In the previous article, we introduced the Q test based on 1-way 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 self-ligating 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.
|Mean||SD||n||Mean||SD||n||Y i||v i||T2p||w i||w2i||w i Y i||wiY2i|
|Randomized controlled studies (A)|
|Controlled clinical studies (B)|
The Figure illustrates the forest plot for the study and subgroup effect sizes under the random-effects 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 1-way 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||Q∗B||Q w||Q B|
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 meta-analysis, was equal to 0.07. Therefore, the R 2 index is as follows:
1. Spineli L., Pandis N.: Exploring heterogeneity in meta-analysis: sub-group analysis. Part 1. Am J Orthod Dentofacial Orthop 2020; 158: pp. 302-304.
2. Scott P., DiBiase A.T., Sherriff M., Cobourne M.T.: Alignment efficiency of Damon3 self-ligating and conventional orthodontic bracket systems: a randomized clinical trial. Am J Orthod Dentofacial Orthop 2008; 134: pp. 470.e1-470.e8.
3. Ong E., McCallum H., Griffin M.P., Ho C.: Efficiency of self-ligating vs conventionally ligated brackets during initial alignment. Am J Orthod Dentofacial Orthop 2010; 138: pp. 138.e1-138.e7. discussion 138-139
4. Pandis N., Polychronopoulou A., Katsaros C., Eliades T.: Comparative assessment of conventional and self-ligating appliances on the effect of mandibular intermolar distance in adolescent nonextraction patients: a single-center randomized controlled trial. Am J Orthod Dentofacial Orthop 2011; 140: pp. e99-e105.
5. Miles P.G., Weyant R.J., Rustveld L.: A clinical trial of Damon 2 vs conventional twin brackets during initial alignment. Angle Orthod 2006; 76: pp. 480-485.
6. Pandis N., Polychronopoulou A., Eliades T.: Self-ligating vs conventional brackets in the treatment of mandibular crowding: a prospective clinical trial of treatment duration and dental effects. Am J Orthod Dentofacial Orthop 2007; 132: pp. 208-215.
7. Wahab R.M., Idris H., Yacob H., Ariffin S.H.: Comparison of self- and conventional-ligating brackets in the alignment stage. Eur J Orthod 2012; 34: pp. 176-181.
8. Pandis N., Fleming P.S., Spineli L.M., Salanti G.: Initial orthodontic alignment effectiveness with self-ligating and conventional appliances: a network meta-analysis in practice. Am J Orthod Dentofacial Orthop 2014; 145: pp. S152-S163.