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The frequency of bitewing radiographs
The frequency of bitewing radiographs Michael Shwartz, Ph.D.,* Joseph S. Pliskin. Ph.D.,** Hans-G&an Griindahl, D.D.S., O.D.,*** and Joseph Bo$a, D.D.S.,**** Boston, Mass., Beer-Sheva, Israel, and Gothenburg, Sweden
A model for use in analyzing the implications of different rates of caries incidence and progression for the timing of bitewing radiographs was developed. Estimates of progression rates and incidence patterns were derived from an analysis of serial bitewing radiographs. A time schedule for taking the next radiographs was determined so that carious lesions would be detected before radiolucencies reach the inner half of the dentin. For asymptomatic persons with extensive exposure to fluorides and no unrestored enamel lesions on the last radiographs, bitewing films could be scheduled every 2.5 to 3 years. For persons with little exposure to fluorides or with many early enamel lesions or at least one deep enamel lesion that has not been restored, radiographs should be performed every 6 months to 1 year. (ORAL SURG. ORAL MED. ORAL PATHOL. 61:300-305, 1986)
I t has been recommended that dental radiographs not be taken at arbitrary frequencies but that the determination of the need for radiographs should be based on professional judgment in each individual case.These guidelines have been important in stimulating the practitioner to weigh various considerations before taking radiographs. However, they offer little help to him in determining the implications of various patient characteristics or alternative disease hypotheses for the timing of the next set of radiographs. The question of how often to take bitewing radiographs to detect proximal carious lesions in permanent teeth in asymptomatic persons is addressed in this article. Specifically, the implications of different caries incidence rates and estimated caries progression rates in establishing the frequency with which bitewing radiographs should be taken were determined. The time interval was selected so that the probability of detecting a carious radiolucent lesion before it reached the inner ha!f of the dentin was above some threshold level. This project was supported by Grant No. 04858 from the National Center for Health Services Research and Health Care Technology Assessment, OASH. *Health Care Management Program, Boston University. **Department of Industrial Engineering and Center for Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel. ***Department of Oral Radiology, University of Gothenburg. ****Dental Care Management Program, Goldman School of Graduate Dentistry, Boston University.
300
DATA AND METHODS
Serial bitewing radiographs from more than 700 persons from the following five groups were analyzed: Swedish Group 1. Fifty boys and 50 girls, aged 10 to 11 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations and, from age 7, had used biweekly mouth rinses with a sodium fluoride solution. Four to eight sets of bitewing radiographs were analyzed for each child. Swedish Group 2. Fifty-one boys and 48 girls, aged 17 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations, from age 7 had used biweekly mouth rinses with a sodium fluoride solution, and, from age 13, had received applications of fluoride varnishes twice a year. Four to nine sets of bitewing radiographs were analyzed for each child. Swedish Group 3. Fifty men and 50 women, aged 2 1 to 22 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations and used biweekly mouth rinses with a sodium fluoride solution from age 7 to age 19. Six to nine sets of yearly bitewing radiographs were analyzed for each person. United States Group I. Fifty-seven boys and 60 girls, with an average age of 10.7 years at their last examination, from a fluoride-deficient, lower socioeconomic community. Four to thirteen sets of bitewing radiographs were analyzed for each child.
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Table I. Mean time for a carious lesion to progress through the outer and inner halves of the enamel of permanent teeth Group
Age (~4
Swedish Group 1 U.S. Group I Swedish Group 2 U.S. Group 2 Swedish Group 3
IO-I I 10.7 (mean) 17 17-18 21-22
Fluoride
exposure
High, topical Low High, topical Low High, topical
United States Group 2. One hundred seventysevenboys and 165 girls, aged 17 to 18 years at their last examination, from a fluoride-deficient, lower socioeconomic community. Four sets of yearly radiographs were analyzed for each person. Whereas in the first four groups radiographs were taken as part of treatment, in this group radiographs were taken as part of an epidemiologic study to evaluate the effect of topically applied fluorides.’ Using the approach described by Shwartz and associatesin 1984,* the average duration that lesions remained in the enamel was estimated for the premolars and for the first and second permanent molars. The results are summarized in Table I and have been reported in more detail elsewhere.3 Lesions in the outer half of the enamel are called carious state 1 lesions; those in the inner half of the enamel are called carious state 2 lesions. With the exception of younger children, in whom the only permanent tooth erupted was the first molar (Swedish Group 1 and United States Group l), the duration of time that a lesion remains in a particular carious state can be represented by a probability distribution with the following characteristics (a piecewise exponential distribution): for the first year in the carious state (or first 2 years for carious state 1 for Swedish Groups 2 and 3), there is a constant probability that in any month a carious lesion will progress from one carious state to the next. For lesions that have not progressed in the first year (or in 2 years), the probability of progression in subsequent months is still constant but about one half the first period rate. The implication of this distribution for the percentage of lesions still in a specific carious state over time for different average durations is shown in Table II. To model caries incidence, an underlying probability distribution was assumed to represent differences in an individual’s average annual rate of caries development. Thus, in a community some persons are more caries prone and some less. The mean of this probability distribution represents caries risk in the community. The likelihood that an individual from this community will develop different numbers
State 1. Outer half of enamel (mean duration in months)
State 2. Inner half of enamel (mean duration in months)
20.9 22.6 37.6 15.5 41.2
27.9 18.6 47.4 26.5 56.4
of new lesions in a year is generated as follows: (1) The average rate of caries for the year is determined by random selection from the underlying probability distribution of the average annual rate of caries development. Depending on the individual’s risk, values in the high (or low) half of this distribution may be more likely to be selected. (2) The average rate of caries determined in step 1 is adjusted to account for variation in caries risk as a function of the individual’s age: (3) An individual’s probability distribution for new lesions follows a random (Poisson) process with mean equal to the adjusted rate from step 2. This model is capable of predicting an age-specific distribution of new lesions that replicates the observed incidence in permanent teeth.4 The benefit of taking the next set of bitewing radiographs some number of years in the future is calculated for a person who has just had a set of bitewing radiographs and who remains asymptomatic between radiographs. The measure of benefit (the benefit level) is the likelihood that carious lesions will be detected before they reach the inner half of the dentin (for example, 0.95). To evaluate a contemplated time for the next set of bitewing films, our model of caries incidence was used to determine the likelihood that new lesions will develop between radiographs. The model of caries progression was used to determine the likelihood that lesions would not reach the inner half of the dentin by the next radiograph for unrestored enamel lesions at the last radiograph and for new lesions. The results that follow were calculated under the following conditions: (a) three benefit levelsa.90, 0.95, and 0.99; (b) four underlying average annual caries incidences per year-1.5, 1.0, 0.5, and 0.25; (c) with and without .the assumption that clinical examinations are performed between radiographs. It was assumed that a clinical examination had a 10% chance of detecting lesions in the inner half of the enamel and a 30% chance of detecting lesions in the outer half of the dentid; (d) four average durations for caries in states 1 and 2 were used-18, 24, 36,
302
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OEd Surg. March, 1986
II. Probability carious lesions have progressed by different amounts of time in a state for different average durations in the state
Table
Time in state ho) 6 12 18 24 30 36
Average caries duration (in months) for enamel lesions (which progress more rapidly early in a state]
-
Average caries dtiration (in months) when n lesion occurs in the outer half of the dentin (constani rate of progression)
48
36
24
36*
27
18
0.19 0.34 0.4 1 0.41 0.52 0.57
0.24 0.42 0.49 0.55 0.6 I 0.66
0.31 0.52 0.61 0.67 0.73 0.71
0.15 0.28 0.39 0.49 0.56 0.63
0.20 0.36 0.49 0.59 0.67 0.74
0.28 0.49 0.63 0.14 0.81 0.87
*These caries durations are assumed to be three quarters of the duration of a carious lesion in the enamel. (See text for details.)
and 48 months. In each of these states, it was assumedthat progression was more rapid in the first year (or the first 2 years for state 1 lesions with a duration of 36 months or more). It is extremely difficult to estimate the time interval that lesions remain in the outer half of the dentin because dentin lesions, once detected, are almost always restored. Subjective estimates from clinicians regarding the time interval of a radiolucency in half the enamel compared to a lesion in half the dentin have ranged from 1:l to 2:1, the latter ratio suggesting that progression is twice as fast through the dentin as through the enamel. The following results are reported for the midpoint of the range and assumethat the average duration of a carious lesion in the outer half of the dentin is three quarters the duration in the enamel. Enamel lesions were considered to progress more rapidly in the early stages of each state, and dentin lesions were considered to progress at a constant rate from month to month (see Table II). The sensitivity of the results to these and other assumptions was considered. RESULTS
The time interval at which the next set of bitewing films should be taken is shown in Table III, under the assumption that any lesions detected on the last set of bitewing films were restored. Results for different numbers of unrestored state 1 and state 2 enamel lesions from the last set of bitewing films are shown in Table IV, which assumesan average incidence of 1.5 lesions per year. The superscripts a, b, and c in Table IV indicate how the strategy should be adjusted for different incidences (See footnotes to the table.) To illustrate the use of this table, let us assume that lesions have an average duration of 48 months in state 1 and state 2, that clinical examinations are performed every 6 months between radiographs, a benefit level of 0.99 and no state 2 lesions
and one state 1 lesion existed on the last set of radiographs. Then, if the average caries incidence is 0.5 new lesion per year, bitewing radiographs should be taken in 2 years (1.5 modified by the subscript b); if the incidence is 0.25 per year, bitewing radiographs should be taken in 2.5 years (1.5 modified by the subscript bc). If, instead of no state 2 lesions, there were three unrestored state 2 lesions from the last radiographs, the next set of bitewing films should be taken in 1 year for a benefit level of 0.90 and in 0.5 year for a benefit level of 0.95 or 0.99, regardless of the annual incidence of new carious lesions. The sensitivity of these results using different assumptions was determined by identifying the percentage of cases in which the “time until next scheduled radiograph” in Table IV changed. Changes were determined for different benefit levels, incidences, rates of progression, and number of state 1 and state 2 carious enamel lesions. In all casesthe change was 0.5 year. If no clinical examinations were performed, the treatment strategy was unaffected in 62% of the cases; in 38% of the cases the time to the next radiograph was reduced 0.5 year. If the average duration of the lesion in the outer half of the dentin was reduced to 50% of its duration in the enamel, the time until the next scheduled radiograph was unaffected in 63% of the cases; in 37% of the cases it should be reduced 0.5 year. If existing enamel lesions on the last radiograph developed in the year before the radiograph, the time to the next radiograph was unaffected in 70% of the cases; in 30% of the cases the time to the next radiograph should be reduced 0.5 year. If existing enamel lesions are more than 1 year old, the time to the next radiograph should be increased 0.5 year in 18% of the cases.Finally, if the likelihood of a radiolucency progressing through the outer half of the dentin is not constant but it progresses more rapidly in the first year, the time
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303
Table III. Number of years until next set of bitewing radiographs, assuming that lesions from the last radiographs were restored* Average caries incidence per year Average duration (t?lOdtSi
48 ct NC 36 C NC 24 C NC 18 c NC
is evaluated
tFor
average
(NC) $For benefit
examinations a given levels
average (that
1.5
0.90
0.95
0.99
0.90
0.95
0.99
0.90
0.95
0.99
3.0 3.0 3.0 3.0 2.5 2.0 2.0 2.0
2.5 2.0 2.0 2.0 1.5 1.5 1.0 1.0
3.0 3.0 3.0 3.0 2.5 2.5 2.0 2.0
3.0 3.0 3.0 2.5 2.0 2.0 1.5 1.5
2.0 2.0 1.5 1.5 1.0 1.0 1.0 1.0
3.0 3.0 3.0 2.5 2.0 2.0 1.5 1.5
2.5 2.5 2.0 1.o 1.5 1.5 1.0 1.o
1.5 1.5 1.5 1.o 1.0 I .o 0.5 0.5
3.0 2.5 2.5 2.0 2.0 1.5 1.5 I .o
2.5 2.0 2.0 1.5 1.5 1.o 1.0 1.o
I.5 1.5 1.o I .o I.0 1.0 0.5 0.5
the range,
0.5 years
to 3 years.
and incidence
of caries,
the first row is applicable
are performed duration
1.0
0.99
within
duration
0.5
0.95
3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.5
*Scheduling a given
0.25
, 1 0.90#
or if the assumption
and incidence
is, for the likelihood
that
of caries, no lesions
is made the columns reach
Thus, that
0.5 year proximal
under
the inner
corresponds if 6-month lesions
0.90.0.95, hatf
until the next scheduled radiograph should be reduced 0.5 year in 53% of the cases. DISCUSSION
As implied by the recommendations of dental professional organizations, and as is intuitively obvious to the practicing clinician, the frequency of bitewing radiographs depends upon a variety of factors. In this analysis, the relationship between the frequency of radiographs and benefit measuresusing different assumptions about these factors has been explicitly analyzed. For some of these factors, information is available; for some, judgment must be used. An important consideration in determining the frequency of bitewing radiographs is the rate of progression of carious lesions. In the study of Shwartz and co-workers,3 the results of which are summarized in the Methods section, the duration of a carious lesion in the outer and inner halves of the enamel in permanent teeth has been estimated. The Swedish groups in our data set had undergone extensive treatment with topical fluorides. It is possible that caries progression will be slower when there has been early and continuous systemic exposure to fluoridated water than when topical fluorides are used at a later age. Therefore, the average duration of carious lesions in each half of the enamel might be expected to be at least 36 months in younger teenagers and over 48 months in older teenagers and young adults who have lived in communities with fluoridated water. In very-high-risk groups with no fluoride exposure, caries duration in each half of the enamel may be in the 1% to 24-month range. It is important to note that averages are of little
to 0.5 year clinical
cannot
be detected
and 0.99 represent
of the dentin)
or less, 3 years
(C) examinations
of 0.90,
or more. the second
row if no clinical
clinically.
the number
0.95,
to 3 years
arc performed:
and
of years
until
the next
radiographs
for the
0.99.
use in planning diagnostic and treatment strategies. Our concern is really with the low-risk but potentially serious event that the pulp is threatened as a result of extremely rapid progression. For example, even if the average duration of caries in each half of the enamel is 4 years, 19% of the lesions will progress through half the enamel in less than 6 months; about 4% of the lesions will progress through the entire enamel in less than 6 months. To incorporate these possibilities, probability distributions rather than averages must be used in the analysis. There are almost no data on the average duration of a carious lesion or the probability distribution for the time that a carious lesion remains in the outer half of the dentin, since most lesions are restored once they enter this state. In the results reported, an average duration for the dentin carious lesion midway between the extremes provided by a sample of dentists was used. To develop a probability distribution for dentin lesions, we assumed that the likelihood of progression to the inner half of the dentin would be constant from month to month. This is in contrast to enamel carious lesions, where progression is less likely for lesions that remain in an enamel state for more than 1 or 2 years. It is our belief that the slower rate of caries progression for older enamel lesions results from remineralization possibilities, something not likely for dentin lesions. Thus our assumption of a constant rate of progression. There are a variety of additional factors that one must consider in deciding when to obtain the next bitewing radiographs. A clinician faced with an individual patient must evaluate individual characteristics in order to estimate an average rate of caries development. Again, the issueof probability distribu-
304
Shwartz et al.
Oral Surg. March. 1986
Table IV. Number of years until next set of bitewing radiographs for different numbers of enamel lesions on last radiographs that are not restored* No. of state Duration (months) 48
No. of state 2 lesions 0
36 I
24
1 18
0
1 lesions
0 0.90#
CT NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC
2.0 1.5 1.5 I.0 1.0 I.0 I.0 #
1.5 1.oc I .o 1.0 0.5a #
1.0 0.5a
0.95
1.5 I .o I.0
I 0.99
0.90
0.95
0.99
0.90
0.95
0.99
2.0b 1 Sa 1.0 1.0 1.0
1.5bc
0.5
2.5a 2.0ac 1.5a
2.5~ 2.oc 1.5 I.5 1.Ob 1.0 I .o 1.0 1 .o
2.0 1.5 I.0 1 .o 1.0 # # # #
I .Ob 1 .o # # #
# 2.0 1.5 I .Ob 1.0 1.0 0.5a
I .5 I .Ob 1.0 # # #
0.5a 0.5 #
I.0 1.0
# 8
# #
# # # #
1.0 1 .o # # #
2
# 0.5
# #
1.5 1.5 1.0 I .o I .o 1.0
# # # #
# 2.0bc 2.occ 1.5 1.0 1 .o 1.o
1.5b 1.5 1.0 0.5 # #
# # 1.5b l.Oa I .o # 1.Ob I .o
I .o 1.0 # 1.0 0.5a
1.0 # # #
1.0 1.0 # #
0.5 #
0.5
#
# * l.Oa I .o 1.0 #
1.0 1.0
# # #
# #
*The number of years in the table applies to an incidence of 1.5 per year. This number is modified by letters as indicated below: a-Increase time by 0.5 year for incidence of I .O per year or less. b-Increase time by 0.5 year for incidence of 0.5 per year or less. c-Increase time by 0.5 year for incidence of 0.25 per year. Double letters-If the same letter, increase time by I year for the indicated incidence or less (for example, b&increase time by I year for incidence of 0.5 per year or less); if a different letter, increase time by 0.5 year at each of the indicated incidences or less (for example, ab-increase time 0.5 year for incidence of I .O per year or less, increase time another 0.5 year for incidence of 0.5 per year or less). #-For a given number of state I and state 2 lesions for all benefit levels not indicated, time between radiographs should be 0.5 year. tFor a given average duration and number of state I and state 2 lesions, the first row is applicable if 6-month clinical examinations (C) are performed; the second row if no clinical examinations (NC) are performed. $For a given average duration and number of state I and state 2 lesions, the columns under 0.90, 0.95, 0.99 represent the number of years until the next radiographs for the benefit levels (that is, for the likelihood that no lesions will reach the inner half of the dentin) of 0.90, 0.95, and 0.99.
tion must be confronted. Although the average annual rate of caries might be 0.5 lesion per year, 5% of the individuals from a population with this rate will develop three or more new lesions in a year; if the rate is 1.5 per year, 50% of this group will develop no new lesions. There is no satisfactory method of identifying, within a population group that has some average caries rate, the persons who will or will not develop new lesions. Thus, probability distributions for the number of new lesions developing in a year must be incorporated in the analysis. In addition, clinicians must evaluate, on the basis of patient characteristics and the time they spend on clinical examinations, the likelihood that patients will return for 6-month clinical examinations and the likelihood that proximal lesions will be detected
clinically. Finally, both clinicians and patients will differ in the amount of risk they are willing to accept that a lesion will be detected in the inner half of the dentin. For all of the foregoing reasons, there is no arbitrary frequency with which bitewing radiographs should be taken. It is necessary to use judgment about a variety of factors, such as how rapidly caries progressesthrough the dentin, the patient’s risk of new lesions, the frequency and quality of clinical examinations, and the acceptable risk that a lesion may reach the inner half of the dentin before treatment occurs. These judgments have implications for when next to schedule radiographs. This analysis has in no senseobviated the need for clinical judgment. Rather, we have explicitly determined the
Frequency of bitewing radiographs
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4
3
5
0.90
0.95
0.99
0.90
0.95
0.99
0.90
0.95
0.95
2.0b 2.0 1.5 1.5 1.0 I.0 1.0 1.0 I.0 # 1.5c 1.5 I .o I.0 1.0 # # # I .o 1.0 0.5c # 1.0 0.5b
I.% 1.5 1.0 I.0 1.0 # # # #
1.0 1.o # # #
1.5 1.5 I.0 1.0 1.0 # # # #
I .o 0.5b # # #
OSb # # # #
# # #
I.0 1.0 0.5c # #
# # #
I.0 I.0 0.5 # #
# #t #
1.0 1.0 #
# #
0.5a #
#
2.0 1.5 1.5 I .o 1.0 1.0 1.0 1.0 1.0 # 1.5 I.0 I.0 1.0 1.0 # # # 1.0 1.0 # #
1.5 1.0 1.0 1.0 0.5b # # # #
I.Ob 1.0 I.0 # #
2.0 1.5b 1.5 1.oc 1.0 1.0 1.0 1.0 1.0 # 1.5 1.5 1.0 1.0 I.0 # # # I .o 1.0 # # 0.5 #
# #
305
clinical decision-making aid. A clinician could supply information on estimated disease-progression rates, community caries incidence, and individual patient risk. For a contemplated time for a next set of bitewing radiographs, the output of the program would indicate the probability that carious lesions were in different parts of the enamel or dentin. This information could be used as an aid to the decision as to both the timing of radiographs and treatment strategies. We would like to thank Stephanie McGregor for her help in coding the radiographs and Paul DePaola for his comments on our earlier draft of this article. REFERENCES
# #
#
1. DePaola PF, Soparkar M, Van Leeuwen M, DeVehs R: The anticaries effect of single and combined topical fluoride systems in school children. Arch Oral Biol 25: 649-653, 1980. 2. Shwartz M, Pliskin JS, Grijndahl H-G, Boffa J: Use of the Kaplan-Meier estimate to reduce biases in estimating the rate of caries progression. Community Dent Oral Epidemiol 12: 103-108, 1984. 3. Shwartz M, Grondahl H-G, Pliskin JS, Botfa J: A longitudinal analysis from bitewing radiographs of the rate of progression of proximal carious lesions through human dental enamel. Arch Oral Biol 29: 529-536, 1984. 4. Shwartz M, Pliskin JS, Grondahl H-G, Boffa J: A “deep” model of the incidence of dental caries on proximal surfaces. Med Decis Making. (In press.) 5. Mejare I. Grijndahl H-G, Carlstedt K, Grever A-C, Gttosson E: Accuracy at radiography and probing for the diagnosis of proximal caries. Stand J Dent Res 93: 178-184, 1985. Reprint requests 10:
implications of judgment about these factors for when to schedule the next bitewing radiographs. The results presented in Tables III and IV are for general cases.The computer program that generated these results is really designed as an individual
Dr. Michael Shwartz School of Management Boston University 621 Commonwealth Ave. Boston. MA 02215
A model for use in analyzing the implications of different rates of caries incidence and progression for the timing of bitewing radiographs was developed. Estimates of progression rates and incidence patterns were derived from an analysis of serial bitewing radiographs. A time schedule for taking the next radiographs was determined so that carious lesions would be detected before radiolucencies reach the inner half of the dentin. For asymptomatic persons with extensive exposure to fluorides and no unrestored enamel lesions on the last radiographs, bitewing films could be scheduled every 2.5 to 3 years. For persons with little exposure to fluorides or with many early enamel lesions or at least one deep enamel lesion that has not been restored, radiographs should be performed every 6 months to 1 year. (ORAL SURG. ORAL MED. ORAL PATHOL. 61:300-305, 1986)
I t has been recommended that dental radiographs not be taken at arbitrary frequencies but that the determination of the need for radiographs should be based on professional judgment in each individual case.These guidelines have been important in stimulating the practitioner to weigh various considerations before taking radiographs. However, they offer little help to him in determining the implications of various patient characteristics or alternative disease hypotheses for the timing of the next set of radiographs. The question of how often to take bitewing radiographs to detect proximal carious lesions in permanent teeth in asymptomatic persons is addressed in this article. Specifically, the implications of different caries incidence rates and estimated caries progression rates in establishing the frequency with which bitewing radiographs should be taken were determined. The time interval was selected so that the probability of detecting a carious radiolucent lesion before it reached the inner ha!f of the dentin was above some threshold level. This project was supported by Grant No. 04858 from the National Center for Health Services Research and Health Care Technology Assessment, OASH. *Health Care Management Program, Boston University. **Department of Industrial Engineering and Center for Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel. ***Department of Oral Radiology, University of Gothenburg. ****Dental Care Management Program, Goldman School of Graduate Dentistry, Boston University.
300
DATA AND METHODS
Serial bitewing radiographs from more than 700 persons from the following five groups were analyzed: Swedish Group 1. Fifty boys and 50 girls, aged 10 to 11 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations and, from age 7, had used biweekly mouth rinses with a sodium fluoride solution. Four to eight sets of bitewing radiographs were analyzed for each child. Swedish Group 2. Fifty-one boys and 48 girls, aged 17 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations, from age 7 had used biweekly mouth rinses with a sodium fluoride solution, and, from age 13, had received applications of fluoride varnishes twice a year. Four to nine sets of bitewing radiographs were analyzed for each child. Swedish Group 3. Fifty men and 50 women, aged 2 1 to 22 years at their last examination, from an area with a low water fluoride content (under 0.1 ppm), who had yearly dental examinations and used biweekly mouth rinses with a sodium fluoride solution from age 7 to age 19. Six to nine sets of yearly bitewing radiographs were analyzed for each person. United States Group I. Fifty-seven boys and 60 girls, with an average age of 10.7 years at their last examination, from a fluoride-deficient, lower socioeconomic community. Four to thirteen sets of bitewing radiographs were analyzed for each child.
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Table I. Mean time for a carious lesion to progress through the outer and inner halves of the enamel of permanent teeth Group
Age (~4
Swedish Group 1 U.S. Group I Swedish Group 2 U.S. Group 2 Swedish Group 3
IO-I I 10.7 (mean) 17 17-18 21-22
Fluoride
exposure
High, topical Low High, topical Low High, topical
United States Group 2. One hundred seventysevenboys and 165 girls, aged 17 to 18 years at their last examination, from a fluoride-deficient, lower socioeconomic community. Four sets of yearly radiographs were analyzed for each person. Whereas in the first four groups radiographs were taken as part of treatment, in this group radiographs were taken as part of an epidemiologic study to evaluate the effect of topically applied fluorides.’ Using the approach described by Shwartz and associatesin 1984,* the average duration that lesions remained in the enamel was estimated for the premolars and for the first and second permanent molars. The results are summarized in Table I and have been reported in more detail elsewhere.3 Lesions in the outer half of the enamel are called carious state 1 lesions; those in the inner half of the enamel are called carious state 2 lesions. With the exception of younger children, in whom the only permanent tooth erupted was the first molar (Swedish Group 1 and United States Group l), the duration of time that a lesion remains in a particular carious state can be represented by a probability distribution with the following characteristics (a piecewise exponential distribution): for the first year in the carious state (or first 2 years for carious state 1 for Swedish Groups 2 and 3), there is a constant probability that in any month a carious lesion will progress from one carious state to the next. For lesions that have not progressed in the first year (or in 2 years), the probability of progression in subsequent months is still constant but about one half the first period rate. The implication of this distribution for the percentage of lesions still in a specific carious state over time for different average durations is shown in Table II. To model caries incidence, an underlying probability distribution was assumed to represent differences in an individual’s average annual rate of caries development. Thus, in a community some persons are more caries prone and some less. The mean of this probability distribution represents caries risk in the community. The likelihood that an individual from this community will develop different numbers
State 1. Outer half of enamel (mean duration in months)
State 2. Inner half of enamel (mean duration in months)
20.9 22.6 37.6 15.5 41.2
27.9 18.6 47.4 26.5 56.4
of new lesions in a year is generated as follows: (1) The average rate of caries for the year is determined by random selection from the underlying probability distribution of the average annual rate of caries development. Depending on the individual’s risk, values in the high (or low) half of this distribution may be more likely to be selected. (2) The average rate of caries determined in step 1 is adjusted to account for variation in caries risk as a function of the individual’s age: (3) An individual’s probability distribution for new lesions follows a random (Poisson) process with mean equal to the adjusted rate from step 2. This model is capable of predicting an age-specific distribution of new lesions that replicates the observed incidence in permanent teeth.4 The benefit of taking the next set of bitewing radiographs some number of years in the future is calculated for a person who has just had a set of bitewing radiographs and who remains asymptomatic between radiographs. The measure of benefit (the benefit level) is the likelihood that carious lesions will be detected before they reach the inner half of the dentin (for example, 0.95). To evaluate a contemplated time for the next set of bitewing films, our model of caries incidence was used to determine the likelihood that new lesions will develop between radiographs. The model of caries progression was used to determine the likelihood that lesions would not reach the inner half of the dentin by the next radiograph for unrestored enamel lesions at the last radiograph and for new lesions. The results that follow were calculated under the following conditions: (a) three benefit levelsa.90, 0.95, and 0.99; (b) four underlying average annual caries incidences per year-1.5, 1.0, 0.5, and 0.25; (c) with and without .the assumption that clinical examinations are performed between radiographs. It was assumed that a clinical examination had a 10% chance of detecting lesions in the inner half of the enamel and a 30% chance of detecting lesions in the outer half of the dentid; (d) four average durations for caries in states 1 and 2 were used-18, 24, 36,
302
Shwartz et al.
OEd Surg. March, 1986
II. Probability carious lesions have progressed by different amounts of time in a state for different average durations in the state
Table
Time in state ho) 6 12 18 24 30 36
Average caries duration (in months) for enamel lesions (which progress more rapidly early in a state]
-
Average caries dtiration (in months) when n lesion occurs in the outer half of the dentin (constani rate of progression)
48
36
24
36*
27
18
0.19 0.34 0.4 1 0.41 0.52 0.57
0.24 0.42 0.49 0.55 0.6 I 0.66
0.31 0.52 0.61 0.67 0.73 0.71
0.15 0.28 0.39 0.49 0.56 0.63
0.20 0.36 0.49 0.59 0.67 0.74
0.28 0.49 0.63 0.14 0.81 0.87
*These caries durations are assumed to be three quarters of the duration of a carious lesion in the enamel. (See text for details.)
and 48 months. In each of these states, it was assumedthat progression was more rapid in the first year (or the first 2 years for state 1 lesions with a duration of 36 months or more). It is extremely difficult to estimate the time interval that lesions remain in the outer half of the dentin because dentin lesions, once detected, are almost always restored. Subjective estimates from clinicians regarding the time interval of a radiolucency in half the enamel compared to a lesion in half the dentin have ranged from 1:l to 2:1, the latter ratio suggesting that progression is twice as fast through the dentin as through the enamel. The following results are reported for the midpoint of the range and assumethat the average duration of a carious lesion in the outer half of the dentin is three quarters the duration in the enamel. Enamel lesions were considered to progress more rapidly in the early stages of each state, and dentin lesions were considered to progress at a constant rate from month to month (see Table II). The sensitivity of the results to these and other assumptions was considered. RESULTS
The time interval at which the next set of bitewing films should be taken is shown in Table III, under the assumption that any lesions detected on the last set of bitewing films were restored. Results for different numbers of unrestored state 1 and state 2 enamel lesions from the last set of bitewing films are shown in Table IV, which assumesan average incidence of 1.5 lesions per year. The superscripts a, b, and c in Table IV indicate how the strategy should be adjusted for different incidences (See footnotes to the table.) To illustrate the use of this table, let us assume that lesions have an average duration of 48 months in state 1 and state 2, that clinical examinations are performed every 6 months between radiographs, a benefit level of 0.99 and no state 2 lesions
and one state 1 lesion existed on the last set of radiographs. Then, if the average caries incidence is 0.5 new lesion per year, bitewing radiographs should be taken in 2 years (1.5 modified by the subscript b); if the incidence is 0.25 per year, bitewing radiographs should be taken in 2.5 years (1.5 modified by the subscript bc). If, instead of no state 2 lesions, there were three unrestored state 2 lesions from the last radiographs, the next set of bitewing films should be taken in 1 year for a benefit level of 0.90 and in 0.5 year for a benefit level of 0.95 or 0.99, regardless of the annual incidence of new carious lesions. The sensitivity of these results using different assumptions was determined by identifying the percentage of cases in which the “time until next scheduled radiograph” in Table IV changed. Changes were determined for different benefit levels, incidences, rates of progression, and number of state 1 and state 2 carious enamel lesions. In all casesthe change was 0.5 year. If no clinical examinations were performed, the treatment strategy was unaffected in 62% of the cases; in 38% of the cases the time to the next radiograph was reduced 0.5 year. If the average duration of the lesion in the outer half of the dentin was reduced to 50% of its duration in the enamel, the time until the next scheduled radiograph was unaffected in 63% of the cases; in 37% of the cases it should be reduced 0.5 year. If existing enamel lesions on the last radiograph developed in the year before the radiograph, the time to the next radiograph was unaffected in 70% of the cases; in 30% of the cases the time to the next radiograph should be reduced 0.5 year. If existing enamel lesions are more than 1 year old, the time to the next radiograph should be increased 0.5 year in 18% of the cases.Finally, if the likelihood of a radiolucency progressing through the outer half of the dentin is not constant but it progresses more rapidly in the first year, the time
Frequency of bitewing radiographs
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303
Table III. Number of years until next set of bitewing radiographs, assuming that lesions from the last radiographs were restored* Average caries incidence per year Average duration (t?lOdtSi
48 ct NC 36 C NC 24 C NC 18 c NC
is evaluated
tFor
average
(NC) $For benefit
examinations a given levels
average (that
1.5
0.90
0.95
0.99
0.90
0.95
0.99
0.90
0.95
0.99
3.0 3.0 3.0 3.0 2.5 2.0 2.0 2.0
2.5 2.0 2.0 2.0 1.5 1.5 1.0 1.0
3.0 3.0 3.0 3.0 2.5 2.5 2.0 2.0
3.0 3.0 3.0 2.5 2.0 2.0 1.5 1.5
2.0 2.0 1.5 1.5 1.0 1.0 1.0 1.0
3.0 3.0 3.0 2.5 2.0 2.0 1.5 1.5
2.5 2.5 2.0 1.o 1.5 1.5 1.0 1.o
1.5 1.5 1.5 1.o 1.0 I .o 0.5 0.5
3.0 2.5 2.5 2.0 2.0 1.5 1.5 I .o
2.5 2.0 2.0 1.5 1.5 1.o 1.0 1.o
I.5 1.5 1.o I .o I.0 1.0 0.5 0.5
the range,
0.5 years
to 3 years.
and incidence
of caries,
the first row is applicable
are performed duration
1.0
0.99
within
duration
0.5
0.95
3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.5
*Scheduling a given
0.25
, 1 0.90#
or if the assumption
and incidence
is, for the likelihood
that
of caries, no lesions
is made the columns reach
Thus, that
0.5 year proximal
under
the inner
corresponds if 6-month lesions
0.90.0.95, hatf
until the next scheduled radiograph should be reduced 0.5 year in 53% of the cases. DISCUSSION
As implied by the recommendations of dental professional organizations, and as is intuitively obvious to the practicing clinician, the frequency of bitewing radiographs depends upon a variety of factors. In this analysis, the relationship between the frequency of radiographs and benefit measuresusing different assumptions about these factors has been explicitly analyzed. For some of these factors, information is available; for some, judgment must be used. An important consideration in determining the frequency of bitewing radiographs is the rate of progression of carious lesions. In the study of Shwartz and co-workers,3 the results of which are summarized in the Methods section, the duration of a carious lesion in the outer and inner halves of the enamel in permanent teeth has been estimated. The Swedish groups in our data set had undergone extensive treatment with topical fluorides. It is possible that caries progression will be slower when there has been early and continuous systemic exposure to fluoridated water than when topical fluorides are used at a later age. Therefore, the average duration of carious lesions in each half of the enamel might be expected to be at least 36 months in younger teenagers and over 48 months in older teenagers and young adults who have lived in communities with fluoridated water. In very-high-risk groups with no fluoride exposure, caries duration in each half of the enamel may be in the 1% to 24-month range. It is important to note that averages are of little
to 0.5 year clinical
cannot
be detected
and 0.99 represent
of the dentin)
or less, 3 years
(C) examinations
of 0.90,
or more. the second
row if no clinical
clinically.
the number
0.95,
to 3 years
arc performed:
and
of years
until
the next
radiographs
for the
0.99.
use in planning diagnostic and treatment strategies. Our concern is really with the low-risk but potentially serious event that the pulp is threatened as a result of extremely rapid progression. For example, even if the average duration of caries in each half of the enamel is 4 years, 19% of the lesions will progress through half the enamel in less than 6 months; about 4% of the lesions will progress through the entire enamel in less than 6 months. To incorporate these possibilities, probability distributions rather than averages must be used in the analysis. There are almost no data on the average duration of a carious lesion or the probability distribution for the time that a carious lesion remains in the outer half of the dentin, since most lesions are restored once they enter this state. In the results reported, an average duration for the dentin carious lesion midway between the extremes provided by a sample of dentists was used. To develop a probability distribution for dentin lesions, we assumed that the likelihood of progression to the inner half of the dentin would be constant from month to month. This is in contrast to enamel carious lesions, where progression is less likely for lesions that remain in an enamel state for more than 1 or 2 years. It is our belief that the slower rate of caries progression for older enamel lesions results from remineralization possibilities, something not likely for dentin lesions. Thus our assumption of a constant rate of progression. There are a variety of additional factors that one must consider in deciding when to obtain the next bitewing radiographs. A clinician faced with an individual patient must evaluate individual characteristics in order to estimate an average rate of caries development. Again, the issueof probability distribu-
304
Shwartz et al.
Oral Surg. March. 1986
Table IV. Number of years until next set of bitewing radiographs for different numbers of enamel lesions on last radiographs that are not restored* No. of state Duration (months) 48
No. of state 2 lesions 0
36 I
24
1 18
0
1 lesions
0 0.90#
CT NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC C NC
2.0 1.5 1.5 I.0 1.0 I.0 I.0 #
1.5 1.oc I .o 1.0 0.5a #
1.0 0.5a
0.95
1.5 I .o I.0
I 0.99
0.90
0.95
0.99
0.90
0.95
0.99
2.0b 1 Sa 1.0 1.0 1.0
1.5bc
0.5
2.5a 2.0ac 1.5a
2.5~ 2.oc 1.5 I.5 1.Ob 1.0 I .o 1.0 1 .o
2.0 1.5 I.0 1 .o 1.0 # # # #
I .Ob 1 .o # # #
# 2.0 1.5 I .Ob 1.0 1.0 0.5a
I .5 I .Ob 1.0 # # #
0.5a 0.5 #
I.0 1.0
# 8
# #
# # # #
1.0 1 .o # # #
2
# 0.5
# #
1.5 1.5 1.0 I .o I .o 1.0
# # # #
# 2.0bc 2.occ 1.5 1.0 1 .o 1.o
1.5b 1.5 1.0 0.5 # #
# # 1.5b l.Oa I .o # 1.Ob I .o
I .o 1.0 # 1.0 0.5a
1.0 # # #
1.0 1.0 # #
0.5 #
0.5
#
# * l.Oa I .o 1.0 #
1.0 1.0
# # #
# #
*The number of years in the table applies to an incidence of 1.5 per year. This number is modified by letters as indicated below: a-Increase time by 0.5 year for incidence of I .O per year or less. b-Increase time by 0.5 year for incidence of 0.5 per year or less. c-Increase time by 0.5 year for incidence of 0.25 per year. Double letters-If the same letter, increase time by I year for the indicated incidence or less (for example, b&increase time by I year for incidence of 0.5 per year or less); if a different letter, increase time by 0.5 year at each of the indicated incidences or less (for example, ab-increase time 0.5 year for incidence of I .O per year or less, increase time another 0.5 year for incidence of 0.5 per year or less). #-For a given number of state I and state 2 lesions for all benefit levels not indicated, time between radiographs should be 0.5 year. tFor a given average duration and number of state I and state 2 lesions, the first row is applicable if 6-month clinical examinations (C) are performed; the second row if no clinical examinations (NC) are performed. $For a given average duration and number of state I and state 2 lesions, the columns under 0.90, 0.95, 0.99 represent the number of years until the next radiographs for the benefit levels (that is, for the likelihood that no lesions will reach the inner half of the dentin) of 0.90, 0.95, and 0.99.
tion must be confronted. Although the average annual rate of caries might be 0.5 lesion per year, 5% of the individuals from a population with this rate will develop three or more new lesions in a year; if the rate is 1.5 per year, 50% of this group will develop no new lesions. There is no satisfactory method of identifying, within a population group that has some average caries rate, the persons who will or will not develop new lesions. Thus, probability distributions for the number of new lesions developing in a year must be incorporated in the analysis. In addition, clinicians must evaluate, on the basis of patient characteristics and the time they spend on clinical examinations, the likelihood that patients will return for 6-month clinical examinations and the likelihood that proximal lesions will be detected
clinically. Finally, both clinicians and patients will differ in the amount of risk they are willing to accept that a lesion will be detected in the inner half of the dentin. For all of the foregoing reasons, there is no arbitrary frequency with which bitewing radiographs should be taken. It is necessary to use judgment about a variety of factors, such as how rapidly caries progressesthrough the dentin, the patient’s risk of new lesions, the frequency and quality of clinical examinations, and the acceptable risk that a lesion may reach the inner half of the dentin before treatment occurs. These judgments have implications for when next to schedule radiographs. This analysis has in no senseobviated the need for clinical judgment. Rather, we have explicitly determined the
Frequency of bitewing radiographs
Volume 6 I Number 3
4
3
5
0.90
0.95
0.99
0.90
0.95
0.99
0.90
0.95
0.95
2.0b 2.0 1.5 1.5 1.0 I.0 1.0 1.0 I.0 # 1.5c 1.5 I .o I.0 1.0 # # # I .o 1.0 0.5c # 1.0 0.5b
I.% 1.5 1.0 I.0 1.0 # # # #
1.0 1.o # # #
1.5 1.5 I.0 1.0 1.0 # # # #
I .o 0.5b # # #
OSb # # # #
# # #
I.0 1.0 0.5c # #
# # #
I.0 I.0 0.5 # #
# #t #
1.0 1.0 #
# #
0.5a #
#
2.0 1.5 1.5 I .o 1.0 1.0 1.0 1.0 1.0 # 1.5 I.0 I.0 1.0 1.0 # # # 1.0 1.0 # #
1.5 1.0 1.0 1.0 0.5b # # # #
I.Ob 1.0 I.0 # #
2.0 1.5b 1.5 1.oc 1.0 1.0 1.0 1.0 1.0 # 1.5 1.5 1.0 1.0 I.0 # # # I .o 1.0 # # 0.5 #
# #
305
clinical decision-making aid. A clinician could supply information on estimated disease-progression rates, community caries incidence, and individual patient risk. For a contemplated time for a next set of bitewing radiographs, the output of the program would indicate the probability that carious lesions were in different parts of the enamel or dentin. This information could be used as an aid to the decision as to both the timing of radiographs and treatment strategies. We would like to thank Stephanie McGregor for her help in coding the radiographs and Paul DePaola for his comments on our earlier draft of this article. REFERENCES
# #
#
1. DePaola PF, Soparkar M, Van Leeuwen M, DeVehs R: The anticaries effect of single and combined topical fluoride systems in school children. Arch Oral Biol 25: 649-653, 1980. 2. Shwartz M, Pliskin JS, Grijndahl H-G, Boffa J: Use of the Kaplan-Meier estimate to reduce biases in estimating the rate of caries progression. Community Dent Oral Epidemiol 12: 103-108, 1984. 3. Shwartz M, Grondahl H-G, Pliskin JS, Botfa J: A longitudinal analysis from bitewing radiographs of the rate of progression of proximal carious lesions through human dental enamel. Arch Oral Biol 29: 529-536, 1984. 4. Shwartz M, Pliskin JS, Grondahl H-G, Boffa J: A “deep” model of the incidence of dental caries on proximal surfaces. Med Decis Making. (In press.) 5. Mejare I. Grijndahl H-G, Carlstedt K, Grever A-C, Gttosson E: Accuracy at radiography and probing for the diagnosis of proximal caries. Stand J Dent Res 93: 178-184, 1985. Reprint requests 10:
implications of judgment about these factors for when to schedule the next bitewing radiographs. The results presented in Tables III and IV are for general cases.The computer program that generated these results is really designed as an individual
Dr. Michael Shwartz School of Management Boston University 621 Commonwealth Ave. Boston. MA 02215