FEmrt: Fixed effect meta-tree

In metacart: Meta-CART: A Flexible Approach to Identify Moderators in Meta-Analysis

Description

A function to fit fixed effect meta-trees to meta-analytic data. The model is assuming a fixed effect within subgroups and between subgroups. The tree growing process is equivalent to the approach described in Li et al. (2017) using fixed effect weights in the function rpart() developed by Therneau, Atkinson & Ripley (2014).

Usage

FEmrt(
  formula,
  data,
  vi,
  subset,
  c = 1,
  control = rpart.control(xval = 10, minbucket = 3, minsplit = 6, cp = 1e-04),
  ...
)

Arguments

formula	A formula, with an outcome variable (usually the effect size) and the potential moderator variables but no interaction terms.
data	A data frame of a meta-analytic data set, including the study effect sizes, sampling variance, and the potential moderators.
vi	sampling variance of the effect size.
subset	optional expression that selects only a subset of the rows of the data.
c	A non-negative scalar.The pruning parameter to prune the initial tree by the "c*standard-error" rule.
control	the control object (similar to rpart.control from the rpart package) that is used in the tree algorithm
...	Additional arguments passed to the tree growing algorithm based on rpart.

Value

If (a) moderator effect(s) is(are) detected, the function will return a FEmrt object including the following components:

tree: The pruned tree that represents the moderator effect(s) and interaction effect(s) between them.

n: The number of the studies in each subgroup

Qb: The between-subgroups Q-statistic

df: The degree of freedoms of the between-subgroups Q test

pval.Qb: The p-value of the between-subgroups Q test

Qw: The within-subgroup Q-statistic in each subgroup

g: The subgroup summary effect size, based on Hedges'g

se: The standard error of the subgroup summary effect size

zval: The test statistic of the subgroup summary effect size

pval: The p-value for the test statistics of the subgroup summary effect size

ci.lb: The lower bound of the confidence interval

ci.ub: The upper bound of the confidence interval

call: The matched call

If no moderator effect is detected, the function will return a FEmrt object including the following components:

n: The total number of the studies

Q: The Q-statistic of the heterogeneity test

df: The degrees of freedom of the heterogeneity test

pval.Q: The p-value of the heterogeneity test

g: The summary effect size for all studies

se: The standard error of the summary effect size

zval: The test statistic of the summary effect size

pval: The p-value of the test statistic of the summary effect size

ci.lb: The lower bound of the confidence interval for the summary effect size

ci.ub: The upper bound of the confidence interval for the summary effect size

call: The matched call

References

Dusseldorp, E., van Genugten, L., van Buuren, S., Verheijden, M. W., & van Empelen, P. (2014). Combinations of techniques that effectively change health behavior: Evidence from meta-cart analysis. Health Psychology, 33(12), 1530-1540. doi: 10.1037/hea0000018.

Li, X., Dusseldorp, E., & Meulman, J. J. (2017). Meta-CART: A tool to identify interactions between moderators in meta-analysis. British Journal of Mathematical and Statistical Psychology, 70(1), 118-136. doi: 10.1111/bmsp.12088.

Therneau, T., Atkinson, B., & Ripley, B. (2014) rpart: Recursive partitioning and regression trees. R package version, 4-1.

See Also

summary.FEmrt, plot.FEmrt, rpart,rpart.control

Examples

data(dat.BCT2009)
library(Rcpp)
FEtree <- FEmrt(g ~ T1 + T2+ T4 + T25, vi = vi, data = dat.BCT2009, c = 0)
print(FEtree)
summary(FEtree)
plot(FEtree)

Example output

Loading required package: ggplot2
Loading required package: gridExtra
Loading required package: rpart

Fixed Effects Meta-tree (K = 106 studies); 
FEmrt(formula = g ~ T1 + T2 + T4 + T25, data = dat.BCT2009, vi = vi, 
    c = 0)

A tree with 6 terminal nodes was detected
The moderators are T1, T25, T4, T2
Use summary() and plot() to inspect the moderator analysis results and the tree structure.
n= 106 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 106 253.035700 0.22948370  
   2) T1=0 69 168.396500 0.20188000  
     4) T25=0 60 149.163400 0.19032720  
       8) T4=1 43  79.852450 0.17154330 *
       9) T4=0 17  63.864210 0.25561400 *
     5) T25=1 9  15.045810 0.27193330 *
   3) T1=1 37  67.447150 0.32225630  
     6) T4=0 15  20.195030 0.19067890  
      12) T2=0 5   4.004851 0.07326808 *
      13) T2=1 10  11.976410 0.24054760 *
     7) T4=1 22  23.854780 0.43776610 *

Fixed Effects meta-tree (K = 106 studies); 
FEmrt(formula = g ~ T1 + T2 + T4 + T25, data = dat.BCT2009, vi = vi, 
    c = 0)

A tree with 6 terminal nodes was detected
Moderators were detected as: T1, T25, T4, T2

Test for Between-Subgroups Heterogeneity under FE assumption:
Qb = 54.437 (df = 5), p-value < 1e-04;

Subgroup Meta-analysis Results:
    K     Qw     g    se   zval  pval  ci.lb ci.ub    
8  43 79.852 0.172 0.017 10.075 0.000  0.138 0.205 ***
9  17 63.864 0.256 0.032  8.052 0.000  0.193 0.318 ***
5   9 15.046 0.272 0.037  7.360 0.000  0.200 0.344 ***
12  5  4.005 0.073 0.068  1.073 0.283 -0.061 0.207    
13 10 11.976 0.241 0.044  5.406 0.000  0.153 0.328 ***
7  22 23.855 0.438 0.035 12.534 0.000  0.369 0.506 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

metacart documentation built on July 10, 2020, 5:06 p.m.