llplot: Log-Likelihood Plot of a Parameter Corresponding to an Outcome or Effect Size Measure

Description

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

Usage

llplot(measure="OR", 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, ...)

Arguments

measure

a character string indicating for which effect size or outcome measure the log-likelihood should be calculated. See Details for possible options and how the data should be specified.

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

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

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

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 vector indicating the subset of studies that should be used. This can be a logical vector or a numeric vector indicating the indices of the studies to include.

drop00

logical indicating whether studies with no cases (or only cases) in both groups should be dropped. See Details.

xvals

integer specifying for how many distinct values of the (log) odds ratio the log-likelihood should be evaluated.

xlim

x-axis limits. If unspecified, the function tries to set the x-axis limits to some sensible values.

ylim

y-axis limits. If unspecified, the function tries to set the y-axis limits to some sensible values.

xlab

title for the x-axis. If unspecified, the function tries to set an appropriate axis title.

ylab

title for the y-axis. If unspecified, the function tries to set an appropriate axis title.

scale

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

lty

the line type (either a single value or a vector of length $k$). If unspecified, the function uses solid lines for tables where the MLE of the odds ratio is finite and dashed/dotted lines otherwise.

lwd

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

level

numerical value between 0 and 100 specifying the plotting limits for each density line in terms of the confidence interval (default is 99.99).

refline

value at which a vertical reference line should be drawn (default is 0). The line can be suppressed by setting this argument to NA.

...

other arguments.

Details

At the moment, the function only accepts measure="OR". For each $2 \times 2$ table, the function then plots the log-likelihood of the (log) odds ratio based on the non-central hypergeometric distribution. 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). For studies that have a single zero count, the MLE of the odds ratio is infinite and these likelihoods are indicated by a dashed line.

References

van Houwelingen, H. C., Zwinderman, K. H., & Stijnen, T. (1993). A bivariate approach to meta-analysis. Statistics in Medicine, 12, 2273--2284. Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. http://www.jstatsoft.org/v36/i03/.

Examples

Run this code

### load BCG vaccine data
data(dat.bcg)

### create plot
llplot(measure="OR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### load histamine H2 antagonist data
data(dat.collins1985a)

### create plot (Figure 2 in van Houwelingen, Zwinderman, & Stijnen, 1993)
llplot(measure="OR", ai=xci, n1i=nci, ci=xti, n2i=nti, data=dat.collins1985a,
       lwd=1, refline=NA, xlim=c(-4,4), drop00=FALSE)