metanalisis
Ismael Calandri
4/4/2021
Part 0 data correction
knitr::opts_chunk$set(echo = T)
library(estmeansd)
# BoxCox estimacion del grupo expuesto Raman,2020
bc.mean.sd(q1.val=25,med.val=27,q3.val=29,n=19)## $est.mean
## [1] 26.93041
##
## $est.sd
## [1] 3.214925# BoxCoxestimacion del grupo no expuesto Raman,2020
bc.mean.sd(q1.val=27,med.val=28,q3.val=29,n=30)## $est.mean
## [1] 27.92846
##
## $est.sd
## [1] 1.618756Part 1 Metanalisis
Metanalysis tabular results
knitr::opts_chunk$set(echo = F)
m.raw <- metacont(Ne,
Me,
Se,
Nc,
Mc,
Sc,
data=meta,
studlab=paste(Author),
comb.fixed = FALSE,
comb.random = TRUE,
prediction=TRUE,
sm="MD")
m.raw## MD 95%-CI %W(random)
## Amalakanti et al. 2021 -0.1000 [ -0.8862; 0.6862] 23.9
## Del Brutto, et al 2021 -2.1000 [ -3.7740; -0.4260] 20.2
## Ortelli et al 2021 -9.0000 [-12.4740; -5.5260] 12.2
## Raman et al 2021* -0.7400 [ -2.2695; 0.7895] 20.9
## Triana et al. 2020 -1.6900 [ -2.8251; -0.5549] 22.7
##
## Number of studies combined: k = 5
##
## MD 95%-CI z p-value
## Random effects model -2.0862 [-3.7756; -0.3968] -2.42 0.0155
## Prediction interval [-8.1948; 4.0224]
##
## Quantifying heterogeneity:
## tau^2 = 2.9414 [1.7606; 60.4080]; tau = 1.7151 [1.3269; 7.7723]
## I^2 = 86.0% [69.4%; 93.6%]; H = 2.67 [1.81; 3.96]
##
## Test of heterogeneity:
## Q d.f. p-value
## 28.59 4 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Jackson method for confidence interval of tau^2 and tauForest plot
Part 2 Bias analysis
Influential assesment
Lucia, In this section we analyze the possibility that some of the data have a different origin from those presented by the other studies (outlier) and if so, what weight it has in the results (influentia).
Outlier detection
## Identified outliers (random-effects model)
## ------------------------------------------
## "Ortelli et al 2021"
##
## Results with outliers removed
## -----------------------------
## MD 95%-CI %W(random) exclude
## Amalakanti et al. 2021 -0.1000 [ -0.8862; 0.6862] 33.2
## Del Brutto, et al 2021 -2.1000 [ -3.7740; -0.4260] 19.0
## Ortelli et al 2021 -9.0000 [-12.4740; -5.5260] 0.0 *
## Raman et al 2021* -0.7400 [ -2.2695; 0.7895] 20.9
## Triana et al. 2020 -1.6900 [ -2.8251; -0.5549] 27.0
##
## Number of studies combined: k = 4
##
## MD 95%-CI z p-value
## Random effects model -1.0416 [-2.0239; -0.0594] -2.08 0.0377
## Prediction interval [-5.0004; 2.9172]
##
## Quantifying heterogeneity:
## tau^2 = 0.5954 [0.0000; 12.3469]; tau = 0.7716 [0.0000; 3.5138]
## I^2 = 61.2% [0.0%; 87.0%]; H = 1.61 [1.00; 2.77]
##
## Test of heterogeneity:
## Q d.f. p-value
## 7.73 3 0.0520
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Jackson method for confidence interval of tau^2 and tauInfluential analysis
## [===========================================================================] DONE
In red: extreme influential studies according Viechtbauer and Cheung rule
Please interpretate the subplots as follow:
dffits: The DIFFITS value of a study indicates in standard deviations how much the predicted pooled effect changes after excluding this study. cook.d: The Cook’s distance resembles the Mahalanobis distance you may know from outlier detection in conventional multivariate statistics. It is the distance between the value once the study is included compared to when it is excluded. cov.r: The covariance ratio is the determinant of the variance-covariance matrix of the parameter estimates when the study is removed, divided by the determinant of the variance-covariance matrix of the parameter estimates when the full dataset is considered. Importantly, values of cov.r < 1 indicate that removing the study will lead to a more precise effect size estimation (i.e., less heterogeneity).
**Influential analysis summary**: Ortelli is an outlier according the rest of the data! It has enormous effect on results! I strongly suggest discuss this on the paper.
Publication bias assesment
In this section we analyze the possibility that negative studies have not been submitted because they are of less interest to the journals to be published (publication bias).
Funnel plot
The funnel plot method assumes that the effects should cluster symmetrically around the estimated mean of the effect.
In this case distribution is simmetric if we do not take into account Ortelli results (Ortelli, always Ortelli!)
Egger´s test
This test provides a numerica measure of effects asimmetry
## Warning in eggers.test(x = m.raw): Your meta-analysis contains k = 5 studies.
## Egger's test may lack the statistical power to detect bias when the number of
## studies is small (i.e., k<10).## Eggers' test of the intercept
## =============================
##
## intercept 95% CI t p
## -5.319 -8.22 - -2.42 -3.596 0.03687483
##
## Eggers' test indicates the presence of funnel plot asymmetry.Trim and fill
In this part of the workflow. I used the Duval & Tweedie’s trim-and-fill procedure to correct assimetry after input theorical data to fill the gap
## MD 95%-CI %W(random)
## Amalakanti et al. 2021 -0.1000 [ -0.8862; 0.6862] 16.9
## Del Brutto, et al 2021 -2.1000 [ -3.7740; -0.4260] 15.1
## Ortelli et al 2021 -9.0000 [-12.4740; -5.5260] 10.5
## Raman et al 2021* -0.7400 [ -2.2695; 0.7895] 15.5
## Triana et al. 2020 -1.6900 [ -2.8251; -0.5549] 16.3
## Filled: Del Brutto, et al 2021 0.8313 [ -0.8427; 2.5053] 15.1
## Filled: Ortelli et al 2021 7.7313 [ 4.2573; 11.2053] 10.5
##
## Number of studies combined: k = 7 (with 2 added studies)
##
## MD 95%-CI z p-value
## Random effects model -0.7326 [-2.5199; 1.0546] -0.80 0.4217
## Prediction interval [-6.8124; 5.3471]
##
## Quantifying heterogeneity:
## tau^2 = 4.7624 [3.8709; 60.7593]; tau = 2.1823 [1.9675; 7.7948]
## I^2 = 89.2% [80.2%; 94.1%]; H = 3.04 [2.25; 4.12]
##
## Test of heterogeneity:
## Q d.f. p-value
## 55.56 6 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Jackson method for confidence interval of tau^2 and tau
## - Trim-and-fill method to adjust for funnel plot asymmetryTo correct publication bias is necessary to add **2 studies**
corrected funnel plot
Effect vs corrected effect
## [1] "Effect"## [1] -2.086214## [1] "Publication bias corrected effect"## [1] -0.7326456