618
Periodontal Disease
Morbidity
Quantification. I. Optimal Selection of Teeth for Periodontal Bone Loss Surveys Michael K. Shrout, Charles F. and Edward P. Vahey11 *
Hildebolt,ft Michael
W.
Vannier, * Michael Province,s
bite-wing radiographs is attractive because bite wings are relatively convenient, inexpensive, and available. The choice of teeth used influences the validity of global bone loss assessments based on partial mouth measurements. The objective of this study was to validate periodontal bone loss indices The
assessment of alveolar bone loss
with
based on a few teeth. The mandibular posterior teeth were considered as a basis for abbreviated indices. The optimum number of teeth included was evaluated, and the utility of abbreviated indices was determined experimentally. The teeth from 75 skulls were measured from the cemento-enamel junction (CEJ) to the alveolar bone at six locations per tooth. The subsets of teeth which best represent the average whole mouth bone loss were found with all-possible-subsets regression analysis. Bone loss data from 179 prehistoric skulls were used to test the validity of selected teeth indices. Bone loss measurements from the mandibular posterior areas were representative of full-mouth bone loss measurements. Mandibular second premolars plus any other mandibular posterior teeth were the optimal combination of tooth for an abbreviated index. This subset is suitable for use with bite-wing radiographs. J Periodontol 1990; 61:618-622.
Key Words:
Bone
resorption/diagnosis; bone resorption/radiography;
Periodontal disease epidemiology is hindered by the lack of validated, objective methods for quantitative disease assessment. The extent of disease is usually assessed with a "morbidity index" which indicates the cumulative alveolar bone résorption throughout adult life. Such an index should be precise, accurate, and easy to use. Moreover, because time management is an overriding factor in large periodontal surveys, the index must require minimal field time. Periodontal probing has been extensively used in dentistry as an indicator of alveolar bone loss. It is, and will continue to be, an important diagnostic tool; yet considerations of tissue tonus, inflammatory exúdate, pain control, patient cooperation, observer standardization, and utilization of observer time render surveys and examinations by probing
Diagnosis and Patient Services, Medical College of Georgia, Aupreviously, Washington University School of Dental Medicine, St. Louis, MO. 'Diagnostic Services, Washington University School of Dental Medicine, "Oral
gusta, GA;
St. Louis, MO. 'Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, MO. "Division of Biostatistics. "Northwestern University School of Dentistry, Chicago, IL; previously, Washington University School of Dental Medicine, St. Louis, MO.
bone loss index.
problematic in large studies, particularly for comparing populations and/or patients over time and space. The problems associated with the use of periodontal probing have led to development of alternative morbidity indices based on dental radiographie measurements. Considerable time can be saved in gathering these measurements if partial mouth scoring is employed. The six Ramfjord teeth are the most commonly used set for partial mouth scoring.1"4 The use of these teeth for determining gingivitis, bleeding, and the presence of plaque and calculus deposits is well established.5"8 They are not, however, as well established as predictors of periodontal disease.8'9 The locations of these teeth in the mouth make
them poor candidates for a radiograph-based index (4 of the 6 Ramfjord teeth are difficult to measure on radiographs due to superimposition of anatomic structures and angulations errors).10 The mandibular premolar and molar region is the easiest area of the mouth for collection of radiographie bone loss measurements.10 Measurements extracted from these teeth are highly correlated with whole-mouth scores10 and have also been shown to have small inter- and intraexaminer variation.11,12 Moreover, measurements from the lower-
Volume 61 Number 10
SHROUT, HILDEBOLT, VANNIER, PROVINCE, VAHEY
posterior region have been shown to have the least amount of error of any mouth region when radiographie measurements were compared with those taken from cadavers.13 With bite-wing radiographs of these posterior teeth, precise
619
Full mouth measurements were made twice on each skull. The first set of measurements were from the CEJ to the
alveolar bone. For the second set, bone loss obviously attributable to non-periodontal causes was not measured (alveolar height was estimated instead). Missing bone due to postmortem fractures, dehiscences, and pulpal pathology were considered non-periodontal. Bone loss measurements were repeated on 11 skulls to test reproducibility. Data analysis was performed using SAS.#17 Average bone loss per tooth and per individual was calculated. Intraclass correlation coefficients were determined for the first set of measurements versus the second set and for the original versus repeat measurements. The intraclass correlation coefficient (ICC) is an estimate of the correlation between any pair of corresponding measurements.18 The ICC is calculated in an analysis of variance procedure. The ICC is more sensitive to differences in sets of measurements than tests for significant differences in means (which test only for systematic biases). An all-possible-subsets regression analysis was performed to determine which teeth should be measured to best estimate an individual's average bone loss (as determined by measuring all teeth). Only subsets with 8 or fewer teeth were examined, because the number of regressions possible in such testing was extremely large. The program employed performs residual analyses and, by means of a leaps-and-bounds procedure, identifies the best subsets while performing only a fraction of the regressions.17 Mallows Cp was used as the selection criterion.19 Mallows Cp is based on the residual sum of squares, the residual mean square, and the number of variables in the subset. Smaller values of Mallows Cp indicates larger R2 (coefficient of determination) for a smaller number of variables. The skulls selected for use in this study contained both pre- and postmortem tooth loss. Because the all-possible-subsets regression includes only cases for which there are data on all teeth, the number of variables exceeded the number of observations if all 32 teeth were included in a single analysis. To overcome this limitation, we performed over 50 analyses using various combinations of teeth, including combinations of mandibular premolare and molars. Results of these analyses were compared to determine which subsets were most often selected as best. Because the sample sizes are reduced in performing the all-possible-subsets regression, the R2 values are often inflated compared with R2 values determined by regressing average bone loss for a specific subset of teeth on full-mouth average bone loss. For the best subsets, we, therefore, performed a general linear model regression analysis (SAS GLM) to more accurately determine the values for R2. In this paper, we report statistics from these regressions.17 To further test the validity of the best subsets, bone loss data from a previous study of 179 prehistoric inhabitants of Missouri were analyzed.20 The average bone loss per skull was calculated from periodontal probe measurements and compared with the average bone loss as calculated from the
'Hu-Friedy Manufacturing, Chicago,
"SAS
alignment of teeth, film, and central roentgen beam is readily achieved. Conventional bite-wing radiographs are considered adequate for periodontal disease surveys.14-15 The use of partial mouth measurements for abbreviated indices is justified, provided they faithfully represent av-
erage whole-mouth bone loss. Prior studies10-13 that used selected teeth on bite-wings have two important limitations: validation and sample size. In studies where sample sizes were large, partial-mouth measurements from radiographs were compared with full-mouth measurements from radiographs, but validation of radiographie measures from dry skulls, cadavers, or patients (at the time of surgery) was not included.10-12 In the one study in which validation was performed with cadaver material, the sample size was small, with only 28 disassociated cadaver quadrants used.13 We sought to validate abbreviated periodontal disease indices that can be subsequently used with bite-wing radiographs. We used dry skulls to test mandibular posterior teeth in partial-mouth scoring and determined the optimum number of teeth for inclusion. We compared them with indices based on teeth from any mouth region. A priori, we decided to focus on indices with 5 or fewer teeth, although we did perform analyses with 6, 7, and 8 tooth subsets. MATERIALS AND METHODS Two hundred and fifty-five adult skulls from collections in Washington University's Department of Anthropology, School of Dental Medicine and School of Medicine were examined to determine their suitability for the study. Seventy-five adult skulls with the greatest number of teeth and in the best state of preservation were selected for further study. Only adult skulls, with an estimated age range from early to late adulthood, were included in the study. Both male and female skulls from contemporary and prehistoric time periods were used. Skulls came from North America, Central America, Asia, and the subcontinent of India, with several of unknown origin. Each tooth was measured from the cemento-enamel junction (CEJ) to the alveolar bone at the following six locations: the mesial-facial point just mesial to the line angle, mid-facial or the point of maximum bone loss on the facial, the distal-facial just distal to the line angle, and the three corresponding positions on the lingual. By making these six traditional measurements per tooth, error due to site selection was minimized.16 All measurements were made to the nearest millimeter by one investigator (MKS) using a
PQW periodontal probe.1
IL.
Institute, Inc., Cary, NC.
620
Table 1. 6-Tooth
Ramfjord
Teeth in Subset
Ramfjord
Subset and Selected 5-Tooth Subsets
Mean Square Error (mm) 0.037
Selected 5-Tooth Subsets 38 4,11,14,18,27 44 3,20,21,27,29
0.125 0.109
= =
Equation for Regression*
Table 2.
R2
6-Tooth
3,9,12,19,25,28* 32
y
J Periodontol October 1990
RADIOGRAPHIC ASSESSMENT OF PERIODONTAL MORBIDITY. I. SELECTION OF TEETH
0.921
0.978
0.197 + 0.935 -0.053 + 1.112
0.932
0.057
+
0.942
predicted whole-mouth
average bone loss, average bone loss for teeth in subset.
60 20,29 20,21,29 56 20,28,29 59 20,29,30 54 19,20,29 53 y
=
Subsets
Measured Mean Square Error Bone Loss
Teeth in Subset
=
teeth in the test subsets. These abbreviated averages were regressed against the whole-mouth averages to determine the values of R2. The abbreviated averages were also entered into the regression formulas for the best subsets to yield predicted bone loss.
Optimum
(mm)
(mm)
Equation for Regression*
2.86 2.36 2.33 2.50 2.50
0.270 0.204 0.252 0.239 0.219
0.358 0.194 0.301 0.348 0.378
1.077 1.112
1.081 1.008 0.988
R2 0.844 0.888 0.856 0.862 0.884
whole-mouth average bone loss, average bone loss for teeth in subset.
predicted
a
o
Ss to
RESULTS Of the 2,400
2o
teeth in the 75 skulls, 516 (21.5%) were missing or nonmeasurable. Teeth were nonmeasurable because the CEJ had been obliterated by caries or by preor postmortem fracture. Forty-six teeth (1.9%) had been lost premortem. Twenty-two of these were in individuals who had caries and only slight alveolar bone loss. We, therefore, suspect that these 22 teeth were lost due to caries. Conversely, the other 24 teeth that were missing premortem are in individuals who had severe alveolar résorption and few caries; so we suspect that these teeth were lost due to
periodontal
possible
reasons.
The intraclass correlation coefficient for bone loss due to periodontal disease versus bone loss due to all factors was 0.87 with a mean square error of 0.23. The intraclass correlation coefficient for the repeatability of bone-loss measurements was 0.97 with a mean square error of 0.02. In general, the more teeth in an abbreviated index, the better the index's ability to reflect whole mouth scores. The six Ramfjord teeth, for example, had an R2 value of 0.978. These teeth, however, represent only one of dozens of 6tooth subsets that are equally as good, and for 7- and 8tooth combinations, there were literally hundreds of subsets with R2 values in the 0.99 range. Of the thousands of models produced by the all-possible-subsets regression, only two 5-tooth subsets were selected. Table 1 contains statistics and regression equations for these 2 subsets and for the Ramfjord teeth. Based on a consideration of Mallow's Cp, R2, and tooth position, 5 subsets were selected as being optimum: 1 is a 2-tooth subset and the others are 3-tooth subsets. No 4tooth subsets were selected as being optimum. Data on the optimum subsets are presented in Table 2. The plot of the data for the worst case (the 2 tooth subset with an R2 of 0.844) is presented in Figure 1. The regression line is overlaid on the data points. Table 3 contains the results of applying the optimum subsets to 179 prehistoric skulls. The average whole mouth
Ze
LU
3 0
Figure
molars
I
3 4 5 6 2 AVERAGE BONE LOSS FOR ALL TEETH
7
1.
Regression of average bone loss of the mandibular second pre(20 and 29) against average whole mouth bone loss (see Table 2).
Table 3.
Optimum
Subsets
Teeth in Subset
20,29 20,21,29 20,28,29 20,29,30 19,20,29
71
58 59 63 61
R2 0.858 0.917 0.868 0.882 0.894
Applied
to Prehistoric Skulls
Measured Bone Loss*
Predicted Bone Loss*
2.26 2.34 2.32 2.41 2.36
2.79 2.81 2.81 2.78 2.71
0.53 0.47 0.49 0.37 0.35
in mm.
'(Measured bone loss)
(Predicted bone loss).
bone loss for the 179 skulls was 2.54 mm. For the optimum subsets, measurements of bone loss varied from 2.26 to 2.41 mm. These values accounted for 86% to 92% of the variation that occurred in the average whole-mouth bone loss measurements. When these values were used in the regression equations given in Table 2, predicted bone loss varied from 2.71 to 2.81 mm. DISCUSSION In our study, we determined how well measurements from subsets of teeth (and specifically subsets of mandibular posterior teeth) represent whole-mouth averages. If teeth were lost due to periodontal disease, measurements based on all of the remaining teeth or on subsets of the remaining teeth will underestimate the actual bone loss. To partially control
Volume 61 Number 10
for this effect in periodontal disease surveys where populations are compared, bone-loss scores should be regressed against age and regressions for individual populations should be compared.20 With this technique, under estimations of bone loss will occur if teeth have been lost due to periodontal disease. Yet in populations in which the prevalences of periodontal diseases are highest, the regressions should either be steeper, have higher intercepts, or both; that is, in populations in which people are losing more teeth due to periodontal disease than are other populations, there should be more bone loss on the remaining teeth. An ideal index would consider bone loss associated with missing teeth, but because of the difficulty in assigning cause of tooth loss to missing teeth, these data are rarely available for use in population surveys. The intraclass correlation coefficient of 0.97 indicates that the repeatability of dry skull measurements was good. The intraclass correlation coefficient of 0.87 for measurements of bone loss due to periodontal disease versus bone loss due to periodontal disease plus other factors suggests that if bone loss due to dehiscences, postmortem fracture, and pulpal pathology are not carefully accounted for, average bone loss scores for skeletal collections are likely to be artificially inflated. It has been suggested that bone loss due to pulpal pathology has resulted in inflated values of bone loss in periodontal surveys.21 For the 75 skulls in this study, we found that many 7or 8-tooth subsets can account for more than 99% of the variation that occurs among whole-mouth measures, and that there are dozens of 6-tooth subsets (such as the Ramfjord teeth) that account for as much as 98% of the variation. Several 5-tooth subsets can account for more than 93% of the variation. The major drawbacks to indices based on these subsets is that they depend on measurements that are time intensive and difficult to make on dental
radiographs.10'22
Mandibular posterior teeth on dental bite-wings are relatively free from errors due to superimposition of anatomical structures and to faulty alignments of the film, beam, and tooth. Moreover, if just the mandibular second pre-
molare are used in a subset, this index accounts for 84% of whole mouth variation. If an additional posterior tooth (excluding third molars) is included, the amount of variation accounted for is 86% to 89%. When we used these 2and 3-tooth subsets to calculate average bone loss for 179 skulls that were independent of the 75 skulls for which the optimum subsets were determined, the subsets accounted for 87% to 92% of whole-mouth variation. Moreover, the maximum difference between the whole-mouth average bone loss and subset average bone loss was 0.28 mm. All of the averages based on subsets slightly underestimate bone loss. When the regression formulas that were developed for the 75 skulls were applied to the 179 skulls, bone loss averages were slightly overestimated (0.17 to 0.27 mm). Thus no apparent gain is achieved from utilizing the regression formulas beyond that obtained by using the optimum subsets.
SHROUT, HILDEBOLT, VANNIER, PROVINCE, VAHEY
621
CONCLUSION Based on our analysis of alveolar bone loss patterns in dry skulls, we confirmed Bjorn et al.10 statement that bone loss measurements from the mandibular posterior areas satisfactorily represent full-mouth bone loss measurements. If a bite-wing-based abbreviated index is to be employed, we suggest the optimal combination of teeth for the index are the mandibular second premolare plus any one of the other posterior teeth.
Acknowledgment This study was supported in part by NIDR Grant DE08173. The cooperation of Dr. Thomas Schiff is appreciated. REFERENCES 1. 2.
3. 4. 5. 6. 7.
8.
Ramfjord SP. Indices for prevalence and incidence of periodontal disease. / Periodontal 1959; 30:51-59. Ramfjord SP. Design of studies or clinical trials to evaluate the effectiveness of agents or procedures for the prevention, or treatment, of loss of the periodontium. J Dent Res 1974; 14:78-87. Ramfjord SP. The periodontal disease index (P.D.I.). / Periodontal 1967; 38:602-610. Jamison HC. Some comparisons of two methods of assessing periodontal disease. Am J Public Health 1963; 53:1102-1106. Alexander AG. Partial mouth recording of gingivitis, plaque and calculus in epidemiological surveys. J Periodont Res 1970; 5:141-147. Downer MC. The relative efficiencies of some periodontal partial recording selections. J Periodont Res 1972; 7:334-340. Mills WH, Thompson GW, Beagrie GS. Partial-mouth recording of plaque and periodontal pockets. J Periodont Res 1975; 10:36-43. Fleiss JL, Park MH, Chilton NW, Alman JE, Feldman RS, Chauncey HH. Representativeness of the "Ramfjord teeth" for epidemiologie studies of gingivitis and Periodontitis. Comm Dent Oral Epidemiol 1987;
15:221-224.
9. Ainamo J, Ainamo A. Partial indices as indicators of the severity and prevalence of periodontal disease. Int Dent J 1985; 35:322-326. 10. Bjorn A, Bjorn H, Hailing H. An abbreviated index for periodontal bone height. Odont Revy 1975; 26:225-230. 11. Wouters FR, Jon-And C, Frithiof L, Söder , Lavstedt S. A computerized system to measure interproximal alveolar bone levels in epidemiologie, radiographie investigations. I. Methodologie study. Acta Odontol Scand 1988; 46:25-31. 12. Wouters FR, Jon-And C, Frithiof L, Soder , Lavstedt S. A computerized system to measure interproximal alveolar bone levels in epidemiologie, radiographie investigations. II Intra- and inter-examiner variation study. Acta Odontol Scand 1988; 46:33-39. 13. Regan JE, Mitchell DF. Roentgenographic and dissection measurements of alveolar crest height. J Am Dent Assoc 1963; 66:356-359. 14. Aass AM, Albandar J, Aasenden R, Tollefsen T, Gjermo P. Variation in prevalence of radiographie alveolar bone loss in subgroups of 14year old school children in Oslo. J Clin Periodontal 1988; 15:130133. 15. Selikowitz H-S, Sheiham A, Albert D, Williams GM. Retrospective longitudinal study of the rate of alveolar bone loss in humans using bite-wing radiographs. J Clin Periodontal 1981; 8:421-438. 16. Kingman K, Morrison E, Löe H, Smith J. Systematic errors in estimating prevalence and severity of periodontal disease. J Periodontal 1988; 59:707-713. 17. SAS Institute Inc. SAS ISTAT Guide for Personal Computers, Version 6 Edition. Cary NC: SAS Institute Inc.; 1987. 18. Blalock HM. Social Statistics. St. Louis: McGraw-Hill; 1979:374375. 19. Mallows CL. Some comments on Cp. Technometrics 1973; 15:661675.
622
J Periodontol October 1990
RADIOGRAPHIC ASSESSMENT OF PERIODONTAL MORBIDITY. I. SELECTION OF TEETH
20. Hildebolt
Molnar S, Elvin-Lewis M, McKee JK. The effect of factors on prevalences of dental diseases for prehistoric inhabitants of the state of Missouri. AmerJPhys Anthrol 1988; 75:1-
CF,
geochemical
14. 21. Clark NG, Carey SE, Srikandi W, Hirsh RS, Leppard PI. Periodontal disease in ancient populations. Amer J Phys Anthrol 1986; 72:173183. 22. Sjolien T, Zachrisson BU. A method for radiographie assessment of
periodontal Dent Res
bone support
following
orthodontic
treatment.
Scand J
1973; 81:210-217.
Send reprint requests to: Dr. Michael K. Shrout, Assistant Professor in Oral Diagnosis and Patient Services, Medical College of Georgia, School of Dentistry, Augusta, Georgia 30912-1241. Accepted for publication April 11, 1990.
Periodontal Disease
Morbidity
Quantification. I. Optimal Selection of Teeth for Periodontal Bone Loss Surveys Michael K. Shrout, Charles F. and Edward P. Vahey11 *
Hildebolt,ft Michael
W.
Vannier, * Michael Province,s
bite-wing radiographs is attractive because bite wings are relatively convenient, inexpensive, and available. The choice of teeth used influences the validity of global bone loss assessments based on partial mouth measurements. The objective of this study was to validate periodontal bone loss indices The
assessment of alveolar bone loss
with
based on a few teeth. The mandibular posterior teeth were considered as a basis for abbreviated indices. The optimum number of teeth included was evaluated, and the utility of abbreviated indices was determined experimentally. The teeth from 75 skulls were measured from the cemento-enamel junction (CEJ) to the alveolar bone at six locations per tooth. The subsets of teeth which best represent the average whole mouth bone loss were found with all-possible-subsets regression analysis. Bone loss data from 179 prehistoric skulls were used to test the validity of selected teeth indices. Bone loss measurements from the mandibular posterior areas were representative of full-mouth bone loss measurements. Mandibular second premolars plus any other mandibular posterior teeth were the optimal combination of tooth for an abbreviated index. This subset is suitable for use with bite-wing radiographs. J Periodontol 1990; 61:618-622.
Key Words:
Bone
resorption/diagnosis; bone resorption/radiography;
Periodontal disease epidemiology is hindered by the lack of validated, objective methods for quantitative disease assessment. The extent of disease is usually assessed with a "morbidity index" which indicates the cumulative alveolar bone résorption throughout adult life. Such an index should be precise, accurate, and easy to use. Moreover, because time management is an overriding factor in large periodontal surveys, the index must require minimal field time. Periodontal probing has been extensively used in dentistry as an indicator of alveolar bone loss. It is, and will continue to be, an important diagnostic tool; yet considerations of tissue tonus, inflammatory exúdate, pain control, patient cooperation, observer standardization, and utilization of observer time render surveys and examinations by probing
Diagnosis and Patient Services, Medical College of Georgia, Aupreviously, Washington University School of Dental Medicine, St. Louis, MO. 'Diagnostic Services, Washington University School of Dental Medicine, "Oral
gusta, GA;
St. Louis, MO. 'Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, MO. "Division of Biostatistics. "Northwestern University School of Dentistry, Chicago, IL; previously, Washington University School of Dental Medicine, St. Louis, MO.
bone loss index.
problematic in large studies, particularly for comparing populations and/or patients over time and space. The problems associated with the use of periodontal probing have led to development of alternative morbidity indices based on dental radiographie measurements. Considerable time can be saved in gathering these measurements if partial mouth scoring is employed. The six Ramfjord teeth are the most commonly used set for partial mouth scoring.1"4 The use of these teeth for determining gingivitis, bleeding, and the presence of plaque and calculus deposits is well established.5"8 They are not, however, as well established as predictors of periodontal disease.8'9 The locations of these teeth in the mouth make
them poor candidates for a radiograph-based index (4 of the 6 Ramfjord teeth are difficult to measure on radiographs due to superimposition of anatomic structures and angulations errors).10 The mandibular premolar and molar region is the easiest area of the mouth for collection of radiographie bone loss measurements.10 Measurements extracted from these teeth are highly correlated with whole-mouth scores10 and have also been shown to have small inter- and intraexaminer variation.11,12 Moreover, measurements from the lower-
Volume 61 Number 10
SHROUT, HILDEBOLT, VANNIER, PROVINCE, VAHEY
posterior region have been shown to have the least amount of error of any mouth region when radiographie measurements were compared with those taken from cadavers.13 With bite-wing radiographs of these posterior teeth, precise
619
Full mouth measurements were made twice on each skull. The first set of measurements were from the CEJ to the
alveolar bone. For the second set, bone loss obviously attributable to non-periodontal causes was not measured (alveolar height was estimated instead). Missing bone due to postmortem fractures, dehiscences, and pulpal pathology were considered non-periodontal. Bone loss measurements were repeated on 11 skulls to test reproducibility. Data analysis was performed using SAS.#17 Average bone loss per tooth and per individual was calculated. Intraclass correlation coefficients were determined for the first set of measurements versus the second set and for the original versus repeat measurements. The intraclass correlation coefficient (ICC) is an estimate of the correlation between any pair of corresponding measurements.18 The ICC is calculated in an analysis of variance procedure. The ICC is more sensitive to differences in sets of measurements than tests for significant differences in means (which test only for systematic biases). An all-possible-subsets regression analysis was performed to determine which teeth should be measured to best estimate an individual's average bone loss (as determined by measuring all teeth). Only subsets with 8 or fewer teeth were examined, because the number of regressions possible in such testing was extremely large. The program employed performs residual analyses and, by means of a leaps-and-bounds procedure, identifies the best subsets while performing only a fraction of the regressions.17 Mallows Cp was used as the selection criterion.19 Mallows Cp is based on the residual sum of squares, the residual mean square, and the number of variables in the subset. Smaller values of Mallows Cp indicates larger R2 (coefficient of determination) for a smaller number of variables. The skulls selected for use in this study contained both pre- and postmortem tooth loss. Because the all-possible-subsets regression includes only cases for which there are data on all teeth, the number of variables exceeded the number of observations if all 32 teeth were included in a single analysis. To overcome this limitation, we performed over 50 analyses using various combinations of teeth, including combinations of mandibular premolare and molars. Results of these analyses were compared to determine which subsets were most often selected as best. Because the sample sizes are reduced in performing the all-possible-subsets regression, the R2 values are often inflated compared with R2 values determined by regressing average bone loss for a specific subset of teeth on full-mouth average bone loss. For the best subsets, we, therefore, performed a general linear model regression analysis (SAS GLM) to more accurately determine the values for R2. In this paper, we report statistics from these regressions.17 To further test the validity of the best subsets, bone loss data from a previous study of 179 prehistoric inhabitants of Missouri were analyzed.20 The average bone loss per skull was calculated from periodontal probe measurements and compared with the average bone loss as calculated from the
'Hu-Friedy Manufacturing, Chicago,
"SAS
alignment of teeth, film, and central roentgen beam is readily achieved. Conventional bite-wing radiographs are considered adequate for periodontal disease surveys.14-15 The use of partial mouth measurements for abbreviated indices is justified, provided they faithfully represent av-
erage whole-mouth bone loss. Prior studies10-13 that used selected teeth on bite-wings have two important limitations: validation and sample size. In studies where sample sizes were large, partial-mouth measurements from radiographs were compared with full-mouth measurements from radiographs, but validation of radiographie measures from dry skulls, cadavers, or patients (at the time of surgery) was not included.10-12 In the one study in which validation was performed with cadaver material, the sample size was small, with only 28 disassociated cadaver quadrants used.13 We sought to validate abbreviated periodontal disease indices that can be subsequently used with bite-wing radiographs. We used dry skulls to test mandibular posterior teeth in partial-mouth scoring and determined the optimum number of teeth for inclusion. We compared them with indices based on teeth from any mouth region. A priori, we decided to focus on indices with 5 or fewer teeth, although we did perform analyses with 6, 7, and 8 tooth subsets. MATERIALS AND METHODS Two hundred and fifty-five adult skulls from collections in Washington University's Department of Anthropology, School of Dental Medicine and School of Medicine were examined to determine their suitability for the study. Seventy-five adult skulls with the greatest number of teeth and in the best state of preservation were selected for further study. Only adult skulls, with an estimated age range from early to late adulthood, were included in the study. Both male and female skulls from contemporary and prehistoric time periods were used. Skulls came from North America, Central America, Asia, and the subcontinent of India, with several of unknown origin. Each tooth was measured from the cemento-enamel junction (CEJ) to the alveolar bone at the following six locations: the mesial-facial point just mesial to the line angle, mid-facial or the point of maximum bone loss on the facial, the distal-facial just distal to the line angle, and the three corresponding positions on the lingual. By making these six traditional measurements per tooth, error due to site selection was minimized.16 All measurements were made to the nearest millimeter by one investigator (MKS) using a
PQW periodontal probe.1
IL.
Institute, Inc., Cary, NC.
620
Table 1. 6-Tooth
Ramfjord
Teeth in Subset
Ramfjord
Subset and Selected 5-Tooth Subsets
Mean Square Error (mm) 0.037
Selected 5-Tooth Subsets 38 4,11,14,18,27 44 3,20,21,27,29
0.125 0.109
= =
Equation for Regression*
Table 2.
R2
6-Tooth
3,9,12,19,25,28* 32
y
J Periodontol October 1990
RADIOGRAPHIC ASSESSMENT OF PERIODONTAL MORBIDITY. I. SELECTION OF TEETH
0.921
0.978
0.197 + 0.935 -0.053 + 1.112
0.932
0.057
+
0.942
predicted whole-mouth
average bone loss, average bone loss for teeth in subset.
60 20,29 20,21,29 56 20,28,29 59 20,29,30 54 19,20,29 53 y
=
Subsets
Measured Mean Square Error Bone Loss
Teeth in Subset
=
teeth in the test subsets. These abbreviated averages were regressed against the whole-mouth averages to determine the values of R2. The abbreviated averages were also entered into the regression formulas for the best subsets to yield predicted bone loss.
Optimum
(mm)
(mm)
Equation for Regression*
2.86 2.36 2.33 2.50 2.50
0.270 0.204 0.252 0.239 0.219
0.358 0.194 0.301 0.348 0.378
1.077 1.112
1.081 1.008 0.988
R2 0.844 0.888 0.856 0.862 0.884
whole-mouth average bone loss, average bone loss for teeth in subset.
predicted
a
o
Ss to
RESULTS Of the 2,400
2o
teeth in the 75 skulls, 516 (21.5%) were missing or nonmeasurable. Teeth were nonmeasurable because the CEJ had been obliterated by caries or by preor postmortem fracture. Forty-six teeth (1.9%) had been lost premortem. Twenty-two of these were in individuals who had caries and only slight alveolar bone loss. We, therefore, suspect that these 22 teeth were lost due to caries. Conversely, the other 24 teeth that were missing premortem are in individuals who had severe alveolar résorption and few caries; so we suspect that these teeth were lost due to
periodontal
possible
reasons.
The intraclass correlation coefficient for bone loss due to periodontal disease versus bone loss due to all factors was 0.87 with a mean square error of 0.23. The intraclass correlation coefficient for the repeatability of bone-loss measurements was 0.97 with a mean square error of 0.02. In general, the more teeth in an abbreviated index, the better the index's ability to reflect whole mouth scores. The six Ramfjord teeth, for example, had an R2 value of 0.978. These teeth, however, represent only one of dozens of 6tooth subsets that are equally as good, and for 7- and 8tooth combinations, there were literally hundreds of subsets with R2 values in the 0.99 range. Of the thousands of models produced by the all-possible-subsets regression, only two 5-tooth subsets were selected. Table 1 contains statistics and regression equations for these 2 subsets and for the Ramfjord teeth. Based on a consideration of Mallow's Cp, R2, and tooth position, 5 subsets were selected as being optimum: 1 is a 2-tooth subset and the others are 3-tooth subsets. No 4tooth subsets were selected as being optimum. Data on the optimum subsets are presented in Table 2. The plot of the data for the worst case (the 2 tooth subset with an R2 of 0.844) is presented in Figure 1. The regression line is overlaid on the data points. Table 3 contains the results of applying the optimum subsets to 179 prehistoric skulls. The average whole mouth
Ze
LU
3 0
Figure
molars
I
3 4 5 6 2 AVERAGE BONE LOSS FOR ALL TEETH
7
1.
Regression of average bone loss of the mandibular second pre(20 and 29) against average whole mouth bone loss (see Table 2).
Table 3.
Optimum
Subsets
Teeth in Subset
20,29 20,21,29 20,28,29 20,29,30 19,20,29
71
58 59 63 61
R2 0.858 0.917 0.868 0.882 0.894
Applied
to Prehistoric Skulls
Measured Bone Loss*
Predicted Bone Loss*
2.26 2.34 2.32 2.41 2.36
2.79 2.81 2.81 2.78 2.71
0.53 0.47 0.49 0.37 0.35
in mm.
'(Measured bone loss)
(Predicted bone loss).
bone loss for the 179 skulls was 2.54 mm. For the optimum subsets, measurements of bone loss varied from 2.26 to 2.41 mm. These values accounted for 86% to 92% of the variation that occurred in the average whole-mouth bone loss measurements. When these values were used in the regression equations given in Table 2, predicted bone loss varied from 2.71 to 2.81 mm. DISCUSSION In our study, we determined how well measurements from subsets of teeth (and specifically subsets of mandibular posterior teeth) represent whole-mouth averages. If teeth were lost due to periodontal disease, measurements based on all of the remaining teeth or on subsets of the remaining teeth will underestimate the actual bone loss. To partially control
Volume 61 Number 10
for this effect in periodontal disease surveys where populations are compared, bone-loss scores should be regressed against age and regressions for individual populations should be compared.20 With this technique, under estimations of bone loss will occur if teeth have been lost due to periodontal disease. Yet in populations in which the prevalences of periodontal diseases are highest, the regressions should either be steeper, have higher intercepts, or both; that is, in populations in which people are losing more teeth due to periodontal disease than are other populations, there should be more bone loss on the remaining teeth. An ideal index would consider bone loss associated with missing teeth, but because of the difficulty in assigning cause of tooth loss to missing teeth, these data are rarely available for use in population surveys. The intraclass correlation coefficient of 0.97 indicates that the repeatability of dry skull measurements was good. The intraclass correlation coefficient of 0.87 for measurements of bone loss due to periodontal disease versus bone loss due to periodontal disease plus other factors suggests that if bone loss due to dehiscences, postmortem fracture, and pulpal pathology are not carefully accounted for, average bone loss scores for skeletal collections are likely to be artificially inflated. It has been suggested that bone loss due to pulpal pathology has resulted in inflated values of bone loss in periodontal surveys.21 For the 75 skulls in this study, we found that many 7or 8-tooth subsets can account for more than 99% of the variation that occurs among whole-mouth measures, and that there are dozens of 6-tooth subsets (such as the Ramfjord teeth) that account for as much as 98% of the variation. Several 5-tooth subsets can account for more than 93% of the variation. The major drawbacks to indices based on these subsets is that they depend on measurements that are time intensive and difficult to make on dental
radiographs.10'22
Mandibular posterior teeth on dental bite-wings are relatively free from errors due to superimposition of anatomical structures and to faulty alignments of the film, beam, and tooth. Moreover, if just the mandibular second pre-
molare are used in a subset, this index accounts for 84% of whole mouth variation. If an additional posterior tooth (excluding third molars) is included, the amount of variation accounted for is 86% to 89%. When we used these 2and 3-tooth subsets to calculate average bone loss for 179 skulls that were independent of the 75 skulls for which the optimum subsets were determined, the subsets accounted for 87% to 92% of whole-mouth variation. Moreover, the maximum difference between the whole-mouth average bone loss and subset average bone loss was 0.28 mm. All of the averages based on subsets slightly underestimate bone loss. When the regression formulas that were developed for the 75 skulls were applied to the 179 skulls, bone loss averages were slightly overestimated (0.17 to 0.27 mm). Thus no apparent gain is achieved from utilizing the regression formulas beyond that obtained by using the optimum subsets.
SHROUT, HILDEBOLT, VANNIER, PROVINCE, VAHEY
621
CONCLUSION Based on our analysis of alveolar bone loss patterns in dry skulls, we confirmed Bjorn et al.10 statement that bone loss measurements from the mandibular posterior areas satisfactorily represent full-mouth bone loss measurements. If a bite-wing-based abbreviated index is to be employed, we suggest the optimal combination of teeth for the index are the mandibular second premolare plus any one of the other posterior teeth.
Acknowledgment This study was supported in part by NIDR Grant DE08173. The cooperation of Dr. Thomas Schiff is appreciated. REFERENCES 1. 2.
3. 4. 5. 6. 7.
8.
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9. Ainamo J, Ainamo A. Partial indices as indicators of the severity and prevalence of periodontal disease. Int Dent J 1985; 35:322-326. 10. Bjorn A, Bjorn H, Hailing H. An abbreviated index for periodontal bone height. Odont Revy 1975; 26:225-230. 11. Wouters FR, Jon-And C, Frithiof L, Söder , Lavstedt S. A computerized system to measure interproximal alveolar bone levels in epidemiologie, radiographie investigations. I. Methodologie study. Acta Odontol Scand 1988; 46:25-31. 12. Wouters FR, Jon-And C, Frithiof L, Soder , Lavstedt S. A computerized system to measure interproximal alveolar bone levels in epidemiologie, radiographie investigations. II Intra- and inter-examiner variation study. Acta Odontol Scand 1988; 46:33-39. 13. Regan JE, Mitchell DF. Roentgenographic and dissection measurements of alveolar crest height. J Am Dent Assoc 1963; 66:356-359. 14. Aass AM, Albandar J, Aasenden R, Tollefsen T, Gjermo P. Variation in prevalence of radiographie alveolar bone loss in subgroups of 14year old school children in Oslo. J Clin Periodontal 1988; 15:130133. 15. Selikowitz H-S, Sheiham A, Albert D, Williams GM. Retrospective longitudinal study of the rate of alveolar bone loss in humans using bite-wing radiographs. J Clin Periodontal 1981; 8:421-438. 16. Kingman K, Morrison E, Löe H, Smith J. Systematic errors in estimating prevalence and severity of periodontal disease. J Periodontal 1988; 59:707-713. 17. SAS Institute Inc. SAS ISTAT Guide for Personal Computers, Version 6 Edition. Cary NC: SAS Institute Inc.; 1987. 18. Blalock HM. Social Statistics. St. Louis: McGraw-Hill; 1979:374375. 19. Mallows CL. Some comments on Cp. Technometrics 1973; 15:661675.
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Send reprint requests to: Dr. Michael K. Shrout, Assistant Professor in Oral Diagnosis and Patient Services, Medical College of Georgia, School of Dentistry, Augusta, Georgia 30912-1241. Accepted for publication April 11, 1990.
