frag.nma.alpha {fragility}

Assessing Fragility of a Network Meta-Analysis at Different Significance Levels

Description

Produces fragility index or fragility quotient for altering statistical significance of treatment comparison(s) in a network meta-analysis with a binary outcome at different significance levels.

Usage

frag.nma.alpha(sid, tid, e, n, data, measure = "OR", random = TRUE,
               alpha.from = 0.005, alpha.to = 0.05, alpha.breaks = 10,
               mod.dir = "both", tid1.f, tid2.f, OR = 1, RR = 1, RD = 0,
               incr, allincr, addincr, allstudies, ...)

Arguments

sid

a numeric vector or the corresponding column name in the argument data, indicating the study IDs in the network meta-analysis.

tid

a numeric vector or the corresponding column name in the argument data, indicating the treatment IDs in the network meta-analysis.

e

a numeric vector or the corresponding column name in the argument data, indicating the event count in each study's each treatment group in the network meta-analysis.

n

a numeric vector or the corresponding column name in the argument data, indicating the sample size in each study's each treatment group in the network meta-analysis.

data

an optional data frame containing the dataset of the collected studies on multiple treatment comparisons in the network meta-analysis with a binary outcome. If data is specified, the previous arguments, sid, tid, e, and n, 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).

random

a logical value indicating whether the network meta-analysis is performed under the fixed-effects setting (FALSE) or the random-effects setting (TRUE, the default).

alpha.from

a numeric value between 0 and 1, indicating the smallest value of the statistical significance levels to be considered (the default is 0.005). It should be smaller than the argument alpha.to.

alpha.to

a numeric value between 0 and 1, indicating the largest value of the statistical significance levels to be considered (the default is 0.05). It should be larger than the argument alpha.from.

alpha.breaks

a positive integer indicating the number of statistical significance levels to be considered (the default is 100). The candidate significance levels are thus equally-spaced between alpha.from and alpha.to.

mod.dir

a character string or a square matrix of character strings indicating the direction of the confidence interval change for each treatment comparison 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). When it is specified as a matrix, the dimension should be the number of treatments, and the element (h, k) specifies the direction for treatment h compared with treatment k.

tid1.f

the first treatment(s) of comparison(s) of interest; if not specified, the fragility of all comparisons will be assessed.

tid2.f

the second treatment(s) of comparison(s) of interest.

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".

incr

A numerical value which is added to each cell frequency for studies with a zero cell count. It is passed to the function pairwise in the package netmeta.

allincr

A logical value indicating whether incr is added to each cell frequency of all studies if at least one study has a zero cell count. If FALSE (the default), incr is added only to each cell frequency of studies with a zero cell count. It is passed to the function pairwise in the package netmeta.

addincr

A logical value indicating whether incr is added to each cell frequency of all studies irrespective of zero cell counts (the default is FALSE). It is passed to the function pairwise in the package netmeta.

allstudies

A logical value indicating whether studies with zero or all events in two treatment groups are to be included in the network meta-analysis (the default is FALSE). It is used only for measure = "OR" and "RR". It is passed to the function pairwise in the package netmeta.

...

other arguments that can be passed to netmeta. See details in the manual of the package netmeta.

Value

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

data

original data of the network meta-analysis.

measure

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

alphas

different statistical significance levels.

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.

est.ori

a matrix containing the point estimate of the overall effect size for each pair of treatment comparisons based on the original network meta-analysis. Each element presents the treatment corresponding to the row compared with the treatment corresponding to the column; a similar interpretation applies to other outputs in the form of a matrix.

se.ori

a matrix containing the standard error of the overall effect size for each pair of treatment comparisons based on the original network meta-analysis.

pval.ori

the p-value of the overall effect size for each pair of treatment comparisons based on the original network meta-analysis.

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).

tid.f

treatment comparisons whose fragility is assessed.

FI

fragility indexes at different statistical significance levels in alphas.

FI.avg

average fragility indexes.

FQ

fragility quotients at different statistical significance levels in alphas, calculated as fragility indexes divided by the total sample sizes associated with the specific treatment comparisons.

FQ.avg

average fragility quotients based on the total sample sizes associated with the specific treatment comparisons.

FQ.nma

fragility quotients at different statistical significance levels in alphas, calculated as fragility indexes divided by the total sample size in the whole network meta-analysis (across all treatment groups).

FQ.nma.avg

average fragility quotients based on the total sample size in the whole network meta-analysis (across all treatment groups).

Note

When the network meta-analysis contains many studies and many treatments, the assessment of fragility may be very computationally demanding. In such cases, one may focus on certain treatment comparisons that are of primary interest by specifying the arguments tid1.f and tid2.f.

References

Benjamin DJ, Berger JO, Johannesson M, Nosek BA, Wagenmakers EJ, Berk R, Bollen KA, Brembs B, Brown L, Camerer C, Cesarini D, Chambers CD, Clyde M, Cook TD, De Boeck P, Dienes Z, Dreber A, Easwaran K, Efferson C, Fehr E, Fidler F, Field AP, Forster M, George EI, Gonzalez R, Goodman S, Green E, Green DP, Greenwald AG, Hadfield JD, Hedges LV, Held L, Ho TH, Hoijtink H, Hruschka DJ, Imai K, Imbens G, Ioannidis JPA, Jeon M, Jones JH, Kirchler M, Laibson D, List J, Little R, Lupia A, Machery E, Maxwell SE, McCarthy M, Moore DA, Morgan SL, Munafo M, Nakagawa S, Nyhan B, Parker TH, Pericchi L, Perugini M, Rouder J, Rousseau J, Savalei V, Schonbrodt FD, Sellke T, Sinclair B, Tingley D, Van Zandt T, Vazire S, Watts DJ, Winship C, Wolpert RL, Xie Y, Young C, Zinman J, Johnson VE (2018). "Redefine statistical significance." Nature Human Behaviour, 2, 6–10. <doi: 10.1038/s41562-017-0189-z>

Ioannidis JPA (2018). "The proposal to lower P value thresholds to .005." JAMA, 319(14), 1429–30. <doi: 10.1001/jama.2018.1536>

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.nma

Examples

## Load datasets of network meta-analysis of
##  chronic obstructive pulmonary disease (COPD)
data(dat.copd)

## Assess fragility of network  meta-analysis of COPD
##  at multiple significance levels
out1 <- frag.nma.alpha(sid, tid, e, n, data = dat.copd)
out1

## Generate plot to show fragility measures against significance levels;
##  see more options of usage in examples of frag.study.alpha()
plot(out1, tid1 = 2, tid2 = 1)
plot(out1, tid1 = 3, tid2 = 1)
plot(out1, tid1 = 4, tid2 = 1)
plot(out1, tid1 = 3, tid2 = 2)
plot(out1, tid1 = 4, tid2 = 2)
plot(out1, tid1 = 4, tid2 = 3)