.5

mmiss.imor0.5 = metamiss(m.publ, drop.h, drop.p, method = "IMOR", IMOR.e = 0.5)

```

Summarise results using R function *metabind()*.

```{r}

meths = c("Available case analysis (ACA)",

"Impute no events (ICA-0)", "Impute events (ICA-1)",

"Observed risk in control group (ICA-pc)",

"Observed risk in experimental group (ICA-pe)",

"Observed group-specific risks (ICA-p)",

"Best-case scenario (ICA-b)", "Worst-case scenario (ICA-w)",

"Gamble-Hollis analysis",

"IMOR.e = 2, IMOR.c = 2", "IMOR.e = 0.5, IMOR.c = 0.5")

# Use inverse-variance method for pooling (which is used for

# imputation methods)

m.publ.iv = update(m.publ, method = "Inverse")

# Combine results (random effects)

mbr = metabind(m.publ.iv,

mmiss.0, mmiss.1,

mmiss.pc, mmiss.pe, mmiss.p,

mmiss.b, mmiss.w, mmiss.gh,

mmiss.imor2, mmiss.imor0.5,

name = meths, pooled = "random")

```

Create Figure 4 (file 'figure4.pdf').

```{r}

forest(mbr, xlim = c(0.5, 4),

leftcols = c("studlab", "I2", "tau2", "Q", "pval.Q"),

leftlab = c("Meta-Analysis Method", "I2", "Tau2", "Q", "P-value"),

type = "diamond",

digits.addcols = c(4, 2, 2, 2), just.addcols = "right",

file = "figure4.pdf", width = 10)

```

```{r, echo = FALSE, out.width = "95%"}

knitr::include_graphics("figure4.pdf")

```

## Section 'Assessing and accounting for small-study effects'

### Funnel plot

```{r, eval = FALSE}

funnel(m.publ)

```

### Harbord's score test for funnel plot asymmetry

```{r}

metabias(m.publ, method.bias = "score")

```

### Trim-and-fill method

```{r}

tf.publ = trimfill(m.publ)

tf.publ

```

```{r}

summary(tf.publ)

```

```{r, eval = FALSE}

funnel(tf.publ)

```

### Limit meta-analysis

```{r, eval = FALSE}

l1.publ = limitmeta(m.publ)

```

Note, the printout for the limit meta-analysis is not shown in this

vignette as the installation of R package **metasens** is optional.

```{r, eval = FALSE}

l1.publ

```

Create Figure 5 (file 'figure5.pdf').

```{r, eval = FALSE}

pdf("figure5.pdf", width = 10, height = 10)

#

par(mfrow = c(2, 2), pty = "s",

oma = c(0, 0, 0, 0), mar = c(4.1, 3.1, 2.1, 1.1))

#

funnel(m.publ, xlim = c(0.05, 50), axes = FALSE)

axis(1, at = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 50))

axis(2, at = c(0, 0.5, 1, 1.5))

box()

title(main = "Panel A: Funnel plot", adj = 0)

#

funnel(m.publ, xlim = c(0.05, 50), axes = FALSE,

contour.levels = c(0.9, 0.95, 0.99),

col.contour = c("darkgray", "gray", "lightgray"))

legend("topright",

c("p < 1%", "1% < p < 5%", "5% < p < 10%", "p > 10%"),

fill = c("lightgray", "gray", "darkgray", "white"),

border = "white", bg = "white")

axis(1, at = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 50))

axis(2, at = c(0, 0.5, 1, 1.5))

box()

title(main = "Panel B: Contour-enhanced funnel plot", adj = 0)

#

funnel(tf.publ, xlim = c(0.05, 50), axes = FALSE)

axis(1, at = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 50))

axis(2, at = c(0, 0.5, 1, 1.5))

box()

title(main = "Panel C: Trim-and-fill method", adj = 0)

#

funnel(l1.publ, xlim = c(0.05, 50), axes = FALSE,

col.line = 8, lwd.line = 3)

axis(1, at = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 50))

axis(2, at = c(0, 0.5, 1, 1.5))

box()

title(main = "Panel D: Limit meta-analysis", adj = 0)

#

dev.off()

```

```{r, echo = FALSE, out.width = "95%"}

knitr::include_graphics("figure5.pdf")

```

# References