Thank you for giving us the opportunity to clarify some points of our article. The sample calculation was described in the article with enough data to replicate the estimation. As reported in “Material and methods,” we performed all statistical analyses with the software package STATA (version 12; StataCorp, College Station, Tex). For sample size estimation, we used the data of the study by Manni et al, as declared in the article.
In that study, after Herbst treatment, the advancement of pogonion was 1.56 mm in the standard group, without skeletal anchorage, vs 3.44 mm in the group with the Herbst appliance and temporary anchorage devices. The difference between the 2 groups was 1.9 mm. In the sample size estimation, we rounded the value to 2.0 mm, the nearest decimal number. The standard deviation was not available, so we hypothesized a value of 2.0 mm.
It is difficult to believe that a mathematical formula gives a different output with different estimation tools.
Sample size calculations run with the software package STATA under the assumption of 80% of power and an α value of 0.05 (STATA command: sampsi 0 2.0, sd1(2) alpha(0.05) power(0.8)) gave as the output 16 patients per group.
Let us apply the formula described by Pandis :
with f(α,β) = 7.85; μ1 − μ2 = 2; σ = 2.
It results in n = (7.85*2*2 2 )/2 2 = 15.7. Therefore, the output is the same with 16 patients per group as expected.
The second question was about the reliability of the occlusal plane as a reference line in performing the sagittal occlusion analysis. This point is not a concern. In fact, sagittal occlusion analysis is commonly used in the evaluation of Herbst treatment effects.
Pancherz described this measuring procedure in his article in 1982. He wrote:
“For all the linear measurements on the centric occlusion roentgenograms, the occlusal line (OL) and the occlusal line perpendiculare (OLP) from the first head film were used as a reference grid. The grid was transferred from the first tracing to the following tracings by superimposition of the tracings on the nasion-sella line (NSL) with sella (S) as registering point. All registrations were done parallel with OL to OLP (Fig. 4).”
Even though the occlusal plane was used, it is clear that it was traced on the pretreatment cephalometric radiograph and transferred to the posttreatment one. Therefore, any modification produced on the occlusal plane by the appliance could not affect the measurements.
The last question was about the “degree of the force as 100 g in the metallic ligature Herbst group” and its orientation.
We do not really understand the question, but we can reiterate that the force exerted by the metallic ligature on the screw and canine was unknown, whereas the orientation was a few degrees below the occlusal plane; on the other hand, the elastic chain had an initial force of 100 g with a similar orientation.