J. Dent. 1991;
278
19: 278-282
Survival predictions of four types of dental restorative materials R. J. Smales, D. A. Webster and P. I. Department of Dentistry and *Department
Leppard* of Statistics, The University of Adelaide, South Australia
ABSTRACT The present study assessed the survival predictions made for four different types of dental restorative materials, using a mixture model involving the standard Weibull distribution function. A large number of amalgam, anterior resin, glass polyalkenoate (ionomer) cement, and pit and fissure sealant restorations were examined over varying periods of up to 18 years. The materials had been placed by numerous staff and students at a teaching hospital. Based on maximum likelihood estimations of the parameters of the mixture model distribution, survival curves were generated and found to agree closely with the actuarial survival curves estimated from the same data. As the years of data used to fit the mixture model curves decreased, then the fitted curves started to exhibit obvious divergences from the actuarial curves at 12-13 years for amalgams, 3-4 years for anterior resins and sealants, and l-2 years for glass polyalkenoate (ionomer) cements. At least 5 per cent of restorations needed to have failed over any period to allow close agreement of the two curves, with the slower failing materials requiring longer observation periods.
KEY WORDS: Restorations, J. Dent. 1991; 1991)
19:
Survival predictions
278-282
(Received 23 August 1990;
Correspondence should be addressed Adelaide, South Australia 5001.
reviewed 18 December
Many attempts have been made to predict the longevity or survival of restorations of various dental restorative materials based on selected findings from short-term clinical studies. Most of these studies have either evaluated the marginal fracture rates of amalgam alloys or the occlusal wear rates of posterior composite resins. However, attempts to link short-term marginal fracture rates of low- and high-copper alloys with subsequent amalgam restoration longevity have generally been unsuccessful (Hamilton et al., 1983; Moffa, 1989; Osborne et al., 1989a, b), while the present authors are unaware of any publications which have shown significant associations between the short-term occlusal wear rates of different posterior composites and their subsequent longevity. In fact, in one recent study over 5 years and longer of posterior composites, all 19 materials appeared to decrease in their wear rates, and eventually approached the same overall total wear level (Roberson et al.. 1988). As predictions of restoration longevity from short-term studies based on the deterioration rates of selected clinical factors have given variable results, the ability to predict Ltd.
accepted 4 May
to: Dr R. J. Smales. Department of Dentistry, The University of Adelaide,
INTRODUCTION
@ 1991 Butterworth-Heinemann 0300-5712/91/050278-05
1990;
the median survival times of restorations from their earliest failure behaviour may be more relevant. Therefore, in the present study, the long-term survival behaviour of several amalgam, anterior composite, glass polyalkenoate (ionomer) cement, and pit and fissure restorative materials were first generated using an actuarial life-table method. Then, using the same data, a predictive mixture model involving a Weibull distribution function (Weibull, 1951; Mann et al., 1974) was assessed graphically against the actuarial results.
MATERIALS AND METHODS Data were accumulated on the survivals of numerous dental restorations from several clinical studies involving amalgams, anterior composites, glass polyalkenoate (ionomer) cements, and pit and fissure sealants. The restorations were placed by a variety of operators, both staff and students, in patients treated at the Adelaide Dental Hospital since 1966. The dental materials involved are shown in Table 1. There were 1801 amalgams, 1770 composites, 465 glass polyalkenoate (ionomer) cements,
Smales
Tab/e 1. Materials
evaluated
Material Amalgams New True Dentalloy Shofu Spherical Dispersalloy Tytin lndiloy Resins Adaptic Concise Nuva-Fil Silar Glass polyalkenoate Aspa Fuji II Ketac
Manufacturer
S.S. White Co., London,
restorations
279
Number
UK
Shofu Dental Co., Kyoto, Japan Johnson Et Johnson Co., East Windsor, NJ, USA S.S. White Co., Philadelphia, PA, USA Shofu Dental Co., Kyoto, Japan Johnson 8 Johnson Co., New Brunswick, NJ, USA 3M Co., St Paul, MN, USA L.D. Caulk Co., Milford, DE, USA 3M Co., St Paul, MN, USA (ionomer) cements AD International, London, UK GC Dental Co., Tokyo, Japan Espe GmbH, Seefeld, Germany
and 515 pit and fissure sealants which were assessed over varying periods for up to 18 years. 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 by damage from trauma. Only true failures were included in the present analyses, which included repairs and replacements from related caries, fractures and losses of material, and colour mismatches. Partly lost pit and fissure sealants were not treated as failures, as it was assumed that the remaining material still conferred some degree of caries prevention. Actuarial survival curves were generated for the four groups of materials (BMDP Statistical Software, Dixon, 1990; program 1L). Mixture model predictive survival distributions were then calculated using the same data from the total study periods, and then again on the data for decreasing yearly intervals. To allow for the possibility oflong-term survivals, the survival function defined as the mixture model had the form: (Survive > time t) = y + (I-y)
of dental
for lonoevitv
Pit and fissure sealants 3M Co., St Paul, MN, USA Enamel-Bond L.D. Caulk Co., Milford, DE, Nuva-Seal USA S.S. White Co., Philadelphia, S.S. White PA, USA Delton Johnson 8 Johnson Co., East Windsor, NJ, USA
G(t) = Probability
et al.: Survival
exp (- cd)
where 0 < y < 1 and a, p > 0. The unknown parameters f3and y were estimated from the data using the method maximum likelihood estimation (BMDP program AR). the standard Weibull distribution alone is adequate
a, of If to
Lathe-cut (low copper) Spherical (low copper) Admixed (high copper) Spherical (high copper) Spheroidal (high copper)
964
Conventional
321
Conventional Conventional (u.v.-light) Microfil
1115 189
225 178 112 322
145
Type II Type II Type II
142 192 131
Auto-cure U.v.-light
181 87
Auto-cure
70
Auto-cure
describe the data, then y = 0 and G(t) = exp (- ata) which is the standard Weibull survival curve. Graphical comparisons of the two sets of curves were then used for the assessments because ‘there is no satisfactory approach to empirical distribution function goodness of tit tests when data are arbitrarily censored’ (Lawless, 1982).
RESULTS An abbreviated
actuarial life-table analysis of cumulative survivals for the four groups of restorative materials is shown in Table II. The failure rates of the amalgam restorations were too low, even after periods of up to 18 years, to obtain the median survival time. The estimated coefficients and their standard deviations for the mixture model predictions, based on the full data set for each of the four groups of restorative materials, are shown in Table III. A high a coefficient was apparent for the glass polyalkenoate (ionomer) cements and high y coefficients for the amalgams and glass polyalkenoate (ionomer) cements. The actuarial and the fitted G(t) cumulative survival curves, based on the same total data from each of the four groups of materials, closely agreed as shown in Figs 1-4, where the fitted curves lie well within the bounds of the
J. Dent. 1991; 19: No. 5
280
Table II. Abbreviated life-table cumulative survivals of four groups of restorative materials Quartiles
Numbers entered After varying intervals (yr) At start
Material Amalgams Anterior composites Glass ionomer cements Fissure sealants
36 (16yr) 26 (15 yr) 20 (9 yr)
1801 1770 465
17 (7 yr)
515
75th
50th
25th
10.9 + 1.1* 3.4 f 0.2 0.8 + 0.1
7.9 + 0.5 2.2 + 0.2
16.2 t 0.4 6.2 + 1.6
2.4 + 0.2
4.4 Ik 0.1
7.8 + 0.7
*Cumulative survivals + standard errors (years).
Table 111.Estimated coefficients (and standard deviations) for the fitted predictive curves Material Amalgams Anterior resins Glass ionomer cements Fissure sealants
a
P
Y
0.032 0.084 0.486
(0.0 1) (0.006) (0.052)
1.406 1.005 0.764
(0.105) (0.034) (0.050)
0.607 (0.107) 0.000 (0.000) 0.12 1 (0.047)
0.098
(0.0 14)
1.443
(0.097)
0.08 1 (0.088)
actuarial estimates. As the years of data used for fitting G(f) were decreased, there were reasonably close agreements found to the actuarial survival curves (by using their standard error bars as a guide) until only 12-13 years of data were used for the predictions for amalgams, 3-4 years for anterior resins and fissure sealants, and l-2years for glass polyalkenoate (ionomer) cements. At these times, obvious divergences between the two sets of curves began to emerge as also shown in Figs 1-4, where the fitted curves no longer lie entirely within the actuarial bounds.
DISCUSSION Although marginal fracture has dominated the clinical assessment of amalgam restorations, bulk fracture has 1
emerged as the main cause of the low failure rates found in several recent controlled trials (Akerboom et al., 1986; Doglia et al., 1986; Lemmens et al., 1987; Letzel et al., 1989); and again, although occlusal wear had dominated the assessment of posterior composites, recurrent caries and bulk fracture were the main causes of failure found in other controlled trials (Moffa et al., 1984; Hendriks and Letzel, 1988; Bayne et al., 1989; Letzel, 1989; Shintani etal.. 1989; Wierinck et al.. 1989). The authors of the present study are unaware of any publications which have reported significant associations between these failure modes and predictions of the long-term survivals of the amalgam and posterior composite restorations involved. The differing long-term restoration survival behaviours reported for the four different groups of materials 1
0.8
0.8
0.2
0 0
1 2
3
4
5
6
7
8
9 101112
1314
15 1617
18
Age of restorations (yr)
0 1
2
3
4
5
6
7
8
9 IO 11 12 13 14 15 16 17
Age of restorations (vr)
Fig. 7. Actuarial (with 2 X s.e. bars), and predictive survival curves for the full data and the 1966-79 (12- 13 years) data
fig.2. Actuarial (with 2 X s.e. bars), and predictive survival curves for the full data and the 1969-73 (3-4 years) data for
for amalgams. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (12-l 3 years).
anterior resins.-, Actuarial survival; - - -, mixture model (all data); -, mixture model (3-4 years).
Smales et al.: Survival
0
1
234567
of dental restorations
8
9
281
10
11
12
Age of restorations(yr) 0
1
2
3
4
5
6
7
8
9
10
II
1213
Age of restorations(yr) fig.3. Actuarial (with 2 X s.e. bars), and predictive survival curvesforthefulldataand the 1976-78 (I-2years)datafor glass ionomer cements. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (l-2 years).
in the present study allowed the rigorous testing of a predictive survival model of wide applicability. Because attempts at predicting long-term restoration survivals based on the deterioration rates of selected clinical factors have generally been unsuccessful (Hamilton et al., 1983; Moffa, 1989; Osborne et al., 1989a, b), survival rates based on actual early failure behaviour would appear to be more pertinent. Despite the markedly different survival behaviour shown by the four groups of materials, the fitted G(t) predictions based on the total data were in close graphical agreement with the actuarial survivals for all materials (Figs 1-4). In each instance, the two survival curves only diverged when there were insufficient failure data available for the adequate estimation of the parameters of G(t). As our data sets became increasingly smaller, the critical length of time for these divergences to occur varied with each material. For example, more than 12 years of data were needed before a reasonable prediction of the actuarial survival could be determined when using the mixture model for amalgams (Fig. 1) compared to less than 1 year for glass polyalkenoate (ionomer) cements (Fig. 3). This was because no failures occurred in the first 5 years of the study for the amalgams and less than 5 per cent of restorations had failed after more than 12 years of the study, as compared to 39 per cent of restorations failing after only 10 months for the glass polyalkenoate (ionomer) cements. It was found that the percentage of restorations that failed from the initial number entering the study was a reasonably good indicator of the accuracy of prediction. When each material type was analysed, at least 5 per cent of the restorations in any period needed to have failed investigated
Fig.4. Actuarial (with 2 x s.e. bars), and predictive survival curvesforthefulldataand the 1972-76 (3-4years)datafor fissure sealants. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (3-4 years).
before a G(t) estimate could be fitted to achieve an accurate prediction of the actuarial survival curve for the full data set. Those materials with a very high number of early failures required more than 6 or 7 per cent of restorations to fail before an estimate could be calculated. From Table III, the y coefficient is the estimate that indicates the effect of long-term survivals on the failure rates, and both the amalgam and glass polyalkenoate (ionomer) cement failure rates are affected by a group of long-term surviving restorations (Figs 1, 3). Restorative materials with y coefficients around zero, such as the anterior composites and fissure sealants, display a classic Weibull failure behaviour (Figs 2, 4). A high estimate of the a coefficient, as for the glass polyalkenoate (ionomer) cements, reflects early high failure rates, which were probably largely operator dependent in this instance (Fig. 3). The restorations of the patients in the present study could not be reviewed at regular intervals, and there were many patient dropouts or failures to attend for recall examinations, especially in the later years (Table II). Therefore, the predictive model used here for restoration survival needs to be tested on other populations, for various materials.
CONCLUSIONS For the four types of dental restorative materials assessed in this study it was concluded that: 1. Despite the differing long-term restoration behaviours found for the four groups of materials, the mixture model involving the standard Weibull distribution function could be fitted closely to the actuarial survival curves generated, and also allowed for the possibility of long-term survivals.
282
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1991; 19: No. 5
2. At least 5 per cent of restorations needed to have failed over any period before a G (t) estimate could be fitted to achieve an accurate prediction of the actuarial survival curve for the full data set. 3. The more successfully the material performed, then the longer was the observation time rquired before accurate survival predictions could be made. 4. Until more valid information is available on those clinical factors which can be used to accurately predict the longevity or survival of various dental restorative materials, then predictions of their survivals are probably best calculated from their early failure behaviour, using methods similar to these described in this report.
Acknowledgements We would like to thank the Administrator, Adelaide Dental Hospital, for permission to examine the patients involved in this study. References Akerboom H. B. M., Advokaat J. G. A. and Borgmeijer P. J. (1986) Long term evaluation of amalgam restorations. J. Dent. Res. 65, (special issue), abstr. 641, 797. Bayne S. C., Taylor D. F., Roberson T. M. et al. (1989) Long term clinical failures in posterior composites. J. Dent Res. 68, (special issue), abstr. 32, 185. Dixon W. J. (1990) 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. J. Prosthet Dent. 56,406-415. Hamilton J. C., Moffa J. P., Ellison J. A et al. (1983) Marginal fracture not a predictor of longevity for two dental amalgam alloys: a ten-year study. J. Prosfhet. Dent. 50, 200-202.
Hendriks F. H. J. and Letzel H. (1988) The durability of amalgam versus composite restorations. J. Dent. Res. 67, (CE Division), abstr. 54, 689. Lawless J. F. (1982) Statistical Models and Methods for Lifetime Data. New York, John Wiley, p. 437. Lemmens Ph. L. M., Peters M. C. R. B., van’t Hof M. A. et al. (1987) Influences on the bulk fracture incidence of amalgam restorations: a 7-year controlled clinical trial. Dent. Mater. 3, 90-93. Letzel H. (1989) Survival rates and reasons for failure of posterior composite restorations in multicentre clinical trial. J. Dent. 17, SlO-S17. Letzel H., van? Hoff M. A, Vrijhoef M. M. A. et al. (1989) A controlled clinical study of amalgam restorations: survival, failure and causes of failure. Dent. Mater. 5, 115-121. Mann N. R., Schafer R. E. and Singpurwalla N. D. (1974) Methods for Statistical Analysis of Reliability and Life Data. New York, John Wiley. Moffa J. P. (1989) The longevity and reasons for replacement of amalgam alloys. J. Dent. Res. 68, (special issue), abstr. 56, 188. Moffa J. P., Jenkins W. A. and Hamilton J. C. (1984) The longevity of composite resins for the restoration of posterior teeth. J. Dent. Res. 63, (special issue), abstr. 253, 199. Osborne J. W., Norman R. D., Chew C. et al. (1989a) Clinical evaluation 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 restorations. .I. Dent. Res. 68, (special issue), abstr. 57, 189. Roberson T. M., Bayne S. C., Taylor D. F. et al. (1988) 5-year clinical wear analysis of 19 posterior composites. J. Dent Res. 67, (Special issue), (abstr. 63), 120. Shintani H., Satou N. and Satou J. (1989) Clinical evaluation of two posterior composite resins retained with bonding agents. J. Prosthet. Dent 62, 627-632. Weibull W. (1951) A statistical distribution function of wide applicability. J. Appl. Mech. 18,293-297. Wierinck E., Lambrechts P., Braem M. et al. (1989) A five year clinical evaluation of four posterior composites. J. Dent. Res. 68, (CE Division), abstr. 97, 621.
278
19: 278-282
Survival predictions of four types of dental restorative materials R. J. Smales, D. A. Webster and P. I. Department of Dentistry and *Department
Leppard* of Statistics, The University of Adelaide, South Australia
ABSTRACT The present study assessed the survival predictions made for four different types of dental restorative materials, using a mixture model involving the standard Weibull distribution function. A large number of amalgam, anterior resin, glass polyalkenoate (ionomer) cement, and pit and fissure sealant restorations were examined over varying periods of up to 18 years. The materials had been placed by numerous staff and students at a teaching hospital. Based on maximum likelihood estimations of the parameters of the mixture model distribution, survival curves were generated and found to agree closely with the actuarial survival curves estimated from the same data. As the years of data used to fit the mixture model curves decreased, then the fitted curves started to exhibit obvious divergences from the actuarial curves at 12-13 years for amalgams, 3-4 years for anterior resins and sealants, and l-2 years for glass polyalkenoate (ionomer) cements. At least 5 per cent of restorations needed to have failed over any period to allow close agreement of the two curves, with the slower failing materials requiring longer observation periods.
KEY WORDS: Restorations, J. Dent. 1991; 1991)
19:
Survival predictions
278-282
(Received 23 August 1990;
Correspondence should be addressed Adelaide, South Australia 5001.
reviewed 18 December
Many attempts have been made to predict the longevity or survival of restorations of various dental restorative materials based on selected findings from short-term clinical studies. Most of these studies have either evaluated the marginal fracture rates of amalgam alloys or the occlusal wear rates of posterior composite resins. However, attempts to link short-term marginal fracture rates of low- and high-copper alloys with subsequent amalgam restoration longevity have generally been unsuccessful (Hamilton et al., 1983; Moffa, 1989; Osborne et al., 1989a, b), while the present authors are unaware of any publications which have shown significant associations between the short-term occlusal wear rates of different posterior composites and their subsequent longevity. In fact, in one recent study over 5 years and longer of posterior composites, all 19 materials appeared to decrease in their wear rates, and eventually approached the same overall total wear level (Roberson et al.. 1988). As predictions of restoration longevity from short-term studies based on the deterioration rates of selected clinical factors have given variable results, the ability to predict Ltd.
accepted 4 May
to: Dr R. J. Smales. Department of Dentistry, The University of Adelaide,
INTRODUCTION
@ 1991 Butterworth-Heinemann 0300-5712/91/050278-05
1990;
the median survival times of restorations from their earliest failure behaviour may be more relevant. Therefore, in the present study, the long-term survival behaviour of several amalgam, anterior composite, glass polyalkenoate (ionomer) cement, and pit and fissure restorative materials were first generated using an actuarial life-table method. Then, using the same data, a predictive mixture model involving a Weibull distribution function (Weibull, 1951; Mann et al., 1974) was assessed graphically against the actuarial results.
MATERIALS AND METHODS Data were accumulated on the survivals of numerous dental restorations from several clinical studies involving amalgams, anterior composites, glass polyalkenoate (ionomer) cements, and pit and fissure sealants. The restorations were placed by a variety of operators, both staff and students, in patients treated at the Adelaide Dental Hospital since 1966. The dental materials involved are shown in Table 1. There were 1801 amalgams, 1770 composites, 465 glass polyalkenoate (ionomer) cements,
Smales
Tab/e 1. Materials
evaluated
Material Amalgams New True Dentalloy Shofu Spherical Dispersalloy Tytin lndiloy Resins Adaptic Concise Nuva-Fil Silar Glass polyalkenoate Aspa Fuji II Ketac
Manufacturer
S.S. White Co., London,
restorations
279
Number
UK
Shofu Dental Co., Kyoto, Japan Johnson Et Johnson Co., East Windsor, NJ, USA S.S. White Co., Philadelphia, PA, USA Shofu Dental Co., Kyoto, Japan Johnson 8 Johnson Co., New Brunswick, NJ, USA 3M Co., St Paul, MN, USA L.D. Caulk Co., Milford, DE, USA 3M Co., St Paul, MN, USA (ionomer) cements AD International, London, UK GC Dental Co., Tokyo, Japan Espe GmbH, Seefeld, Germany
and 515 pit and fissure sealants which were assessed over varying periods for up to 18 years. 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 by damage from trauma. Only true failures were included in the present analyses, which included repairs and replacements from related caries, fractures and losses of material, and colour mismatches. Partly lost pit and fissure sealants were not treated as failures, as it was assumed that the remaining material still conferred some degree of caries prevention. Actuarial survival curves were generated for the four groups of materials (BMDP Statistical Software, Dixon, 1990; program 1L). Mixture model predictive survival distributions were then calculated using the same data from the total study periods, and then again on the data for decreasing yearly intervals. To allow for the possibility oflong-term survivals, the survival function defined as the mixture model had the form: (Survive > time t) = y + (I-y)
of dental
for lonoevitv
Pit and fissure sealants 3M Co., St Paul, MN, USA Enamel-Bond L.D. Caulk Co., Milford, DE, Nuva-Seal USA S.S. White Co., Philadelphia, S.S. White PA, USA Delton Johnson 8 Johnson Co., East Windsor, NJ, USA
G(t) = Probability
et al.: Survival
exp (- cd)
where 0 < y < 1 and a, p > 0. The unknown parameters f3and y were estimated from the data using the method maximum likelihood estimation (BMDP program AR). the standard Weibull distribution alone is adequate
a, of If to
Lathe-cut (low copper) Spherical (low copper) Admixed (high copper) Spherical (high copper) Spheroidal (high copper)
964
Conventional
321
Conventional Conventional (u.v.-light) Microfil
1115 189
225 178 112 322
145
Type II Type II Type II
142 192 131
Auto-cure U.v.-light
181 87
Auto-cure
70
Auto-cure
describe the data, then y = 0 and G(t) = exp (- ata) which is the standard Weibull survival curve. Graphical comparisons of the two sets of curves were then used for the assessments because ‘there is no satisfactory approach to empirical distribution function goodness of tit tests when data are arbitrarily censored’ (Lawless, 1982).
RESULTS An abbreviated
actuarial life-table analysis of cumulative survivals for the four groups of restorative materials is shown in Table II. The failure rates of the amalgam restorations were too low, even after periods of up to 18 years, to obtain the median survival time. The estimated coefficients and their standard deviations for the mixture model predictions, based on the full data set for each of the four groups of restorative materials, are shown in Table III. A high a coefficient was apparent for the glass polyalkenoate (ionomer) cements and high y coefficients for the amalgams and glass polyalkenoate (ionomer) cements. The actuarial and the fitted G(t) cumulative survival curves, based on the same total data from each of the four groups of materials, closely agreed as shown in Figs 1-4, where the fitted curves lie well within the bounds of the
J. Dent. 1991; 19: No. 5
280
Table II. Abbreviated life-table cumulative survivals of four groups of restorative materials Quartiles
Numbers entered After varying intervals (yr) At start
Material Amalgams Anterior composites Glass ionomer cements Fissure sealants
36 (16yr) 26 (15 yr) 20 (9 yr)
1801 1770 465
17 (7 yr)
515
75th
50th
25th
10.9 + 1.1* 3.4 f 0.2 0.8 + 0.1
7.9 + 0.5 2.2 + 0.2
16.2 t 0.4 6.2 + 1.6
2.4 + 0.2
4.4 Ik 0.1
7.8 + 0.7
*Cumulative survivals + standard errors (years).
Table 111.Estimated coefficients (and standard deviations) for the fitted predictive curves Material Amalgams Anterior resins Glass ionomer cements Fissure sealants
a
P
Y
0.032 0.084 0.486
(0.0 1) (0.006) (0.052)
1.406 1.005 0.764
(0.105) (0.034) (0.050)
0.607 (0.107) 0.000 (0.000) 0.12 1 (0.047)
0.098
(0.0 14)
1.443
(0.097)
0.08 1 (0.088)
actuarial estimates. As the years of data used for fitting G(f) were decreased, there were reasonably close agreements found to the actuarial survival curves (by using their standard error bars as a guide) until only 12-13 years of data were used for the predictions for amalgams, 3-4 years for anterior resins and fissure sealants, and l-2years for glass polyalkenoate (ionomer) cements. At these times, obvious divergences between the two sets of curves began to emerge as also shown in Figs 1-4, where the fitted curves no longer lie entirely within the actuarial bounds.
DISCUSSION Although marginal fracture has dominated the clinical assessment of amalgam restorations, bulk fracture has 1
emerged as the main cause of the low failure rates found in several recent controlled trials (Akerboom et al., 1986; Doglia et al., 1986; Lemmens et al., 1987; Letzel et al., 1989); and again, although occlusal wear had dominated the assessment of posterior composites, recurrent caries and bulk fracture were the main causes of failure found in other controlled trials (Moffa et al., 1984; Hendriks and Letzel, 1988; Bayne et al., 1989; Letzel, 1989; Shintani etal.. 1989; Wierinck et al.. 1989). The authors of the present study are unaware of any publications which have reported significant associations between these failure modes and predictions of the long-term survivals of the amalgam and posterior composite restorations involved. The differing long-term restoration survival behaviours reported for the four different groups of materials 1
0.8
0.8
0.2
0 0
1 2
3
4
5
6
7
8
9 101112
1314
15 1617
18
Age of restorations (yr)
0 1
2
3
4
5
6
7
8
9 IO 11 12 13 14 15 16 17
Age of restorations (vr)
Fig. 7. Actuarial (with 2 X s.e. bars), and predictive survival curves for the full data and the 1966-79 (12- 13 years) data
fig.2. Actuarial (with 2 X s.e. bars), and predictive survival curves for the full data and the 1969-73 (3-4 years) data for
for amalgams. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (12-l 3 years).
anterior resins.-, Actuarial survival; - - -, mixture model (all data); -, mixture model (3-4 years).
Smales et al.: Survival
0
1
234567
of dental restorations
8
9
281
10
11
12
Age of restorations(yr) 0
1
2
3
4
5
6
7
8
9
10
II
1213
Age of restorations(yr) fig.3. Actuarial (with 2 X s.e. bars), and predictive survival curvesforthefulldataand the 1976-78 (I-2years)datafor glass ionomer cements. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (l-2 years).
in the present study allowed the rigorous testing of a predictive survival model of wide applicability. Because attempts at predicting long-term restoration survivals based on the deterioration rates of selected clinical factors have generally been unsuccessful (Hamilton et al., 1983; Moffa, 1989; Osborne et al., 1989a, b), survival rates based on actual early failure behaviour would appear to be more pertinent. Despite the markedly different survival behaviour shown by the four groups of materials, the fitted G(t) predictions based on the total data were in close graphical agreement with the actuarial survivals for all materials (Figs 1-4). In each instance, the two survival curves only diverged when there were insufficient failure data available for the adequate estimation of the parameters of G(t). As our data sets became increasingly smaller, the critical length of time for these divergences to occur varied with each material. For example, more than 12 years of data were needed before a reasonable prediction of the actuarial survival could be determined when using the mixture model for amalgams (Fig. 1) compared to less than 1 year for glass polyalkenoate (ionomer) cements (Fig. 3). This was because no failures occurred in the first 5 years of the study for the amalgams and less than 5 per cent of restorations had failed after more than 12 years of the study, as compared to 39 per cent of restorations failing after only 10 months for the glass polyalkenoate (ionomer) cements. It was found that the percentage of restorations that failed from the initial number entering the study was a reasonably good indicator of the accuracy of prediction. When each material type was analysed, at least 5 per cent of the restorations in any period needed to have failed investigated
Fig.4. Actuarial (with 2 x s.e. bars), and predictive survival curvesforthefulldataand the 1972-76 (3-4years)datafor fissure sealants. I, Actuarial survival; - - -, mixture model (all data); -, mixture model (3-4 years).
before a G(t) estimate could be fitted to achieve an accurate prediction of the actuarial survival curve for the full data set. Those materials with a very high number of early failures required more than 6 or 7 per cent of restorations to fail before an estimate could be calculated. From Table III, the y coefficient is the estimate that indicates the effect of long-term survivals on the failure rates, and both the amalgam and glass polyalkenoate (ionomer) cement failure rates are affected by a group of long-term surviving restorations (Figs 1, 3). Restorative materials with y coefficients around zero, such as the anterior composites and fissure sealants, display a classic Weibull failure behaviour (Figs 2, 4). A high estimate of the a coefficient, as for the glass polyalkenoate (ionomer) cements, reflects early high failure rates, which were probably largely operator dependent in this instance (Fig. 3). The restorations of the patients in the present study could not be reviewed at regular intervals, and there were many patient dropouts or failures to attend for recall examinations, especially in the later years (Table II). Therefore, the predictive model used here for restoration survival needs to be tested on other populations, for various materials.
CONCLUSIONS For the four types of dental restorative materials assessed in this study it was concluded that: 1. Despite the differing long-term restoration behaviours found for the four groups of materials, the mixture model involving the standard Weibull distribution function could be fitted closely to the actuarial survival curves generated, and also allowed for the possibility of long-term survivals.
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2. At least 5 per cent of restorations needed to have failed over any period before a G (t) estimate could be fitted to achieve an accurate prediction of the actuarial survival curve for the full data set. 3. The more successfully the material performed, then the longer was the observation time rquired before accurate survival predictions could be made. 4. Until more valid information is available on those clinical factors which can be used to accurately predict the longevity or survival of various dental restorative materials, then predictions of their survivals are probably best calculated from their early failure behaviour, using methods similar to these described in this report.
Acknowledgements We would like to thank the Administrator, Adelaide Dental Hospital, for permission to examine the patients involved in this study. References Akerboom H. B. M., Advokaat J. G. A. and Borgmeijer P. J. (1986) Long term evaluation of amalgam restorations. J. Dent. Res. 65, (special issue), abstr. 641, 797. Bayne S. C., Taylor D. F., Roberson T. M. et al. (1989) Long term clinical failures in posterior composites. J. Dent Res. 68, (special issue), abstr. 32, 185. Dixon W. J. (1990) 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. J. Prosthet Dent. 56,406-415. Hamilton J. C., Moffa J. P., Ellison J. A et al. (1983) Marginal fracture not a predictor of longevity for two dental amalgam alloys: a ten-year study. J. Prosfhet. Dent. 50, 200-202.
Hendriks F. H. J. and Letzel H. (1988) The durability of amalgam versus composite restorations. J. Dent. Res. 67, (CE Division), abstr. 54, 689. Lawless J. F. (1982) Statistical Models and Methods for Lifetime Data. New York, John Wiley, p. 437. Lemmens Ph. L. M., Peters M. C. R. B., van’t Hof M. A. et al. (1987) Influences on the bulk fracture incidence of amalgam restorations: a 7-year controlled clinical trial. Dent. Mater. 3, 90-93. Letzel H. (1989) Survival rates and reasons for failure of posterior composite restorations in multicentre clinical trial. J. Dent. 17, SlO-S17. Letzel H., van? Hoff M. A, Vrijhoef M. M. A. et al. (1989) A controlled clinical study of amalgam restorations: survival, failure and causes of failure. Dent. Mater. 5, 115-121. Mann N. R., Schafer R. E. and Singpurwalla N. D. (1974) Methods for Statistical Analysis of Reliability and Life Data. New York, John Wiley. Moffa J. P. (1989) The longevity and reasons for replacement of amalgam alloys. J. Dent. Res. 68, (special issue), abstr. 56, 188. Moffa J. P., Jenkins W. A. and Hamilton J. C. (1984) The longevity of composite resins for the restoration of posterior teeth. J. Dent. Res. 63, (special issue), abstr. 253, 199. Osborne J. W., Norman R. D., Chew C. et al. (1989a) Clinical evaluation 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 restorations. .I. Dent. Res. 68, (special issue), abstr. 57, 189. Roberson T. M., Bayne S. C., Taylor D. F. et al. (1988) 5-year clinical wear analysis of 19 posterior composites. J. Dent Res. 67, (Special issue), (abstr. 63), 120. Shintani H., Satou N. and Satou J. (1989) Clinical evaluation of two posterior composite resins retained with bonding agents. J. Prosthet. Dent 62, 627-632. Weibull W. (1951) A statistical distribution function of wide applicability. J. Appl. Mech. 18,293-297. Wierinck E., Lambrechts P., Braem M. et al. (1989) A five year clinical evaluation of four posterior composites. J. Dent. Res. 68, (CE Division), abstr. 97, 621.
