272

Survival predictions restorations R. J. Smales, D. A. Webster Department

of Dentistry

19: 272-277

of amalgam

and P. I. Leppard*

and *Department

of Statistics,

The University

of Adelaide,

South Australia

ABSTRACT The purpose of this study was to evaluate survival predictions made for four different amalgam alloy restorations, using a mixture model involving the standard Weibull function. The amalgam alloys were placed by students and staff in patients attending a dental hospital, and 1680 restorations were examined over periods of up to 18 years. Based on maximum likelihood estimations of the parameters of the mixture model distribution, predictive survival distributions were generated and found to match closely the actuarial survival estimates established from the same data. The 13-year restoration survivals of one low-copper alloy could be predicted accurately from the 6-year survival results. However, another low-copper alloy and two high-copper alloys with much lower restoration faillure rates required 18 years of data for accurate long-term survival predictions. KEY WORDS: J. Dent. 1991; 1991)

Restorations,

Amalgam,

19: 272-277

Survival

(Received

Correspondence should be addressed Adelaide, South Australia 5001.

predictions

16 November

1990:

reviewed

to: Dr R. J. Smales, Department

23 January

of Dentistry,

1991;

accepted

The University

4 May

of Adelaide,

INTRODUCTION

MATERIALS AND METHODS

With exceptions (Osborne et al., 1980; Letzel et al., 1989; Osborne and Norman, 1990), attempts to link short-term marginal fracture rates of low- and high-copper amalgam alloy restorations with their subsequent longevity or survival have been unsuccessful (Hamilton et al., 1983; Moffa, 1989; Osborne er al., 1989). Therefore, it may be pertinent and informative to be able to predict the longterm survivals of different amalgam alloy restorations from their earlier failure behaviour, and one previous study of a large group of amalgam restorations found that the 6-year survival data could be used as the base from which to accurately predict restoration survivals over 16-17 years (Smales et al., 1991). Therefore, in the present study, long-term actuarial survival estimates of amalgam restorations made from four different alloys were first generated. Then, using the same data from the total study periods, and of shorter periods, predictive survival distributions were calculated and compared for matching with the actuarial estimates.

Survival data were accumulated over varying periods of up to 18 years on 1680 amalgam restorations placed by students and staff in a large number of patients treated at the Adelaide Dental Hospital from 1967 to 1989. The four amalgam alloys involved are shown in Table I. First, actuarial cumulative survival estimates were generated for the four alloys (BMDP Statistical Software, Dixon, 1990; program 1L). Then, mixture model predictive survival distributions, involving a Weibull function (Weibull, 1951; Mann et al., 1974) were calculated using the same survival data from the total study periods, and again on the data for decreasing yearly intervals. To allow for the possibility of long-term survivors, the survival function defined as the mixture model had the form:

e 1991 Butterworth-Heinemann 0300-5712/91/050272-06

Ltd

G (t) = Probability (Survive > time t) = y + (1 - y) exp (- a tb) where 0 4 y 4 1 and a, p > 0. The unknown parameters a, p and y were estimated from the data using the method of maximum likelihood estimation (BMDP program AR). If

Smales et al.: Survival

of amalgam

restorations

273

Table 1. Materials evaluated Material

Manufacturer

Composition

Insertion

New True Dentalloy (NTD)

S.S. White Co., London, UK

Fine lathe cut 2%Cu, l%Zn

1967-80

Shofu Spherical

Shofu Dental Co., Kyoto, Japan

Spherical 3% Cu, Zn-free

1973-78

Dispersalloy

Johnson Et Johnson Co., East Windsor, NJ, USA

Blended 12%Cu,

1975-87

Shofu Dental Co., Kyoto, Japan

Spheroidal 13% Cu, 4% In, Zn-free

lndiloy

the Weibull distribution is adequate to describe the data, then y = 0 and G (t) = exp (- ate) which is the standard Weibull survival curve. The actuarial and the predictive survival curves were compared visually, for closeness of matching.

RESULTS The numbers of restorations entered or available at each yearly interval, and the corresponding failures, are shown in Table II. There were 143 true failures which included restoration repairs and replacements related to caries, fractures and losses of material. There were also 31 apparent failures, which involved sound restorations in unrelated tooth extractions, endodontic treatments, incorporation into other restorations, or in damage from acute trauma, and which were not included in the present survival analysis.

l%Zn 1977-80

Actuarial cumulative survival estimates of the restorations from the four amalgam alloys are also shown in Table II, and illustrated in Fig. 1. The significant differences reported between restorations made from the four alloys were caused by the much lower survivals shown by Shofu Spherical (P < 0.0001). Because there were no significant differences in the cumulative restoration survivals of New True Dentalloy (NTD), Dispersalloy and Indiloy, these three alloys were grouped and designated as the low fail amalgams. True failures accounted for 15.9 per cent of the total Shofu Spherical restorations placed, and 7.4 per cent of the low fail amalgam restorations. The G(t) mixture model predictive cumulative survival curves for each alloy, based on the same data as for the actuarial estimates, are illustrated in Fig. 2. Visually, both sets of curves matched closely. Based on the information obtained until 1989, the actuarial and the fitted G(t) predictive cumulative

1

1

0.8

0.8

5 '2 0.6 31 J .ti 5 E 0.4 0'

0.2

0 0

1 2

3 4

5 6

7 8

9 10 1112 13 14 1516 17 18

Age of restorations(yr) Fig. 7. Actuarial cumulative survival curves for the four amalgam alloys.+-, New True Dentalloy; -, Indiloy;Q, Dispersalloy;-x- , Shofu Spherical.

0

0

1 2

3 4

5 6

7

8 9 10 11 121314

15 16 17 18

Age of restorations(yr) Fig. 2. Predictive mixture model cumulative survival curves for each alloy.-*-, New True Dentalloy: -, Indiloy; +, Dispersalloy; -x-, Shofu Spherical.

248 185 161 135 121 104 82 68 57 36 13

7-8 8-9 9-10 IO-I 1 11-12 12-13 13-14 14-15 15-16 16-17 17-18

0

0 1 1 :,

12 3 2 :

3 5

7 10 11 ::

NTD Failed

survival

C_1.9 +_ 2.1 I!I 2.2 zk 2.5 + 2.5 + 2.5 + 2.7 + 2.9 + 3.3 * 3.3 + 3.3

I?z0.3 + 0.5 + 0.7 + 1.0 + 1.3 + 1.4 +_ 1.5 10 6 5 2 1 1

220 190 163 124 76 20 24

Entered

alloys

0

:, :,

;

4 4 4 8 7 2

k 1.0 + 1.4 + 1.9 * 3.0 _+ 4.8 AI 6.2 + 7.2

44 + 10.0 36+ 11.2 36 + 11.2 18 + 14.0 18 k 14.0 18 _+ 14.0

98 96 93 86 75 64 68

Shofu Spherical Failed CS + se. %

of the four amalgam

survivals + standard error percentages 0.0001 (for all four alloys). 0.8339 (for NTD, Dispersalloy, Indiloy). 0.0001 (for Shofu Spherical vs other alloys).

84 82 81 78 78 78 77 76 74 74 74

99 98 96 94 91 88 89

*CS + s.e. 96

of cumulative

*CS + s.e. %, restoration cumulative Mantel-Cox = 35.845, d.f. = 3, P < Mantel-Cox = 0.363, d.f. = 2, P = Mantel-Cox = 30.529, d.f. = 1, P