J. Dent. 1991;
18
Prediction longevity
of amalgam
R. J. Smales, D. A. Webster,
P. I. Leppard*
19: 18-23
restoration
and A. S. Dawsont
Department of Dentistry and *Department of Statistics, The University of Adelaide, Adelaide, South Australia and tBase Squadron, RAAF Base, Wagga Wagga, New South Wales, Australia
ABSTRACT The purpose of the present study was to assess predictions of longevity for amalgam restorations using a fitted Weibull distribution against base estimates using actuarial methods. The 1345 restorations involved were from 100 members of the Royal Australian Air Force whose dental conditions had been monitored regularly over a minimum period of 10 years. Based on maximum likelihood estimates of the parameters of a Weibull distribution, Weibull curves could be determined add were found to be very close to actuarial survival curves established from the same data set. However, Weibull estimates based on survival experience of less than 5-6 years failed to predict long-term survival. Using the 6 year actuarial survival data, the predicted and observed survival curves disagreed by less than 10 per cent for every time period. Twenty-five per cent of restorations had failed for the 6 year data, compared to 22 per cent in these first 6 years for the full 17 year data set. KEY WORDS: Amalgam, Restorations, Longevity J. Dent. 1991;
19: 18-23
(Received 21 May 1990;
Correspondence shouldbeaddressed South Australia 5001, Australia.
reviewed 5 July 1990;
accepted 21 September 1990)
to: Dr R. J. Smales, Department of Dentistry,
University of Adelaide, Adelaide,
INTRODUCTION With increasing numbers of new and modified dental materials being marketed, greater emphasis is being placed on short term laboratory and clinical assessments of such products. However, despite attempts to simulate limited aspects of the clinical performance of dental materials in vitro, the final proving ground is still their long term behaviour in the oral cavity. Attempts to link marginal fracture rates with subsequent amalgam restoration longevity have generally been unsuccessful. No significant correlation could be found between marginal deterioration ana clinical failure for a low and a high copper alloy over 10 years, where both materials had high failure rates in a water-fluoridated area (Hamilton et al., 1983). Similar results were found in another study of many low and high copper alloys over13 years, where failure rates were much lower (Osborne et al., 1989a). However, in a related study over 14 years, a significant correlation was found between the 1 year marginal fractures and the percentages of amalgam restorations lost, for two groups of low and high copper alloys (Osborne et al., 1989b). Again, another recent report @1991 Butterworth-Heinemann 0300-5712/91/010018-06
Ltd.
found no significant differences in the survival functions of low and high copper alloys over 19 years (Moffa, 1989). At this time, there does not appear to be sufficient evidence to base amalgam restoration longevity solely on marginal fracture deterioration results from short term clinical studies. Obviously, many factors are involved. Although it is also possible to predict the median time taken for any amalgam alloy to reach a pre-given level of marginal deterioration which may be considered to be clinically unsatisfactory (Letzel and van? Hof, 1984), this time is not necessarily closely related to the time of actual restoration replacement. Of more relevance, is the ability to be able to predict the median survival of restorations from their earlier failure behaviour, for a given population sample. In the present study, the long term actuarial life-table survivals of amalgam restorations were used to assess the performance of predictive failure models of restoration survival using fitted Weibull distributions (Weibull, 1951; Mann et al., 1974).
Smales et al.: Prediction
MATERIALS AND METHODS
of amalgam
restoration
longevity
showed 50 per cent survival of restorations at 14.43 + 0.72 years (Table I). The life-table cumulative survival curve, and the Weibull curve based on maximum likelihood estimations from this same data, are shown in Fig. 1. The Weibull curve closely matched the life-table survival curve. As we decreased the years of data used for our analysis by using only information gathered between 1972 and 1988, then between 1972 and 1987, etc., we found that the Weibull curves matched the life-table survival curves on each occasion, as illustrated by the 1972-1976 period shown in Fig. 2. However, when Weibull curve estimates from these subsets of data were used to predict failure over the entire 17year period, we found that as we reduced the number of years of data, the Weibull curves closely matched the 17 year life-table cumulative survival curve only until 5-6 years of data were used for our predictions. At this point, obvious divergences emerged as shown in Figs 3 and 4. The divergence of the curves became increasingly larger with further decreasing time periods. When the period 1972-1977 was used to determine Weibull failure rates over the 17 year period, we found that the actual observed proportion of restorations surviving (from life-table analysis of the entire data set) and the predicted survival (using estimates based on 1972-1977 data for the Weibull curve) were within 10 per cent agreement for a period of 10 years. The agreement between observed and predicted survival then diverged, and disagreed by 15 per cent at 14 years and by 12 per cent at 17 years. Twenty-three per cent of restorations had failed for the 5 year data. When looking at the full 17 year data set, 20 per cent of restorations failed in these first 5 years. When we repeated these predictions for the 6 year survival data (1972-1978) we found that the observed and predicted survival curves disagreed by less than 10 per cent for every time period. The predicted proportion of restorations surviving differed by 9 per cent from the observed proportion at 14 years and by 6 per cent at 17 years. Twenty-five per cent of restorations had failed for
Retrospective data were accumulated on the longevity of 1345 amalgam restorations placed by numerous operators in 100 active service personnel over periods of up to 17 years. The restorations were placed in members of the Royal Australian Air Force (RAAF), and their condition monitored regularly at around 1 yearly intervals, over a minimum period of 10 years for all personnel (Dawson, 1989). Restoration failures were classified as either true or apparent, the latter being caused by such procedures as unrelated tooth extractions, endodontic treatments, incorporation into other restorations or damage from trauma, and accounted for only 47 or 10.6 per cent of the 444 replacements. Only true failure types were considered in the present analyses, which included repairs and replacements from related caries, fractures and losses of material. Initially, only restorations placed during the period 1972-1976 were considered, and a non-parametric estimate of the failure time distribution was established using the actuarial life-table method (BMDP Statistical Software, Dixon, 1988,program 1L). The Weibull distribution specifies the survival time as the probability (survive ) time t) = exp(-atb), where a and p are unknown parameters to be estimated from the data. This was done by the method of maximum likelihood, again using the BMDP Statistical Software to perform calculations (program AR). Using the estimates of a and 8, established on survival experience of at most 4 years, extrapolations could be made for any time period. The data base was then successively expanded to the periods 1972-1978, 1972-1980, etc.; at each stage the actuarial and Weibull failure distributions being determined.
RESULTS Cumulative survivals from actuarial life-table analysis of data from RAAF dental records spanning 17 years
Survivalbased on 1972 - 1989 data
c
1
u s mu u r ; y
0.5 ‘.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Years -
19
Weibull distribution - Life table
fig. 7. Life-table survival and Weibull matched curves from the 17 year data.
15
16
17
20
J. Dent. 1991;
19: No. 1
Survivalbased on 1972 - 1976 data
mu u r
I
2
1
4
3
Years -
Weibull distribution _ Life table
Fig. 2. Life-table survival and Weibull matched curves from the 4 year data.
Predictionof survivalbased on 1972 - 1977 data
c u s mu u r I v a i
t v i a v I e
0
4
9
012345678
10
11
12
13
14
15
16
17
Years -
Weibull distribution a Life table
Fig. 3. Life-table survival over 17 years and Weibull predictive curves from the 5 year data.
Predictionof survivalbased on 1972 - 1976 data C
1
u s mu u r
t v i a v I e
0 01234567
8
9
10
11
12
13
14
15
16
17
Years
I
-
Weibull distribution - Life table
Fig. 4. Life-table survival over 17 years and Weibull predictive curves from the 4 year data.
Smales et al.: Prediction
of amalgam
restoration
longevity
21
Table 1. Actuarial life-table of amalgam restoration survivals Interval (Yf)
Entered
Withdrawn
Failed
o-1 l-2 2-3 3-4 4-5 5-6 6-7
1345 1262 1137 1016 962 794 721
::
33 38 40
;I; 9-10 IO-1 1 11-12 12-13 13-14 14-15 15-16 16-17
81 33 76 42 95:
634 508 421 320 228 150 99 68 41 5
Cumulative survivals f s.e. (%)
:; z;
28 18 86: 72 70 42 28 23 33 5
:: 8 9 3 4 :
97.5 94.5 91.0 85.8 80.4 77.2 73.5
f + + f f f f
0.4 0.6 0.8 1.0 1.2 1.3 1.4
67.3 70.0 64.5 60.0 57.5 53.5 51.6 47.9 42.1 42.1
It 1.5 z!I + 1.6 I!Z 1.8 z!I 1.9 + 2.2 + 2.4 + 2.8 + 4.0 +_4.0
Table II. Clinical studies of marginal deterioration of amalgam alloys
Studv Mahler et a/., 1970 Binon et al., 1973 Mahler et al., 1973
Alloys placed
Sig. diff. first seen
IH, 2L lH, 2L (assumed) lH, 2L
1 yr 9 mth
Forsten and Kallio, 1976
2H, 1L
Mahler and Marantz, 1979
IH, 5L
Mjor and Espevik, 1980 Osborne et a/., 198 1
5;L7L
Matsson et al., 1984
1H. IL
Filler et a/., 1986*
2H
Ricker and Greener, 1988
4H
Marker et al.. 1989*
2H
Smales and Rupinskas, 1989
2H
Smales et al., 1990
6H
-
Length of study 1 yr 9 mth
8 B W prints Not given
4 yr
8 Et W prints
6 mth
1v kmwed) 6 mth 6 mth (grzed’ 1 mth (trends only) 4 mth (trends only) 3 mth (trends only) 1.5 yr (treni;;ly)
Assessment method
3 yr (not given) 3 yr 3 yr (grouped) 2 yr
2 yr (not given) 3 yr (trends only) 17mth (trends only) 3 yr
2w
Plaster casts and prints X 5-7 8 8 W prints
8
Et W
Plastic models Transparencies Stone casts and microscope x 50 SEM x 1000 Transparencies SEM x 20 Transparencies Transparencies
H, high copper alloys; L, low copper alloys. *Restorations placed in artificial teeth of removable prostheses.
the 6 year data, compared to 22 per cent in these first 6 years for the full 17 year data set.
DISCUSSION Several clinical studies have now shown that performance differences or trends among various amalgam alloys for marginal fracture or deterioration may be detected as early as 1 month, and that these differences persist and
may become significant over time (Table II). The earliest and largest differences were seen between the low and the high copper non-gamma-2 alloys, with any significant differences among the high copper alloys taking longer to emerge (Smales and Rupinskas, 1989; Smales et al., 1990). Therefore, occlusal marginal fracture or deterioration of amalgam restorations has been suggested as a speculative predictor of clinical longevity (Mahler et al., 1973).
22
J. Dent 1991; 19: No. 1
However, most cross-sectional studies have found that marginal fracture accounted directly for the replacement of only around 5 -20 per cent of all amalgam restorations, although this percentage appears to be increasing despite the use of newer alloys (Richardson and Boyd, 1973; Makinson, 1976; Skogedal and Heloe, 1979; Mjor, 1981; Boyd and Richardson, 1985; Klausner et al., 1987). Again, results from several recent controlled clinical trials of amalgam alloys have reported very low failures of restorations from marginal fracture (Smales and Gerke, 1984; Doglia et al., 1986; Letzel et al., 1989; Robersonet al., 1989). Because attempts to link marginal fracture rates with subsequent amalgam restoration longevity have generally been unsuccessful, the prediction of survival times based on earlier restoration failure patterns would seem to be more relevant and reliable. Weibull probability of failure methods have been used for the lifetime predictions for resin-bonded bridges (Thompson and de Rijk, 1989), but we are unaware of the application of the method to the prediction of amalgam restoration failures, or of being tested against actual long term clinical data. In the present study, Weibull predictive curves vould be matched closely to even relatively short term data as shown in Fig. 2, but the eventual median survival time of 14.43 f 0.72 years could only be predicted reasonably accurately once 6 years of failure data had accumulated (Fig. 3). Therefore, short term failure rates could not be used to predict the median survival time of the amalgam restorations, and predictions based on such studies are likely to underestimate the actual median longevity of the restorations. A similar result was found in another recent study when recalculating the survival predictions for resin-bonded bridges (Thompson et al., 1989). The findings of the present study are not definitive for all restorative materials or populations, and further studies are required to test the reliability of the method. Such studies are in progress. Acknowledgements We would like to thank Group Captain J. Tobler, Director of Dental Services-Air Force, for allowing access to the RAAF records that formed the basis of this study, and for the cooperation received from the staff at Dental Flight, Administrative Support Squadron Edinburgh, South Australia. The statements contained in this article are those of the authors and are not to be construed as official or reflecting those of the Directorate of Dental ServicesAir Force or the RAAF. References
Binon P., Philips R. W., Swartz M. L. et al. (1973)Clinical behaviour of amalgams related to certain mechanical properties. J. Dent. Res. 52, (Special Issue), (Abstr. 509), 186. Boyd M. A. and Richardson A. S. (1985)Frequency of amalgam replacement in general dental practice. J. Can. Dent. Assoc. 51, 763-766.
Dawson A. S. (1989) Dental Treatment and Dental Health. A Study of Some Factors which may Influence Dental Health in Members of the Royal Australian Air Force. Research Report of the Degree of MDS, Department of Dentistry, The University of Adelaide. Dixon W. J. (1988) BMDP Statistical Software. Berkeley, University of California Press. Doglia R., Herr P., Holz J. et al. (1986) Clinical evaluation of four amalgam alloys: a five-year report. 1 Prosthet. Dent. 56,406-415. Filler W. H., McKinney T. W., Miller B. H. et al. (1986) Early detection of marginal deterioration: intraoral VS SEM examination. J. Dent. Res. 65, (Special issue), (Abstr. 205), 192. Forsten L., and Kallio M. L. (1976) Marginal fracture of dental amalgams. &and. J. Dent. Res. 84,430-433. Hamilton J. C., Moffa J. P., Ellison J. k et al. (1983) Marginal fracture not a predictor of longevity for two dental amalgam alloys: a ten-year study. J. Pros&et. Dent. 50, 200-202. Klausner L. H., Green T. G. and Charbeneau G. T. (1987) Placement and replacement of amalgam restorations: a challenge for the profession. Oper. Dent. 12, 105-112. Letzel H. and van’t Hof M. A (1984) Longitudinal durability parameters for dental restorations. J. Dent. Res. 63, (C E Division), (Abstr. 44), 535. Letzel H., van? Hof M. A., Vrijhoef M. M. k et al. (1989) A controlled clinical study of amalgam restorations: survival, failure, and causes of failure. Dent. Mater. 5, 115-121. Mahler D. B. and Marantz R. L. (1979) The effect of time on the marginal fracture hehaviour of amalgam. J. Oral Rehabil. 6, 391-398. Mahler D. B., Terkla L. G., Van Eysden J. et al. (1970) Marginal fracture VS mechanical properties of amalgam. J. Dent Res. 49, 1452-1457. Mahler D. B., Terkla L. G. and Van Eysden J. (1973) Marginal fracture of amalgam restorations. J. Dent. Res. 52, 823-827. Makinson 0. F. (1976) Replacement of Silver Amalgam Restorations: A Clinical Survey and Comparison by the General Practice Study Group, South Australia. Australian Dental Congress, Adelaide. Mann N. R., Schafer R. E. and Singpurwalla N. D. (1974) Methods for Statistical Analysis of Reliability and Life Data. New York, John Wiley. Marker V. A., Miller B. H., Spears R et al. (1989) Quantitative
measure of amalgam marginal breakdown as a function of time. J. Dent. Res. 68, (Special Issue), (Abstr. 229), 210. Matsson L., Granath L. and Ryge G. (1984) Early prediction of long-term margin adaptation of dental amalgam restorations. Stand. J. Dent. Res. 92, 172-176. Mjor I. A (1981) Placement and replacement of restorations. Oper. Dent. 6,49-54.
Mjor I. A. and Espevik S. (1980) Assessment of variables in clinical studies of amalgam restorations. J. Dent. Res. 59, 1511-1515. Moffa J. P. (1989) The longevity and reasons for replacement of amalgam alloys. J. Dent. Res. 68, (Special Issue), (Abstr. 56), 188. Osborne J. W., Schlissel E. R. and Gale E. N. (1981) Clinical test for the development of new amalgam alloys. J. Dent. Res. 60, 999.
Osborne J. W., Norman R D., Chew C. et al. (1989a) Clinical evaluations of 9 high copper amalgams: a 13-year assessment. J. Dent. Res. 68, (Special Issue), (Abstr. 1045), 997. Osborne J. W., Norman R. D., Chew C. et al. (1989b) Long term clinical assessment of amalgam restoration. J. Dent. Res. 68, (Special Issue), (Abstr. 57), 189.
Smales et al.: Prediction of amalgam restoration longevity
Richardson A S. and Boyd M. A. (1973) Replacement of silver amalgam restorations by 50 dentists during 246 working days. J. Can. Dent. Assoc. 39, 556-559. Ricker J. B. and Greener E. H. (1988) Early observations and three-year clinical evaluation of four amalgam alloys. Oper. Dent. 13, 119-127. Roberson T. M., Bayne S. C., Taylor D. F. et al. (1989) Long term clinical failure of dental amalgam. .I Dent, Res. 68, (Special Issue), (Abstr. 216), 208. Skogedal 0. and Heloe L. A. (1979) Clinical quality of amalgam restorations. Stand. J. Dent. Res. 87, 459-461. Smales R. J. and Gerke D. C. (1984) Clinical evaluation of four high-copper amalgam alloys. J. Dent. 12, 127-134.
Forthcoming Original
Smales R. J. and Rupinskas L. (1989) Valiant PhD and Lojic N amalgam alloys: 3-year clinical results. J. Dent Res. 68, (ANZ Division), (Abstr. 12), 550. Smales R. J., Gerke D. C. and Hume W. R. (1990) Clinical behaviour of high-copper amalgams with time, site, size and class of cavity preparation. J. Dent. 18,49-53. Thompson V. P. and de Rijk W. (1989) Clinical evaluation and lifetime predictions for resin-bonded prostheses. In Anusavice K. J. (ed.), Quality Evaluation of Dental Restorations, Criteria for Placement and Replacement.
Chicago, Quintessence, pp. 373-384. Thompson V., Wood M. and de Rijk W. (1989) Bonded bridge recalls and Weibull distributions; results averaging seven years. J. Dent. Res. 68, (Special Issue), (Abstr. 427),920.
Weibull W. (1951)A statistical distribution function of wide applicability. J. Appl. Me& 18,293-297.
Articles
Research
Reports
Amoxycillin with clavulanic acid and tetracycline in periodontal therapy S. H. Abu Fanas, D. B. Drucker and P. S. Hull Evaluation of acrylic strips containing amoxycillin with clavulanic acid for local drug delivery S. H. Abu Fanas, D. B. Drucker and P. S. Hull
Current concepts in the role of fibroblasts and extracellular matrix in wound healing and their relevance to oral implantology P. Sloan Intraoral strain gauge measurements study
on complete dentures: a methodological
G. D. Staford and P.-O. Glantz Injuries to dental patients and visitors K. Porter, S. Porter, C. Scully and Y; Theyer Uptake
of fluoride
by sound
and artificially
carious
application of topical sodium and amine fluorides J C. Y; Chan. F. J Hill and H. N. Navman
23
enamel
in vitro following
18
Prediction longevity
of amalgam
R. J. Smales, D. A. Webster,
P. I. Leppard*
19: 18-23
restoration
and A. S. Dawsont
Department of Dentistry and *Department of Statistics, The University of Adelaide, Adelaide, South Australia and tBase Squadron, RAAF Base, Wagga Wagga, New South Wales, Australia
ABSTRACT The purpose of the present study was to assess predictions of longevity for amalgam restorations using a fitted Weibull distribution against base estimates using actuarial methods. The 1345 restorations involved were from 100 members of the Royal Australian Air Force whose dental conditions had been monitored regularly over a minimum period of 10 years. Based on maximum likelihood estimates of the parameters of a Weibull distribution, Weibull curves could be determined add were found to be very close to actuarial survival curves established from the same data set. However, Weibull estimates based on survival experience of less than 5-6 years failed to predict long-term survival. Using the 6 year actuarial survival data, the predicted and observed survival curves disagreed by less than 10 per cent for every time period. Twenty-five per cent of restorations had failed for the 6 year data, compared to 22 per cent in these first 6 years for the full 17 year data set. KEY WORDS: Amalgam, Restorations, Longevity J. Dent. 1991;
19: 18-23
(Received 21 May 1990;
Correspondence shouldbeaddressed South Australia 5001, Australia.
reviewed 5 July 1990;
accepted 21 September 1990)
to: Dr R. J. Smales, Department of Dentistry,
University of Adelaide, Adelaide,
INTRODUCTION With increasing numbers of new and modified dental materials being marketed, greater emphasis is being placed on short term laboratory and clinical assessments of such products. However, despite attempts to simulate limited aspects of the clinical performance of dental materials in vitro, the final proving ground is still their long term behaviour in the oral cavity. Attempts to link marginal fracture rates with subsequent amalgam restoration longevity have generally been unsuccessful. No significant correlation could be found between marginal deterioration ana clinical failure for a low and a high copper alloy over 10 years, where both materials had high failure rates in a water-fluoridated area (Hamilton et al., 1983). Similar results were found in another study of many low and high copper alloys over13 years, where failure rates were much lower (Osborne et al., 1989a). However, in a related study over 14 years, a significant correlation was found between the 1 year marginal fractures and the percentages of amalgam restorations lost, for two groups of low and high copper alloys (Osborne et al., 1989b). Again, another recent report @1991 Butterworth-Heinemann 0300-5712/91/010018-06
Ltd.
found no significant differences in the survival functions of low and high copper alloys over 19 years (Moffa, 1989). At this time, there does not appear to be sufficient evidence to base amalgam restoration longevity solely on marginal fracture deterioration results from short term clinical studies. Obviously, many factors are involved. Although it is also possible to predict the median time taken for any amalgam alloy to reach a pre-given level of marginal deterioration which may be considered to be clinically unsatisfactory (Letzel and van? Hof, 1984), this time is not necessarily closely related to the time of actual restoration replacement. Of more relevance, is the ability to be able to predict the median survival of restorations from their earlier failure behaviour, for a given population sample. In the present study, the long term actuarial life-table survivals of amalgam restorations were used to assess the performance of predictive failure models of restoration survival using fitted Weibull distributions (Weibull, 1951; Mann et al., 1974).
Smales et al.: Prediction
MATERIALS AND METHODS
of amalgam
restoration
longevity
showed 50 per cent survival of restorations at 14.43 + 0.72 years (Table I). The life-table cumulative survival curve, and the Weibull curve based on maximum likelihood estimations from this same data, are shown in Fig. 1. The Weibull curve closely matched the life-table survival curve. As we decreased the years of data used for our analysis by using only information gathered between 1972 and 1988, then between 1972 and 1987, etc., we found that the Weibull curves matched the life-table survival curves on each occasion, as illustrated by the 1972-1976 period shown in Fig. 2. However, when Weibull curve estimates from these subsets of data were used to predict failure over the entire 17year period, we found that as we reduced the number of years of data, the Weibull curves closely matched the 17 year life-table cumulative survival curve only until 5-6 years of data were used for our predictions. At this point, obvious divergences emerged as shown in Figs 3 and 4. The divergence of the curves became increasingly larger with further decreasing time periods. When the period 1972-1977 was used to determine Weibull failure rates over the 17 year period, we found that the actual observed proportion of restorations surviving (from life-table analysis of the entire data set) and the predicted survival (using estimates based on 1972-1977 data for the Weibull curve) were within 10 per cent agreement for a period of 10 years. The agreement between observed and predicted survival then diverged, and disagreed by 15 per cent at 14 years and by 12 per cent at 17 years. Twenty-three per cent of restorations had failed for the 5 year data. When looking at the full 17 year data set, 20 per cent of restorations failed in these first 5 years. When we repeated these predictions for the 6 year survival data (1972-1978) we found that the observed and predicted survival curves disagreed by less than 10 per cent for every time period. The predicted proportion of restorations surviving differed by 9 per cent from the observed proportion at 14 years and by 6 per cent at 17 years. Twenty-five per cent of restorations had failed for
Retrospective data were accumulated on the longevity of 1345 amalgam restorations placed by numerous operators in 100 active service personnel over periods of up to 17 years. The restorations were placed in members of the Royal Australian Air Force (RAAF), and their condition monitored regularly at around 1 yearly intervals, over a minimum period of 10 years for all personnel (Dawson, 1989). Restoration failures were classified as either true or apparent, the latter being caused by such procedures as unrelated tooth extractions, endodontic treatments, incorporation into other restorations or damage from trauma, and accounted for only 47 or 10.6 per cent of the 444 replacements. Only true failure types were considered in the present analyses, which included repairs and replacements from related caries, fractures and losses of material. Initially, only restorations placed during the period 1972-1976 were considered, and a non-parametric estimate of the failure time distribution was established using the actuarial life-table method (BMDP Statistical Software, Dixon, 1988,program 1L). The Weibull distribution specifies the survival time as the probability (survive ) time t) = exp(-atb), where a and p are unknown parameters to be estimated from the data. This was done by the method of maximum likelihood, again using the BMDP Statistical Software to perform calculations (program AR). Using the estimates of a and 8, established on survival experience of at most 4 years, extrapolations could be made for any time period. The data base was then successively expanded to the periods 1972-1978, 1972-1980, etc.; at each stage the actuarial and Weibull failure distributions being determined.
RESULTS Cumulative survivals from actuarial life-table analysis of data from RAAF dental records spanning 17 years
Survivalbased on 1972 - 1989 data
c
1
u s mu u r ; y
0.5 ‘.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Years -
19
Weibull distribution - Life table
fig. 7. Life-table survival and Weibull matched curves from the 17 year data.
15
16
17
20
J. Dent. 1991;
19: No. 1
Survivalbased on 1972 - 1976 data
mu u r
I
2
1
4
3
Years -
Weibull distribution _ Life table
Fig. 2. Life-table survival and Weibull matched curves from the 4 year data.
Predictionof survivalbased on 1972 - 1977 data
c u s mu u r I v a i
t v i a v I e
0
4
9
012345678
10
11
12
13
14
15
16
17
Years -
Weibull distribution a Life table
Fig. 3. Life-table survival over 17 years and Weibull predictive curves from the 5 year data.
Predictionof survivalbased on 1972 - 1976 data C
1
u s mu u r
t v i a v I e
0 01234567
8
9
10
11
12
13
14
15
16
17
Years
I
-
Weibull distribution - Life table
Fig. 4. Life-table survival over 17 years and Weibull predictive curves from the 4 year data.
Smales et al.: Prediction
of amalgam
restoration
longevity
21
Table 1. Actuarial life-table of amalgam restoration survivals Interval (Yf)
Entered
Withdrawn
Failed
o-1 l-2 2-3 3-4 4-5 5-6 6-7
1345 1262 1137 1016 962 794 721
::
33 38 40
;I; 9-10 IO-1 1 11-12 12-13 13-14 14-15 15-16 16-17
81 33 76 42 95:
634 508 421 320 228 150 99 68 41 5
Cumulative survivals f s.e. (%)
:; z;
28 18 86: 72 70 42 28 23 33 5
:: 8 9 3 4 :
97.5 94.5 91.0 85.8 80.4 77.2 73.5
f + + f f f f
0.4 0.6 0.8 1.0 1.2 1.3 1.4
67.3 70.0 64.5 60.0 57.5 53.5 51.6 47.9 42.1 42.1
It 1.5 z!I + 1.6 I!Z 1.8 z!I 1.9 + 2.2 + 2.4 + 2.8 + 4.0 +_4.0
Table II. Clinical studies of marginal deterioration of amalgam alloys
Studv Mahler et a/., 1970 Binon et al., 1973 Mahler et al., 1973
Alloys placed
Sig. diff. first seen
IH, 2L lH, 2L (assumed) lH, 2L
1 yr 9 mth
Forsten and Kallio, 1976
2H, 1L
Mahler and Marantz, 1979
IH, 5L
Mjor and Espevik, 1980 Osborne et a/., 198 1
5;L7L
Matsson et al., 1984
1H. IL
Filler et a/., 1986*
2H
Ricker and Greener, 1988
4H
Marker et al.. 1989*
2H
Smales and Rupinskas, 1989
2H
Smales et al., 1990
6H
-
Length of study 1 yr 9 mth
8 B W prints Not given
4 yr
8 Et W prints
6 mth
1v kmwed) 6 mth 6 mth (grzed’ 1 mth (trends only) 4 mth (trends only) 3 mth (trends only) 1.5 yr (treni;;ly)
Assessment method
3 yr (not given) 3 yr 3 yr (grouped) 2 yr
2 yr (not given) 3 yr (trends only) 17mth (trends only) 3 yr
2w
Plaster casts and prints X 5-7 8 8 W prints
8
Et W
Plastic models Transparencies Stone casts and microscope x 50 SEM x 1000 Transparencies SEM x 20 Transparencies Transparencies
H, high copper alloys; L, low copper alloys. *Restorations placed in artificial teeth of removable prostheses.
the 6 year data, compared to 22 per cent in these first 6 years for the full 17 year data set.
DISCUSSION Several clinical studies have now shown that performance differences or trends among various amalgam alloys for marginal fracture or deterioration may be detected as early as 1 month, and that these differences persist and
may become significant over time (Table II). The earliest and largest differences were seen between the low and the high copper non-gamma-2 alloys, with any significant differences among the high copper alloys taking longer to emerge (Smales and Rupinskas, 1989; Smales et al., 1990). Therefore, occlusal marginal fracture or deterioration of amalgam restorations has been suggested as a speculative predictor of clinical longevity (Mahler et al., 1973).
22
J. Dent 1991; 19: No. 1
However, most cross-sectional studies have found that marginal fracture accounted directly for the replacement of only around 5 -20 per cent of all amalgam restorations, although this percentage appears to be increasing despite the use of newer alloys (Richardson and Boyd, 1973; Makinson, 1976; Skogedal and Heloe, 1979; Mjor, 1981; Boyd and Richardson, 1985; Klausner et al., 1987). Again, results from several recent controlled clinical trials of amalgam alloys have reported very low failures of restorations from marginal fracture (Smales and Gerke, 1984; Doglia et al., 1986; Letzel et al., 1989; Robersonet al., 1989). Because attempts to link marginal fracture rates with subsequent amalgam restoration longevity have generally been unsuccessful, the prediction of survival times based on earlier restoration failure patterns would seem to be more relevant and reliable. Weibull probability of failure methods have been used for the lifetime predictions for resin-bonded bridges (Thompson and de Rijk, 1989), but we are unaware of the application of the method to the prediction of amalgam restoration failures, or of being tested against actual long term clinical data. In the present study, Weibull predictive curves vould be matched closely to even relatively short term data as shown in Fig. 2, but the eventual median survival time of 14.43 f 0.72 years could only be predicted reasonably accurately once 6 years of failure data had accumulated (Fig. 3). Therefore, short term failure rates could not be used to predict the median survival time of the amalgam restorations, and predictions based on such studies are likely to underestimate the actual median longevity of the restorations. A similar result was found in another recent study when recalculating the survival predictions for resin-bonded bridges (Thompson et al., 1989). The findings of the present study are not definitive for all restorative materials or populations, and further studies are required to test the reliability of the method. Such studies are in progress. Acknowledgements We would like to thank Group Captain J. Tobler, Director of Dental Services-Air Force, for allowing access to the RAAF records that formed the basis of this study, and for the cooperation received from the staff at Dental Flight, Administrative Support Squadron Edinburgh, South Australia. The statements contained in this article are those of the authors and are not to be construed as official or reflecting those of the Directorate of Dental ServicesAir Force or the RAAF. References
Binon P., Philips R. W., Swartz M. L. et al. (1973)Clinical behaviour of amalgams related to certain mechanical properties. J. Dent. Res. 52, (Special Issue), (Abstr. 509), 186. Boyd M. A. and Richardson A. S. (1985)Frequency of amalgam replacement in general dental practice. J. Can. Dent. Assoc. 51, 763-766.
Dawson A. S. (1989) Dental Treatment and Dental Health. A Study of Some Factors which may Influence Dental Health in Members of the Royal Australian Air Force. Research Report of the Degree of MDS, Department of Dentistry, The University of Adelaide. Dixon W. J. (1988) BMDP Statistical Software. Berkeley, University of California Press. Doglia R., Herr P., Holz J. et al. (1986) Clinical evaluation of four amalgam alloys: a five-year report. 1 Prosthet. Dent. 56,406-415. Filler W. H., McKinney T. W., Miller B. H. et al. (1986) Early detection of marginal deterioration: intraoral VS SEM examination. J. Dent. Res. 65, (Special issue), (Abstr. 205), 192. Forsten L., and Kallio M. L. (1976) Marginal fracture of dental amalgams. &and. J. Dent. Res. 84,430-433. Hamilton J. C., Moffa J. P., Ellison J. k et al. (1983) Marginal fracture not a predictor of longevity for two dental amalgam alloys: a ten-year study. J. Pros&et. Dent. 50, 200-202. Klausner L. H., Green T. G. and Charbeneau G. T. (1987) Placement and replacement of amalgam restorations: a challenge for the profession. Oper. Dent. 12, 105-112. Letzel H. and van’t Hof M. A (1984) Longitudinal durability parameters for dental restorations. J. Dent. Res. 63, (C E Division), (Abstr. 44), 535. Letzel H., van? Hof M. A., Vrijhoef M. M. k et al. (1989) A controlled clinical study of amalgam restorations: survival, failure, and causes of failure. Dent. Mater. 5, 115-121. Mahler D. B. and Marantz R. L. (1979) The effect of time on the marginal fracture hehaviour of amalgam. J. Oral Rehabil. 6, 391-398. Mahler D. B., Terkla L. G., Van Eysden J. et al. (1970) Marginal fracture VS mechanical properties of amalgam. J. Dent Res. 49, 1452-1457. Mahler D. B., Terkla L. G. and Van Eysden J. (1973) Marginal fracture of amalgam restorations. J. Dent. Res. 52, 823-827. Makinson 0. F. (1976) Replacement of Silver Amalgam Restorations: A Clinical Survey and Comparison by the General Practice Study Group, South Australia. Australian Dental Congress, Adelaide. Mann N. R., Schafer R. E. and Singpurwalla N. D. (1974) Methods for Statistical Analysis of Reliability and Life Data. New York, John Wiley. Marker V. A., Miller B. H., Spears R et al. (1989) Quantitative
measure of amalgam marginal breakdown as a function of time. J. Dent. Res. 68, (Special Issue), (Abstr. 229), 210. Matsson L., Granath L. and Ryge G. (1984) Early prediction of long-term margin adaptation of dental amalgam restorations. Stand. J. Dent. Res. 92, 172-176. Mjor I. A (1981) Placement and replacement of restorations. Oper. Dent. 6,49-54.
Mjor I. A. and Espevik S. (1980) Assessment of variables in clinical studies of amalgam restorations. J. Dent. Res. 59, 1511-1515. Moffa J. P. (1989) The longevity and reasons for replacement of amalgam alloys. J. Dent. Res. 68, (Special Issue), (Abstr. 56), 188. Osborne J. W., Schlissel E. R. and Gale E. N. (1981) Clinical test for the development of new amalgam alloys. J. Dent. Res. 60, 999.
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Smales et al.: Prediction of amalgam restoration longevity
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Forthcoming Original
Smales R. J. and Rupinskas L. (1989) Valiant PhD and Lojic N amalgam alloys: 3-year clinical results. J. Dent Res. 68, (ANZ Division), (Abstr. 12), 550. Smales R. J., Gerke D. C. and Hume W. R. (1990) Clinical behaviour of high-copper amalgams with time, site, size and class of cavity preparation. J. Dent. 18,49-53. Thompson V. P. and de Rijk W. (1989) Clinical evaluation and lifetime predictions for resin-bonded prostheses. In Anusavice K. J. (ed.), Quality Evaluation of Dental Restorations, Criteria for Placement and Replacement.
Chicago, Quintessence, pp. 373-384. Thompson V., Wood M. and de Rijk W. (1989) Bonded bridge recalls and Weibull distributions; results averaging seven years. J. Dent. Res. 68, (Special Issue), (Abstr. 427),920.
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