## Introduction

The aim of this study was to determine the reliability and the measuring error (by means of the smallest detectable error) of 11 angular and 4 linear measurements commonly used for cephalometric analysis.

## Methods

Twenty-five digital lateral cephalograms were randomly selected and traced with Viewbox software (version 3.1.1.13, dHAL Software, Kifissia, Greece). This was repeated 3 times by 2 observers during 3 sessions. There was at least 1 week between each session. Differences were analyzed with a repeated measurement analysis of variance (ANOVA). Intraobserver and interobserver reliabilities were calculated with intraclass correlation coefficients (ICC) based on absolute agreement. Measurement error was determined by means of the smallest detectable difference.

## Results

The intraobserver agreement of the measurements was good (ICC >0.82). SNA, SNB, ANB, and ANS-Me had the smallest intraobserver errors for both observers (>1.86 mm or degrees). Except for SN-FH (ICC = 0.76), interobserver agreement was good (ICC >0.87).

## Conclusions

Determining the appropriate measuring error of cephalometric measurements by means of the smallest detectable difference is necessary to find the true difference between the start and the end of active treatment. Depending on the magnitude of clinical significance, the measuring error was possibly clinically significant for all variables tested and, therefore, questions the use of these variables to detect the true treatment effect.

Since Hofrath and Broadbent introduced radiographic cephalometry in 1931, it has been an important tool in orthodontic diagnosis, treatment planning and evaluation of treatment results. However, landmark identification error is a major source of variability, probably because this step depends the most on human judgment. The reliability of landmark identification has been studied by using various experimental and statistical methods. Reliability statistics have been reported for landmark identification, but the coefficients derived from these reliability statistics are rather abstract and therefore have limited clinical applicability. The clinical applicability is hampered because these coefficients are not expressed in a unit of cephalometric measurement (millimeters or degrees).

The effect of the variance of landmark identification on cephalometric measurements might be useful clinically, but this requires that the measurement error is quantified to detect true differences. The quantification of the measurement error or technical error of measurement is a critical but often overlooked process. The technical error of measurement can be defined as the variability between dimensions when the same specimens are measured at multiple sessions. The size of the measurement error determines the smallest difference between 2 measurements that can be considered a true difference. The advantage of introducing the calculation of the smallest detectable difference (SDD) in cephalometric analysis is that true treatment effect can be evaluated because the SDD defines the 95% confidence limits of the method error. This means that, to be able to detect changes during orthodontic treatment, the difference between 2 observations must be at least equal to or greater than the SDD for the specific measurement to be statistically significant. Although the influence of landmark variation on cephalometric measurements has been investigated by using various formulas, to our knowledge, few studies have reported the measuring error at a 95% confidence level. Therefore, the aim of this study was to determine the reliability and the measuring error by means of the SDD of angular and linear measurements commonly used for cephalometric analysis.

## Material and methods

A group of 25 digital lateral cephalograms were randomly selected from the archives of the Department of Orthodontics of the University of Groningen in The Netherlands. No distinction was made between sex, age, or dentition in the random selection. The average age of the subjects in the sample was 14.8 years (95% CI, 12.8-16.7 years). Seventeen subjects had permanent dentitions, and 8 subjects were still in the mixed dentition but with the mandibular first premolar erupted into occlusion. Digital cephalograms were made (ProMax, DiMax2 Digital Cephalometric Unit, Planmeca, Helsinki, Finland) with a resolution quality of 2272 × 2045 pixels at a 24-bit depth. The lateral cephalograms were individually imported into the Viewbox software (version 3.1.1.13, dHAL Software, Kifissia, Greece) for landmark identification and cephalometric analysis. For each cephalogram, 21 landmarks were identified by a cursor-driven mouse ( Table I ). The operators were allowed to adjust the digital cephalogram with the software to help with the identification of the landmarks (eg, increase contrast, adjust the gray levels). Each cephalogram was analyzed 3 times (at separate sessions at least a week apart) by 2 examiners. The 14 cephalometric measurements (11 angular and 4 linear) commonly used in cephalometric analysis were used in this study ( Table II ). The measurements were calculated from the coordinates of the identified landmarks with the Viewbox software. The result of each analysis was saved and separately imported into Excel (Microsoft, Redmond, Wash).

Landmark | Abbreviation | Definition |
---|---|---|

1. Sella | S | The midpoint of the pituitary fossa |

2. Nasion | N | The most anterior point of the frontonasal suture in the median plane |

3. Porion | Po | The superior point of the external auditory meatus |

4. Orbitale | Or | The lowest point in the inferior margin of the orbit |

5. Anterior nasal spine | ANS | The tip of the bony anterior nasal spine in the median plane |

6. Subspinale | Ss or A | The point at the deepest midline concavity on the maxilla between the anterior nasal spine and prosthion |

7. Maxillary incisor incisal tip | Isi | The incisal edge of the most anterior maxillary central incisor (incision superius incisalis) |

8. Maxillary incisor apex | Isa | The root apex of the most anterior maxillary central incisor (incision superius apicalis) |

9. Mandibular incisor incisal tip | Iii | The incisal edge of the most anterior mandibular central incisor (incision inferius incisalis) |

10. Mandibular incisor apex | Iia | The root apex of the most anterior mandibular central incisor (incision inferius apicalis) |

11. Mandibular first molar | L6 | The tip of the mesiobuccal cusp of the mandibular first molar |

12. Mandibular first premolar | L4 | The tip of the cusp of the mandibular first premolar |

13. Supramentale | Sm or B | The point at the deepest midline concavity on the mandibular symphysis between infradentale and pogonion |

14. Pogonion | Pog | The most anterior point of the bony chin in the median plane |

15. Gnathion | Gn | The most anteroinferior point on the symphysis of the chin |

16. Menton | Me | The most inferior midline point on the mandibular symphysis |

17. Gonion | Go | The constructed point of intersection of the plane tangent to the posterior border of the ramus and a plane tangent to the inferior border of the mandible |

18. Condylion | Co | The most superior point on the head of the condyle |

19. Glabella | G | The most prominent point in the midsagittal plane of the forehead |

20. Subnasale | Sn | The point where the lower border of the nose meets the outer contour of the upper lip |

21. Soft-tissue pogonion | Pog′ | The most anterior point of the soft-tissue contour of the chin |

Measurement | Unit | Description |
---|---|---|

1. SNA | ° | Angle determined by Points S, N, and A |

2. SNB | ° | Angle determined by Points S, N, and B |

3. ANB | ° | Angle determined by Points A, N, and B |

4. Wits appraisal | mm | Distance between the perpendicular line from Point A to the occlusal plane and a perpendicular line from Point B to the occlusal plane (line passing through L6 and L4) |

5. SN-FH | ° | Angle between the line SN and the Frankfort horizontal line (line connecting Po and Or) |

6. FH-NPog | ° | Angle between the Frankfort horizontal line and a line between N and Pog |

7. GoGn-SN | ° | Angle between the lines SN and GoGn |

8. U1-SN | ° | Angle between the line SN and a line connecting Isa and Isi (U1) |

9. L1-GoGn | ° | Angle between the line GoGn and a line connecting Iia and Iii (L1) |

10. L1-FH | ° | Angle between L1 and the Frankfort horizontal line |

11. Co-A | mm | Linear distance between Point A and Co |

12. Co-Gn | mm | Linear distance between Gn and Co |

13. ANS-Me | mm | Linear distance between ANS and Me |

14. AFC | ° | Angle of facial convexity: the angle between a line passing through G and Sn and a line connecting Sn and Pog′ |

## Statistical analysis

All statistical analyses were performed with a standard statistical software package (version 16, SPSS, Chicago, Ill). Differences were analyzed by using a repeated measurements analysis of variance (ANOVA) with measuring session, observer, and session-observer interaction as the explaining variables. The ANOVA also included tests for sphericity. *P *values less than 0.05 were considered significant. To determine the size of the measurement error, the standard error of measurement (SEM) of the repeated measurements was calculated as the square root of the variance of the random error from a 2-way random-effect ANOVA. The SEM was calculated for each angular and linear measurement. The SDD was then calculated with the formula: 1.96 × √2 × SEM. The SDD was used to calculate intraobserver and interobserver measurement errors.

As a measure of reliability, the intraclass correlation coefficient (ICC) values for absolute agreement based on 2-way random-effects ANOVA were calculated to determine the intraobserver and interobserver reliability values of the cephalometric measurements. Interobserver reliability was tested by comparison of the means of the repeated measurements.

## Results

The data were normally distributed, and no violations in sphericity were found. The results are reported in Tables III and IV . There were no systematic differences between observers. The factor observer was not significant for any of the variables tested ( Table III ). There were significant ( *P *>0.05) differences between the measuring sessions for the variables SNA, SNB, GoGn-SN, L1-GoGn, and Co-A. The interaction of session and observer was significant for the variables SNA, SNB, and L1-GoGn.

Measurement | Unit | Observer 1 | Observer 2 | ANOVA, P |
||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M1 | M2 | M3 | Session | Observer | Session x observer | ||||||||

Mean | SD (±) | Mean | SD (±) | Mean | SD (±) | Mean | SD (±) | Mean | SD (±) | Mean | SD (±) | |||||

1. SNA | ° | 82.48 | 4.47 | 82.55 | 4.23 | 81.73 | 4.38 | 82.70 | 4.69 | 82.40 | 4.37 | 82.28 | 4.58 | 0.01 ^{∗ } |
0.87 | 0.01 ^{∗ } |

2. SNB | ° | 77.55 | 3.87 | 77.62 | 3.80 | 77.10 | 3.76 | 77.69 | 4.25 | 77.44 | 4.26 | 77.34 | 4.24 | 0.01 ^{∗ } |
0.36 | 0.03 ^{∗ } |

3. ANB | ° | 4.92 | 2.88 | 4.93 | 2.78 | 4.63 | 2.67 | 5.01 | 2.68 | 4.96 | 2.61 | 4.93 | 2.47 | 0.32 | 0.85 | 0.28 |

4. Wits | mm | −2.29 | 4.73 | −2.88 | 4.92 | −2.91 | 5.28 | −1.81 | 4.65 | −1.72 | 4.31 | −1.74 | 4.42 | 0.46 | 0.48 | 0.28 |

5. SN-FH | ° | 8.11 | 2.58 | 7.82 | 2.43 | 8.38 | 2.71 | 6.73 | 4.11 | 6.54 | 3.78 | 7.02 | 4.00 | 0.97 | 0.15 | 0.05 |

6. FH-NPog | ° | 93.74 | 3.65 | 93.56 | 3.62 | 93.84 | 3.68 | 94.62 | 3.56 | 94.91 | 3.31 | 94.85 | 3.47 | 0.50 | 0.28 | 0.54 |

7. GoGn-SN | ° | 33.06 | 3.85 | 31.64 | 4.17 | 32.36 | 4.58 | 33.09 | 4.20 | 33.09 | 4.32 | 32.96 | 4.69 | 0.01 ^{∗ } |
0.56 | 0.07 |

8. U1-SN | ° | 99.92 | 9.50 | 100.49 | 9.51 | 100.09 | 9.10 | 102.20 | 9.85 | 101.88 | 9.95 | 102.30 | 9.78 | 0.31 | 0.47 | 0.45 |

9. L1-GoGn | ° | 94.08 | 7.90 | 94.94 | 7.81 | 94.93 | 7.70 | 95.64 | 6.85 | 95.14 | 6.53 | 95.97 | 6.66 | 0.04 ^{∗ } |
0.65 | 0.04 ^{∗ } |

10. L1-FH | ° | 118.98 | 9.73 | 118.94 | 9.33 | 118.87 | 9.34 | 121.76 | 9.26 | 121.22 | 8.99 | 121.87 | 8.85 | 0.31 | 0.31 | 0.50 |

11. Co-A | mm | 88.49 | 5.30 | 87.48 | 4.85 | 88.14 | 5.18 | 87.88 | 5.42 | 87.07 | 4.97 | 86.84 | 4.70 | 0.02 ^{∗ } |
0.59 | 0.60 |

12. Co-Gn | mm | 107.26 | 6.86 | 107.28 | 6.31 | 107.53 | 6.65 | 105.42 | 6.87 | 105.50 | 6.43 | 105.34 | 6.56 | 0.60 | 0.30 | 0.90 |

13. ANS-Me | mm | 63.52 | 5.88 | 63.38 | 5.99 | 63.41 | 5.89 | 64.03 | 5.71 | 63.72 | 6.08 | 63.64 | 5.97 | 0.18 | 0.83 | 0.68 |

14. AFC | ° | 16.67 | 5.12 | 17.05 | 4.51 | 16.75 | 4.51 | 16.06 | 5.00 | 16.12 | 5.02 | 16.22 | 4.52 | 0.29 | 0.61 | 0.78 |