`llplot.Rd`

Function to plot the likelihood of a certain parameter corresponding to an effect size or outcome measure given the study data.

```
llplot(measure, yi, vi, sei, ai, bi, ci, di, n1i, n2i, data, subset, drop00=TRUE,
xvals=1000, xlim, ylim, xlab, ylab, scale=TRUE,
lty, lwd, col, level=99.99, refline=0, ...)
```

- measure
a character string to specify for which effect size or outcome measure the likelihoods should be calculated. See ‘Details’ for possible options and how the data should then be specified.

- yi
vector with the observed effect sizes or outcomes.

- vi
vector with the corresponding sampling variances.

- sei
vector to specify the corresponding standard.

- ai
vector to specify the \(2 \times 2\) table frequencies (upper left cell).

- bi
vector to specify the \(2 \times 2\) table frequencies (upper right cell).

- ci
vector to specify the \(2 \times 2\) table frequencies (lower left cell).

- di
vector to specify the \(2 \times 2\) table frequencies (lower right cell).

- n1i
vector to specify the group sizes or row totals (first group/row).

- n2i
vector to specify the group sizes or row totals (second group/row).

- data
optional data frame containing the variables given to the arguments above.

- subset
optional (logical or numeric) vector to specify the subset of studies that should be included in the plot.

- drop00
logical to specify whether studies with no cases (or only cases) in both groups should be dropped. See ‘Details’.

- xvals
integer to specify for how many distinct values the likelihood should be evaluated.

- xlim
x-axis limits. If unspecified, the function sets the x-axis limits to some sensible values.

- ylim
y-axis limits. If unspecified, the function sets the y-axis limits to some sensible values.

- xlab
title for the x-axis. If unspecified, the function sets an appropriate axis title.

- ylab
title for the y-axis. If unspecified, the function sets an appropriate axis title.

- scale
logical to specify whether the likelihood values should be scaled, so that the total area under each curve is (approximately) equal to 1.

- lty
the line types (either a single value or a vector of length \(k\)). If unspecified, the function sets the line types according to some characteristics of the likelihood function. See ‘Details’.

- lwd
the line widths (either a single value or a vector of length \(k\)). If unspecified, the function sets the widths according to the sampling variances (so that the line is thicker for more precise studies and vice-versa).

- col
the line colors (either a single value or a vector of length \(k\)). If unspecified, the function uses various shades of gray according to the sampling variances (so that darker shades are used for more precise studies and vice-versa).

- level
numeric value between 0 and 100 to specify the plotting limits for each likelihood line in terms of the confidence interval (the default is 99.99).

- refline
numeric value to specify the location of the vertical ‘reference’ line (the default is 0). The line can be suppressed by setting this argument to

`NA`

.- ...
other arguments.

At the moment, the function only accepts `measure="GEN"`

or `measure="OR"`

.

For `measure="GEN"`

, one must specify arguments `yi`

for the observed effect sizes or outcomes and `vi`

for the corresponding sampling variances (instead of specifying `vi`

, one can specify the standard errors via the `sei`

argument). The function then plots the likelihood of the true effect size or outcome based on a normal sampling distribution with observed outcome as given by `yi`

and variance as given by `vi`

for each study.

For `measure="OR"`

, one must specify arguments `ai`

, `bi`

, `ci`

, and `di`

, which denote the cell frequencies of the \(2 \times 2\) tables. Alternatively, one can specify `ai`

, `ci`

, `n1i`

, and `n2i`

. See `escalc`

function for more details. The function then plots the likelihood of the true log odds ratio based on the non-central hypergeometric distribution for each \(2 \times 2\) table. Since studies with no cases (or only cases) in both groups have a flat likelihood and are not informative about the odds ratio, they are dropped by default (i.e., `drop00=TRUE`

) and are hence not drawn (if `drop00=FALSE`

, these likelihood are indicated by dotted lines). For studies that have a single zero count, the MLE of the odds ratio is infinite and these likelihoods are indicated by dashed lines.

van Houwelingen, H. C., Zwinderman, K. H., & Stijnen, T. (1993). A bivariate approach to meta-analysis. *Statistics in Medicine*, **12**(24), 2273–2284. https://doi.org/10.1002/sim.4780122405

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. *Journal of Statistical Software*, **36**(3), 1–48. https://doi.org/10.18637/jss.v036.i03

```
### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
### draw likelihoods
llplot(measure="GEN", yi=yi, vi=vi, data=dat, lwd=1, refline=NA, xlim=c(-3,2))
### create plot (Figure 2 in van Houwelingen, Zwinderman, & Stijnen, 1993)
llplot(measure="OR", ai=b.xci, n1i=nci, ci=b.xti, n2i=nti, data=dat.collins1985a,
lwd=1, refline=NA, xlim=c(-4,4), drop00=FALSE)
#> Warning: 2 studies with NAs omitted from plotting.
```