Description Usage Arguments Details Value Author(s) References Examples
Creates a lineup of funnel plots to conduct visual funnel plot inference (Kossmeier, Tran, & Voracek, 2019). The funnel plot showing the actually supplied data is presented alongside null plots showing simulated data under the null hypothesis.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  funnelinf(
x,
group = NULL,
group_permut = FALSE,
n = 20,
null_model = "REM",
y_axis = "se",
contours = TRUE,
sig_contours = TRUE,
contours_col = "Blues",
trim_and_fill = FALSE,
trim_and_fill_side = "left",
egger = FALSE,
show_solution = FALSE,
rorschach = FALSE,
point_size = 1.5,
text_size = 3,
xlab = "Effect",
ylab = NULL,
x_trans_function = NULL,
x_breaks = NULL
)

x 
data.frame or matrix with the effect sizes of all studies (e.g.,
correlations, log odds ratios, or Cohen d) in the first column and their
respective standard errors in the second column. Alternatively, x can be the
output object of function 
group 
factor indicating the subgroup of each study to show in the funnel plot. Has to be in the same order than 
group_permut 
logical scalar indicating if subgroup membership should be permuted in the null plots. Ignored if no group is supplied. 
n 
integer specifying the absolute number of plots in the lineup. 
null_model 
character string indicating which metaanalytic model should be used to simulate the effect sizes for the null plots. Available options are "FEM" for the fixed effect model and "REM" (default) for the randomeffects model (using the DerSimonianLaird method to estimate the betweenstudy variance tau squared). 
y_axis 
character string indicating which y axis should be used in the funnel plot. Available options are "se" (default) for standard error and "precision" for the reciprocal of the standard error. 
contours 
logical scalar indicating if classic funnel plot confidence contours and the summary effect should be displayed (i.e., summary effect +/ qnorm(0.975) * SE). 
sig_contours 
logical scalar. Should significance contours be drawn? Significance contours show which combination of effect size and standard error lead to study pvalues smaller than 0.05 or 0.01 (using a Wald test). 
contours_col 
character string indicating the color palette used from package RColorBrewer for

trim_and_fill 
logical scalar. Should studies imputed by the trim and fill method be displayed? Also shows the adjusted summary
effect if 
trim_and_fill_side 
character string indicating on which side of the funnel plot studies should be imputed by the trim and fill method (i.e., on which side studies are presumably missing due to publication bias). Must be either "right" or "left" (default). 
egger 
logical scalar. Should Egger's regression line be drawn? Only available if 
show_solution 
logical scalar. Should the realdata plot be highlighted? 
rorschach 
logical scalar. Should the lineup only consist of null plots? 
point_size 
numeric value. Size of the study points in the funnel plots. 
text_size 
numeric value. Size of text in the lineup. 
xlab 
character string specifying the label of the x axis. 
ylab 
character string specifying the label of the y axis. 
x_trans_function 
function to transform the labels of the x axis. Common uses are to transform
logoddsratios or logriskratios with 
x_breaks 
numeric vector of values for the breaks on the xaxis. When used in tandem with 
Funnel plots are widely used in metaanalysis to assess small study effects as potential indicator for publication bias. However, interpretations of funnel plots often lead to false conclusions about the presence and severity of bias (e.g., Terrin, Schmid, and Lau, 2005). Visual inference (Buja et al. 2009; Majumder, Hofmann, and Cook 2013) can help to improve the validity of conclusions based on the visual inspection of a funnel plot by saving investigators from interpreting funnelplot patterns which might be perfectly plausible by chance. Only if the realdata funnel plot is distinguishable from nullplots, the null hypothesis is formally rejected and conclusions based on the visual inspection of the realdata funnel plot might be warranted (for further details, see Kossmeier, Tran, & Voracek, 2019).
Function funnelinf
utilizes package nullabor for null plot simulation and ggplot2 for
plotting the lineup. Several tailored features for visual inference with funnel plots are provided which currently include:
options for nullplot simulation under both FEM and REM metaanalysis (see below).
subgroup analysis.
graphical options specific to the funnel plot (significance and confidence contours, and choice of the ordinate).
additional options to display various statistical information (Egger's regression line, and imputed studies by, as well as the adjusted summary effect from, the trimandfill method).
Null plots are simulated assuming normally distributed effect sizes with expected value equal to the observed summary effect and variance
either equal to the observed study variances (null_model = "FEM"
) or the sum of the observed study variances and the estimated
between study variance tau squared (null_model = "REM"
).
A lineup of n (20 by default) funnel plots; one showing the real data and n1 showing simulated data under the null hypothesis
Michael Kossmeier* <michael.kossmeier@univie.ac.at>
Ulrich S. Tran* <ulrich.tran@univie.ac.at>
Martin Voracek* <martin.voracek@univie.ac.at>
*Department of Basic Psychological Research and Research Methods, School of Psychology, University of Vienna
Buja, A., Cook, D., Hofmann, H., Lawrence, M., Lee, E. K., Swayne, D. F., & Wickham, H. (2009). Statistical inference for exploratory data analysis and model diagnostics. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 367, 43614383.
Kossmeier, M., Tran, U. & Voracek, M. (2019) Visual inference for the funnel plot in metaanalysis. Zeitschrift für Psychologie  Journal of Psychology, 227.
Majumder, M., Hofmann, H., & Cook, D. (2013). Validation of visual statistical inference, applied to linear models. Journal of the American Statistical Association, 108, 942956.
Terrin, N., Schmid, C. H., & Lau, J. (2005). In an empirical evaluation of the funnel plot, researchers could not visually identify publication bias. Journal of clinical epidemiology, 58, 894901.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  ## Not run:
# Plotting a funnel plot lineup with the exrehab data to conduct visual funnel plot inference
funnelinf(x = exrehab[, c("logrr", "logrr_se")])
# Plotting a funnel plot lineup with the mozart data to conduct visual funnel plot inference
# considering subgroups
funnelinf(x = mozart[, c("d", "se")],
group = mozart[, "rr_lab"],
group_permut = TRUE, null_model = "REM")
# Plotting a funnel plot lineup with the brainvolume data to conduct visual funnel plot inference
# considering heterogeneity by using the fixed effect model for null plot simulation
funnelinf(x = brainvol[, c("z", "z_se")],
null_model = "FEM")
## End(Not run)

To see the solution run nullabor::decrypt("Jzis NZoZ qA mKgqoqKA lf")
To see the solution run nullabor::decrypt("Jzis NZoZ qA mKgqoqKA hT")
To see the solution run nullabor::decrypt("Jzis NZoZ qA mKgqoqKA 2b")
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