ssfunnel {altmeta}

Contour-Enhanced Sample-Size-Based Funnel Plot

Description

Generates contour-enhanced sample-size-based funnel plot for a meta-analysis of mean differences, standardized mean differences, (log) odds ratios, (log) relative risks, or risk differences.

Usage

ssfunnel(y, s2, n, data, type, alpha = c(0.1, 0.05, 0.01, 0.001),
         log.ss = FALSE, sigma, p0, xlim, ylim, xlab, ylab,
         cols.contour, col.mostsig, cex.pts, lwd.contour, pch,
         x.legend, y.legend, cex.legend, bg.legend, ...)

Arguments

y

a numeric vector or the corresponding column name in the argument data, specifying the observed effect sizes in the collected studies.

s2

a numeric vector or the corresponding column name in the argument data, specifying the within-study variances.

n

a numeric vector or the corresponding column name in the argument data, specifying the study-specific total sample sizes.

data

an optional data frame containing the meta-analysis dataset. If data is specified, the previous arguments, y, s2, and n, should be specified as their corresponding column names in data.

type

a character string specifying the type of effect size, which should be one of "md" (mean difference), "smd" (standardized mean difference), "lor" (log odds ratio), "lrr" (log relative risk), and "rd" (risk difference).

alpha

a numeric vector specifying the significance levels to be presented in the sample-size-based funnel plot.

log.ss

a logical value indicating whether sample sizes are plotted on a logarithmic scale (TRUE) or not (FALSE, the default).

sigma

a positive numeric value that is required for the mean difference (type = "md"), specifying a rough estimate of the common standard deviation of the samples' continuous outcomes in the two groups across studies. It is not used for other effect size types.

p0

an optional numeric value specifying a rough estimate of the common event rate in the control group across studies. It is only used for the (log) odds ratio, (log) relative risk, and risk difference.

xlim

the x limits c(x1, x2) of the plot.

ylim

the y limits c(y1, y2) of the plot.

xlab

a label for the x axis.

ylab

a label for the y axis.

cols.contour

a vector of character strings; they indicate colors of the contours to be presented in the sample-size-based funnel plot, and correspond to the significance levels specified in the argument alpha.

col.mostsig

a character string specifying the color for the most significant result among the studies in the meta-analysis.

cex.pts

the size of the points.

lwd.contour

the width of the contours.

pch

the symbol of the points.

x.legend

the x co-ordinate or a keyword, such as "topleft" (the default), to be used to position the legend. It is passed to legend.

y.legend

the y co-ordinate to be used to position the legend (the default is NULL).

cex.legend

the size of legend text.

bg.legend

the background color for the legend box.

...

other arguments that can be passed to plot.default.

Details

A contour-enhanced sample-size-based funnel plot is generated; it presents study-specific total sample sizes against the corresponding effect size estimates. It is helpful to avoid the confounding effect caused by the intrinsic association between effect size estimates and standard errors in the conventional standard-error-based funnel plot. See details of the derivations of the contours in Lin (2019).

Value

None.

References

Lin L (2019). "Graphical augmentations to sample-size-based funnel plot in meta-analysis." Research Synthesis Methods, 10(3), 376–388. <doi: 10.1002/jrsm.1340>

Peters JL, Sutton AJ, Jones DR, Abrams KR, Rushton L (2006). "Comparison of two methods to detect publication bias in meta-analysis." JAMA, 295(6), 676–680. <doi: 10.1001/jama.295.6.676>

Examples

## mean difference
data("dat.annane")
# descriptive statistics for sigma (continuous outcomes' standard deviation)
quantile(sqrt(dat.annane$s2/(1/dat.annane$n1 + 1/dat.annane$n2)),
  probs = c(0, 0.25, 0.5, 0.75, 1))
# based on sigma = 8
ssfunnel(y, s2, n, data = dat.annane, type = "md",
  alpha = c(0.1, 0.05, 0.01, 0.001), sigma = 8)
# sample sizes presented on a logarithmic scale with plot title
ssfunnel(y, s2, n, data = dat.annane, type = "md",
  alpha = c(0.1, 0.05, 0.01, 0.001), sigma = 8, log.ss = TRUE,
  main = "Contour-enhanced sample-size-based funnel plot")
# based on sigma = 17, with specified x and y limits
ssfunnel(y, s2, n, data = dat.annane, type = "md",
  xlim = c(-15, 15), ylim = c(30, 500),
  alpha = c(0.1, 0.05, 0.01, 0.001), sigma = 17, log.ss = TRUE)
# based on sigma = 20
ssfunnel(y, s2, n, data = dat.annane, type = "md",
  xlim = c(-15, 15), ylim = c(30, 500),
  alpha = c(0.1, 0.05, 0.01, 0.001), sigma = 20, log.ss = TRUE)

## standardized mean difference
data("dat.barlow")
ssfunnel(y, s2, n, data = dat.barlow, type = "smd",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 1))

## log odds ratio
data("dat.butters")
ssfunnel(y, s2, n, data = dat.butters, type = "lor",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 1.5))
# use different colors for contours
ssfunnel(y, s2, n, data = dat.butters, type = "lor",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 1.5),
  cols.contour = c("blue", "green", "yellow", "red"), col.mostsig = "black")
# based on p0 = 0.3 (common event rate in the control group across studies)
ssfunnel(y, s2, n, data = dat.butters, type = "lor",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 1.5), p0 = 0.3)
# based on p0 = 0.5
ssfunnel(y, s2, n, data = dat.butters, type = "lor",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 1.5), p0 = 0.5)

## log relative risk
data("dat.williams")
ssfunnel(y, s2, n, data = dat.williams, type = "lrr",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-1.5, 2.5))
# based on p0 = 0.2
ssfunnel(y, s2, n, data = dat.williams, type = "lrr",
  alpha = c(0.1, 0.05, 0.01, 0.001), p0 = 0.2, xlim = c(-1.5, 2.5))
# based on p0 = 0.3
ssfunnel(y, s2, n, data = dat.williams, type = "lrr",
  alpha = c(0.1, 0.05, 0.01, 0.001), p0 = 0.3, xlim = c(-1.5, 2.5))

## risk difference
data("dat.kaner")
ssfunnel(y, s2, n, data = dat.kaner, type = "rd",
  alpha = c(0.1, 0.05, 0.01, 0.001), xlim = c(-0.5, 0.5))
# based on p0 = 0.1
ssfunnel(y, s2, n, data = dat.kaner, type = "rd",
  alpha = c(0.1, 0.05, 0.01, 0.001), p0 = 0.1, xlim = c(-0.5, 0.5))
# based on p0 = 0.4
ssfunnel(y, s2, n, data = dat.kaner, type = "rd",
  alpha = c(0.1, 0.05, 0.01, 0.001), p0 = 0.4, xlim = c(-0.5, 0.5))