ABSTRACT
Purpose: The aim of the work was to evaluate what kind of prosthetic restoration could be more convenient for replacing a single loss tooth.

Materials and Methods: We have performed a cost-efficacy analysis (CEA) to compare the various types of prosthetic restorations for the loss of a single tooth. CEA is based on a quantitative parameter given by the ratio between the years of prognosis of a prosthesis and its total costs. Therefore, this analysis takes into account both the clinical outcome and the financial burden to the patient.

Results: We have compared literature data for the success rates over time for the following therapeutic options: small bridge prosthesis, cantilever bridges, single-tooth implant, temporary resin- partial-dentures, and adhesive bridges. By adding cost considerations, our CEA study has quantified the differences, in cost-efficacy terms, among these therapeutic options. Our analysis indicates that an adhesive prosthesis can be advantageous, provided that the life-time of the rehabilitation of the patient is at least 6-7 years.

Conclusion: The preference of the authors goes to the single tooth implant because of the limited psychological impact on the patient and the minor biological cost of this solution.

INTRODUCTION
In dentistry it is possible to restore the physiological and functional viability in the oral cavity by multiple solutions that have unique biological, functional and esthetic features. A major role is played by cost factors, which often determine the patient's choiche of therapy.
There are three approaches to measure the clinical outcome relative to the costs ⁽¹⁾: cost-efficacy analysis (CEA), cost-benefit analysis (CBA), and cost-utility analysis (CUA). The scope of this work is to compare the CEA's for different therapeutic solutions to the replacement of a single tooth.

MATERIALS AND METHODS
To develop a cost analysis for various therapeutic options we will introduce economic parameters that depend directly on the total (initial and maintenance) costs and the prognosis of the various prosthesis options found in the medical literature.
The cost-efficacy analysis (CEA) consists of evaluating the total direct and indirect costs of alternative treatments that yield a common result, thus indicating the least expensive prosthesis for a given end result. For example: in dentistry one can compare the cost of a total vs. Toronto-Branemark prosthesis to address a situation of complete edentulism.
The patient's costs for a therapeutic prosthesis consist of initial costs, direct and indirect, and costs associated with the maintenance and occasional repair that can accumulate during the life of a prosthesis.
These latter costs are protracted over a long period of time and must take into account adjustments based on the inflation rate ⁽¹⁾.
Creugers ⁽²⁾ defines a cost-efficacy analysis (CEA) parameter that is directly proportional to benefits and inversely proportional to the costs. The benefits include esthetics, function, comfort and durability (the prognosis of a prosthesis of that type).

Creugers ⁽²⁾ simplifies the cost efficacy parameter to a fraction, where the numerator is given by the number of years of prognosis and the denominator is the total cost. Under this model, the durability can be represented graphically by a straight line for the years of prognosis versus the costs.
The ratio between these two factors, durability and costs, is given by the slope of this straight line, i.e. the tangent of the angle alpha indicated in Figure 1, and provides a quantitative measure of the relationship between efficacy and costs.

By reviewing the literature, one can evaluate the prognosis during the years of the various therapeutic options to address the loss of a tooth.
The duration in years of a therapeutic surgical process combined with the costs over time allows us to perform a cost analysis that identifies the prosthesis that realizes the best compromise between low cost and high efficacy.

The paradigmatic clinical solutions to address the loss of a single tooth considered in this work are:

1. Small bridge prosthesis of three elements (on natural teeth).
   

2. Extended prosthesis with one element (cantilever bridges on natural teeth).
   

3. Single-tooth implant.
   

4. Adhesive bridges.
   

5. Temporary, removable resin partial dentures for replacement of the missing element.
   

RESULTS
1) Small bridges
Studies relative to the prognosis over time of fixed prostheses have demostrated that all results are in agreement.
What emerges from the literature is that the initial failures of crowns and small bridges are very rare (about 1% per year) with the risk increasing with the passing of time ⁽³⁾. However, there is no direct linear proportionality between the post-treatment time and the failure (Figure 2).

Creugers ⁽⁴⁾ calculated the survival percentage of the fixed prostheses to be 74% after 15 years, while in the meta-analysis of Scurria ⁽⁵⁾ the survival rate was 92% after 10 years and 75% after 15 years.
According to Napankangas ⁽⁶⁾ the survival of fixed bridges is 84% at ten years even though small restorations (3 elements) give better results over the years than the long framework.
The survival percentage seems to diminish drastically after 10 years of prosthesis life ⁽⁷⁾ and this could be technically explained by progressive deterioration of the materials used, typically metallic alloys, porcelain and cement ⁽⁴⁾. Biological issues such as secondary caries on the margin of the prosthetic abutment could also explain the drastic drop in the survival rate after 10 years ⁽⁵⁾. In fact the secondary caries are considered the main cause of the failure in a fixed prostheses: 18-31% of the cases according to Randow ⁽⁸⁾, 22÷24% ⁽⁹⁾, 38% ⁽¹⁰⁾. The lost of retention of the prosthetic device seems to be the result of the deterioration of the abutment caused by the caries ⁽⁷⁾. Other reasons for failure are periodontitis (5%), root fractures (5%), endodontical complications (10-15%) and technical problems like the fracturing of the bridge (1%) and the fracturing of the porcelain (10-15%) ^{(3) (7) (8)}.
There are significant differences between the various types of crowns and bridges: the main survival rates refer to fused restorations and those in metal-ceramics ^(3) (11); amongst the latter, the average longevity of the devices in porcelain and base alloys is exactly half that of bridges in noble alloys and ceramics ⁽¹²⁾. With regard to partial crowns, the expectations are reduced, especially if used as abutments. The worst case regards crowns in integral ceramics ⁽³⁾ used as the bridge abutment, contrary to what happens when this type of crown is used to cover single dental elements ⁽¹³⁾.
The results of the various studies cited above fail to completely clarify whether the length of the framework affects or not the success of fixed bridges over the years. Reuter ⁽¹⁴⁾ concludes that five or more elements fail more frequently than small bridge prostheses, while in the studies of Foster ⁽¹²⁾ and Leempoel ⁽¹⁵⁾ the length of the prostheses does not seem to affect the survival rates in fixed dentures. Napankangas ⁽⁶⁾ states that long bridges have lower survival rates than those with only three elements, the Author concluding that the patient's age does not seem to play a role in the failure rates. This is also the conclusion of Foster ⁽¹²⁾ and Karlsson ⁽⁷⁾ while in the study of Torbjorner ⁽¹⁶⁾ the complications and failure rate were higher among the elderly with teeth reconstructed with posts and cores. Landolt ⁽¹⁷⁾ established that the presence of non-vital teeth accounts for an increased number of failures. The risk seemed to grow when the cast dowel cores were used in the more distal abutment teeth ⁽⁸⁾ especially in the molar site ⁽⁶⁾. According to Raustia ⁽¹⁸⁾ the root fracture is the greatest cause of bridge and crown failure.

2) Cantilever bridges
It is preferable to replace a dental element with a fixed prosthesis rather than a removable one ⁽¹⁹⁾. The fixed cantilever prosthesis is a restoration that has one or more abutments on one side while the other is not supported; therefore a system of first degree levers is created ⁽²⁰⁾.
Whenever the "cantilever bridge" is subjected to occlusal forces, these are discharged onto the abutment teeth. These are fixed bridges, the survival percentage of which is lower than with the conventional methods even when the number of overhanging elements is limited. In a five-year-follow-up Budtz-Jorgensen ⁽²¹⁾ obtained an 80% survival rate for these prostheses arising from the loss of retention or fracture of the abutments. This high percentage of failures is comparable with that observed by Randow ⁽⁸⁾, who found technical problems in 16.1% of patients treated with cantilevers with an extension element, and in 33.7% of patients with cantilevers with two elements in extension after 6-7 years. The primary complications for this type of prosthesis are mainly biological: marginal carious lesions, with fractures in the anchoring cement, loss of vitality of the abutment teeth, and above all root fractures of the prosthetic abutments when devitalized ⁽²²⁾. In particular, the replacement of the canine, both maxillary and mandibular, with a cantilever bridge is advised against ⁽²³⁾.

3) Single-tooth implant
One of the alternatives to the conventional fixed or cantilever prosthesis is represented by implantology.
An implant for replacement of a missing tooth in partial edentulism has one of the best prognosis in the state-of-the-art implantology. Jemt ⁽²⁴⁾ was the first author to introduce the single-tooth concept in the literature in 1986. This type of prosthesis had 96% success after one year and 90% after three years. In following studies ⁽²⁵⁾, the success rate improved, reaching 100% after five years in the mandible and 96.6% after five years in the upper maxillary, with a general average between the two arches of 97.2% with all failures referring to the first year. The loss of marginal bone during the 5-year period did not exceed 1 mm. For all the implants carried out, the most frequent complication recorded during the follow-up period was the loosening of the abutment screw. However, according to the authors this problem can be addressed in the future with the use of new and safer screws in gold instead of titanium abutment screws. Palmer ⁽²⁶⁾ found 100% success after 2-year follow-up for single-tooth implants using Astra implants to replace front maxillary dental elements. No cases of complications are reported in Palmer's study like the unscrewing of the abutment screws, and the loss of marginal bone after two years was negligible. The percentage of implant successes remains just as high in the restoration of posterior areas. Zarb ⁽²⁷⁾ found a success rate of 97.6% in the upper maxillary and 94.3% in the mandible after 7.4 years with an average of 94.3% for the posterior areas. In a 16-year longitudinal study on 1,964 applied implants, Noack ⁽²⁸⁾ found that the best success rates were associated with single-tooth implants after having used IMZ, Frialit-2 and Branemark. The success of implant therapy in partial edentulism also concerns more complex methods compared to the post-extractive one. The advantages of this procedure are the preservation of the alveolar crest and a saving in time. Some studies report a 93% success rate using this technique. The long-term results are the same with respect to the implants applied in osseous areas already healed after extraction ⁽²⁹⁾.
According to the literature, the prosthetic procedure for connecting implants and natural teeth in order to build small bridges also seems to produce good results. In a 5-year follow-up ⁽³⁰⁾, Kindberg noted that the implant survival rate was 90% and he concluded that treatment with periodontally healthy teeth and rigidly connected implants gives excellent results over time, even for posterior restorations ⁽³¹⁾. The intrusion of the natural tooth only takes place if the connections are not rigid between the implants and natural teeth ^(32) (33).

4) Adhesive bridges
The introduction of enamel etching and resin bonding by Buonocore ⁽³⁴⁾ in 1955 started the era of adhesive dentistry. In 1973 Rochette ⁽³⁵⁾ introduced the idea of bonding a fused metal bar to the lingual surfaces of the front teeth and splinting it using enamel etching and a resinous cement. This bar was perforated.
Since then, a number of substantial modifications to the original concept have improved the prognosis of these restorations, and adhesive prosthesis is now considered a valid alternative to the conventional fixed prosthesis. The original design of the bonded prostheses suggested by Howe and Denehy was indicated for the replacement of the anterior single tooth with a minimum preparation of abutment teeth ⁽³⁶⁾. Subsequently, Livaditis ^(37) (38) suggested a modification to the project of these restorations including the preparation of guide planes via the reduction of the lingual and proximal surfaces and occlusal rests. He also suggested electrolyte etching of the base alloy in order to create a rough surface. In a clinical study, Rochette's bridge turned out to have a 28% success rate after 7.5 years, while the electrolytically etched bonded bridge had an amazing success rate of 64% ⁽²⁾. Subsequently, other types of chemical etching with aluminium oxide powder were suggested ⁽³⁹⁾. In order to improve the prognosis of bonded bridges, it has also been suggested to make mesial and distal grooves in the surfaces of the abutment teeth ⁽⁴⁰⁾. These bonded teeth are reported to have a survival rate of 70% at three years ⁽⁴¹⁾. Nevertheless, the use of adhesive bridges should be limited to the replacement of single teeth ⁽⁴²⁾. Front restoration has a better prognosis than rear restoration ⁽²⁾. Among the latter, mandibular restorations are those associated with a more negative prognosis due to the greater height of the maxillary teeth with respect to the mandibular ones, which results in a greater area available for adhesive cementing.
The use of bonded bridges instead of conventional fixed dentures is preferable in some cases for the preservation of a healthy dental tissue, as well as the lower treatment and laboratory costs the patient has to bear.

5) Temporary removable resin partial dentures
As far as removable dentures are concerned, it has been demonstrated by Kerschbaum's studies ⁽³⁾ that only 50% of these restorations are clinically acceptable 10 years after insertion. These rules are valid for cast clasp retained dentures and precision attachment retained dentures. As far as simple acrylic resin partial dentures retained by wire clasps are concerned, these are to be considered as long-term temporary prosthesis; their prognosis is approximately three years and they are capable of causing considerable complications (in the event of being used for too long) like ecological changes to the oral cavity, mechanical trauma of the teeth, oral mucosa and hard tissues, and stress from occlusal trauma on the abutment teeth.

DISCUSSION
The latest results indicate that the small conventional fixed prosthesis has a survival rate of almost 85-90% at ten years, decreasing drastically after ten years because of progressive deterioration of the material used.
The cost to the patient of a conventional three element bridge is about 2400 euro; therefore, the cost-efficacy ratio(CEA) for this prosthesis is about 0.0041 (10 years divided by 2400 euro).
For a cantilever bridge with an extension element, the survival rates at ten years are drastically inferior (about 60%) because of biological complications. The cost to the patient for this prosthesis is equal to that for a conventional fixed bridge (about 2400 euro for a three element bridge). The CEA ratio is about 0.0029.
The replacement of a dental element with a single tooth implant has one of the best prognosis in dentistry at the present time. According to the latest literature, the percentage of success at 10 years is about 90% and the cost of this therapeutic option is similar to that of a three-element bridge (CEA ratio for a single tooth: 0.0041).
The cost of an adhesive bridge of three elements, according to the literature, is 1/3 of the cost of a traditional bridge (800 euro) whereas the prognosis is, at 10 years, much inferior than the other options examined (Figura 3).

The removable prosthesis has a much lower cost then a conventional bridge but also a much inferior prognosis (about 3 years).
CEA cost analysis: the most frequent causes of partial edentulism are the following: dental agenesia (33%), traumatism (20%), endodontical complications (15%), endodontical complications correlated with traumatism (9%), periodontal disease (4%), caries (13%), orthodontic reasons (2%) and dental inclusion (2%). All of these situations can be overcome with removable partial dentures which do, however, involve several problems related to the patient's tolerance, as well as other problems outlined previously ⁽⁴³⁾.
The fixed cantilever prosthesis offers considerable advantages from an esthetic and functional point of view (it is cemented and therefore fixed). However, the negative prognosis over the years (80% survival rate at five years) determines an unfavorable CEA ratio (0.0029) compared to other therapeutic solutions. If we compare the CEA ratio of the single-tooth implant (0.0041) with the CEA ratio of the conventional three-element bridge (0.0041) we have similar survival rates after ten years, with comparable initial and maintenance costs (the unscrewing and replacement of the implant abutment screws is a phenomenon that has been diminishing over recent years) ⁽²⁶⁾. The survival rates of conventional bridges after ten years drops drastically for the above-mentioned biological reasons. Therefore, by considering the benefits of single-tooth implants, namely the saving of dental substance (lower biological costs) and the limited psychological impact on the patient, this latter type of solution is more favorable in cost-efficacy terms.

Finally, an interesting comparison can be made among the conventional prosthesis, the single-tooth implant, and the adhesive prosthesis. Considering the manifacturing costs, which for the adhesive prosthesis are about one third compared to those for a three-element bridge and a single-tooth implant, it can be stated that the balancing point in the CEA ratio for the three types of restoration is obtained when 50% of survival (durability) of the adhesive prostheses is approximately 6 and a half years ⁽²⁾. Clinical data indicates a better CEA ratio for anterior adhesive prosthesis as they have better prospects than posterior ones.

IN CONCLUSION
1) The analytical structure developed in this article offers a quantitative base to evaluate the advantages for the patient using the various therapeutic procedures in the replacement of a single tooth.

2) The initial costs for a conventional bridge and for the implantology are similar. For equal prognosis and of cost-efficacy ratio (0.0041), the preference of the authors goes to the single tooth implant for the limited psychological impact on the patient and the minor biological cost of this solution.

3) Because the adhesive prosthesis has a relatively low cost of manifacturing (1/3 of a conventional one) the authors consider this procedure to be efficient, provided that the life-time of the prosthesis of the patient is at least 6-7 years.

4) The removable partial prosthesis is not considered a suitable therapeutic procedure for the patient as it gives scarce prognosis and may produce tolerance-related problems.

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