---
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,
  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),
  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