frag.mas {fragility}

Assessing Fragility of Multiple Meta-Analyses With Binary Outcomes

Description

Produces fragility indexes or fragility quotients for altering statistical significance of multiple meta-analyses with binary outcomes.

Usage

frag.mas(e0, n0, e1, n1, ma.id, data, measure = "OR", alpha = 0.05,
         mod.dir = "both", OR = 1, RR = 1, RD = 0,
         method = "DL", test = "z", ...)

Arguments

e0

a numeric vector or the corresponding column name in the argument data, indicating event counts in group 0 among the studies in all meta-analyses.

n0

a numeric vector or the corresponding column name in the argument data, indicating sample sizes in group 0 among the studies in all meta-analyses.

e1

a numeric vector or the corresponding column name in the argument data, indicating event counts in group 1 among the studies in all meta-analyses.

n1

a numeric vector or the corresponding column name in the argument data, indicating sample sizes in group 1 among the studies in all meta-analyses.

ma.id

a numeric vector or the corresponding column name in the argument data, indicating the index of each meta-analysis.

data

an optional data frame containing the dataset of the multiple meta-analyses with binary outcomes. If data is specified, the previous arguments, e0, n0, e1, n1, and ma.id, should be specified as their corresponding column names in data.

measure

a character string indicating the measure of treatment effect (i.e., effect size) for the binary outcome. It should be one of "OR" (odds ratio, the default), "RR" (relative risk), and "RD" (risk difference).

alpha

a numeric value between 0 and 1, indicating the statistical significance level (the default is 0.05). It determines the confidence level (1-\alpha)\times100\% of the confidence interval when deriving the fragility index/quotient.

mod.dir

a character string indicating the direction of the confidence interval change due to event status modifications when the original confidence interval covers the null value (i.e., non-significance altered to significance). It is not used when significance is altered to non-significance. It should be one of "left" (moving to the left side of the null value), "right" (moving to the right side of the null value), "one" (based on the direction of the point estimate of the original overall effect size), and "both" (both directions, the default).

OR

a numeric positive value indicating the value of odds ratio under the null hypothesis (the default is 1). It is used only if the argument measure is "OR".

RR

a numeric positive value indicating the value of relative risk under the null hypothesis (the default is 1). It is used only if the argument measure is "RR".

RD

a numeric value between -1 indicating the value of risk difference under the null hypothesis (the default is 0). It is used only if the argument measure is "RD".

method

a character string specifying the method for performing meta-analysis. It is the same with the argument in frag.ma, and is passed to rma.uni. See details in the manual of the package metafor.

test

a character string specifying how confidence intervals are derived. It is the same with the argument in frag.ma, and is passed to rma.uni. See details in the manual of the package metafor.

...

other arguments that can be passed to rma.uni. See details in the manual of the package metafor.

Value

An object of classes "frag.mas" and "frag.multi". The object is a list containing the following components:

measure

measure of treatment effect (i.e., effect size).

alpha

pre-specified statistical significance level.

null

value of odds ratio, relative risk, or risk difference (specified by measure) under the null hypothesis. Note that odds ratio and relative risk are presented on a natural logarithmic scale in all output values.

mod.dir

the direction of the confidence interval change due to event status modifications when the original confidence interval covers the null value (i.e., non-significance altered to significance).

est.ori

the point estimates of the overall effect sizes based on the original datasets of the multiple meta-analyses.

ci.ori

the confidence intervals of the overall effect sizes based on the original datasets of the multiple meta-analyses.

pval.ori

the p-values of the overall effect sizes based on the original datasets of the multiple meta-analyses.

FI

fragility indexes of the multiple meta-analyses.

FQ

fragility quotients of the multiple meta-analyses.

References

Atal I, Porcher R, Boutron I, Ravaud P (2019). "The statistical significance of meta-analyses is frequently fragile: definition of a fragility index for meta-analyses." Journal of Clinical Epidemiology, 111, 32–40. <doi: 10.1016/j.jclinepi.2019.03.012>

Lin L, Chu H (2022). "Assessing and visualizing fragility of clinical results with binary outcomes in R using the fragility package." PLOS ONE, 17(6), e0268754. <doi: 10.1371/journal.pone.0268754>

See Also

frag.ma for assessing fragility of a meta-analysis; and frag.studies for assessing fragility of multiple individual studies.

Examples

## Load datasets of meta-analyses on nutrition support
data(dat.ns)

## Assess fragility of the 11th, 12th, and 13th meta-analyses
out1 <- frag.mas(e0, n0, e1, n1, ma.id,
  data = dat.ns[dat.ns$ma.id >= 11 & dat.ns$ma.id <= 13,], mod.dir = "one")
out1

## Generate bar plot or histogram to show fragility measures' distribution;
##  see more options of usage in examples of frag.studies()
plot(out1)


## Assess fragility of all meta-analyses
##  in the Cochrane systematic review on nutrition support;
##  it takes longer time
out2 <- frag.mas(e0, n0, e1, n1, ma.id, data = dat.ns)
out2
plot(out2)
plot(out2, max.f = 40, cex.name = 0.6, mgp = c(2, 0.5, 0))
plot(out2, fragility = "FQ", breaks = 20)