Exploring heterogeneity in metaanalysis: Subgroup analysis. Part 2
American Journal of Orthodontics and Dentofacial Orthopedics, 20200901, Volume 158, Issue 3, Pages 462463, Copyright © 2020
In the previous article, we introduced the Q test based on 1way analysis of variance —an approach of subgroup analysis to compare more than 2 subgroups of studies as defined on the basis of a categorical characteristic of the trials, and the R ^{ 2 } index that quantifies the proportion of heterogeneity explained by the covariate of interest. In the present article, we use a real example to illustrate the Q test and the R ^{ 2 } index. The interested reader can use the Excel file (See Supplementary Appendix , available at www.ajodo.org ) as an exercise to understand the calculations.
Application to real data
We will use the data from 6 studies that examine the efficiency on the initial orthodontic alignment of a conventional vs a selfligating system. Half of the studies are randomized controlled studies (subgroup A), and the rest are controlled clinical studies (subgroup B). Our goal is to determine whether the effect sizes differ in these 2 study types (subgroups). To answer this question, we will apply a subgroup analysis. Table I illustrates the dataset. The effect size of interest is the mean difference.
Study  Damon  Conventional  Mean difference  

Mean  SD  n  Mean  SD  n  Y _{ i }  v _{ i }  T2p ${\text{T}}_{\text{p}}^{2}$  w _{ i }  w2i ${\text{w}}_{\text{i}}^{2}$  w _{ i } Y _{ i }  wiY2i ${\text{w}}_{\text{i}}{\text{Y}}_{\text{i}}^{2}$  
Randomized controlled studies (A)  
Scott  1.41  1.41  32  1.68  0.66  28  −0.27  0.08  0.048  8.00  64.00  −2.16  0.58 
Pandis  1.98  0.90  25  2.22  0.96  25  −0.24  0.07  0.048  8.70  75.69  −2.09  0.50 
Wahab  2.16  1.08  14  3.15  1.17  15  −0.99  0.17  0.048  4.65  21.62  −4.60  4.56 
Total A  –  –  21.35  161.31  −8.85  5.64  
Controlled clinical studies (B)  
Ong  1.46  0.65  44  1.57  0.59  40  −0.11  0.02  0.048  15.38  236.54  −1.69  0.19 
Miles  0.51  0.66  29  0.60  0.75  29  −0.09  0.03  0.048  13.33  177.69  −1.20  0.11 
Pandis  1.81  0.71  27  1.41  0.63  27  0.40  0.03  0.048  13.33  177.69  5.33  2.13 
Total B  –  –  42.04  591.92  2.44  2.43  
Total  –  –  63.39  753.49  −6.41  8.07 
The Figure illustrates the forest plot for the study and subgroup effect sizes under the randomeffects model. The combined effect for the randomized controlled studies (the first diamond) is −0.40 with a 95% confidence interval (CI) of −0.78 to −0.02, and the combined effect for the controlled clinical studies (the second diamond) is 0.06 with a 95% CI of −0.25 to 0.37. These 2 combined effects have different magnitudes and directions, but their CIs seem to overlap, and this indicates that these 2 study types might not be statistically different in terms of the mean effect size. The results from the Q test based on a 1way analysis of variance are presented in Table II . For Q _{ B } = 3.16 with 1 degree of freedom, the P value is equal to 0.07 (>0.05 significance level), and hence, we fail to reject the null hypothesis that the effect sizes may be the same in both subgroups.
Q measure  Q ^{ ∗ }  Q∗A ${\text{Q}}_{\text{A}}^{\text{\u2217}}$  Q∗B ${\text{Q}}_{\text{B}}^{\text{\u2217}}$  Q _{ w }  Q _{ B } 

Value  7.42  1.97  2.29  4.26  3.16 
T ^{ 2 } was estimated to be equal to 0.03 and 0.05 in subgroup A and subgroup B, respectively. A pooled estimate of these 2 heterogeneities is equal to 0.048. The T ^{ 2 } _{ total } , obtained from a conventional metaanalysis, was equal to 0.07. Therefore, the R ^{ 2 } index is as follows:
Supplementary Data
References

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