2.1

Setting, perspective, population, horizon

This study adopted a mixed public-private-payer perspective in the context of the German healthcare setting. We modelled a population of 1000 60-year old females with one permanent molar with a vital non-painful pulp and a three-surfaced composite or amalgam restoration in need of repair or replacement. The tooth was followed over the patient’s lifetime. The resulting time horizon was 26 years. To avoid clustering effects and simplify modelling and interpretation of findings, only one restoration per mouth was simulated. Restoration surface numbers and the time horizon were varied in sensitivity analyses (see below).

2.2

Comparators

We compared restoration repair versus complete replacement:

• •

  Restoration repair was defined as mending a number of possible complications like tooth (cusp) or restoration fracture, partial restoration loss, secondary caries, or aesthetic reasons. Such mending was performed by partially replacing the original restoration with adhesively placed composite resin and assumed to involve only one surface. Note that we did not assume repair to be provided according to any specific standard. Also note that performing any further conditioning procedures, like application of silane or silica coating, might increase costs of repair, but could also affect effectiveness .

• •

  Complete replacement of the partially defective amalgam and composite restorations was defined as completely removing and replacing the failed restoration either with amalgam or adhesively placed resin composite (depending on the initial, failed restoration) and increasing the restoration surface by +1.

2.3

Model and assumptions

A Markov model was used for this study (TreeAge Pro 2013, TreeAge Software, Williamstown, MA, USA).

Complications of both repaired and replaced restorations were assumed to lead to

• •

  Restorative re-treatments like re-replacement or re-repair (possible reasons might be fracture, including partial loss of restoration and tooth fracture with or without retention loss, secondary caries, or primary caries).

• •

  Repaired restorations could not be repaired again, but needed complete restoration replacement.

• •

  Complete restoration replacement was assumed to generate an additional restoration surface and increased the risk of restorative failure and re-treatment by 1.4 .

• •

  We assumed a direct (composite, amalgam) restoration to have a maximum of five surfaces, therefore limiting the number of re-replacements.

• •

  A full-metal crown was placed if replacements were not possible any longer.

• •

  Endodontic treatment, i.e. root-canal treatment (assuming the treatment of a vital pulp including instrumentation and obturation), followed by placement of a crown (as could be expected after endodontic treatment in extensively restored teeth).

• •

  Extraction for non-mendable complications.

The proportions of the different re-treatments were derived from a large, practice-based study, which had followed repaired and replaced restorations placed by the same operator in the same population of patients (Appendix Table S1):

• •

  In follow-up health states, teeth were again assumed to experience restorative complications (e.g. crown de-cementation, fracture or secondary caries, leading to re-cementation or renewal of crowns, or extractions) or endodontic complications (leading to non-surgical primary or secondary root-canal treatment or surgical re-treatment, i.e. apisectomy, or extraction).

• •

  We assumed 50% of extracted teeth to be replaced using implant-supported single crowns. Implants were assumed to experience restorative complications (requiring re-cementation or renewal of crowns) as well as biologic (e.g. peri-implantitis, possibly with subsequent implant loss) or technical complications (like abutment or implant fracture).

The constructed model is shown in a simplified form in Fig. 1 . Model validation was performed internally by varying key parameters to check their impact on the results, by evaluating different model structures, and by performing the following univariate sensitivity analyses:

• •

  Repairs were assumed to be possible twice, not only once.

• •

  Complete replacement did not add an additional surface to the restoration, but was only possible twice before crown placement was required.

• •

  Between 0% and 100% of removed teeth were replaced using implant-supported crowns.

• •

  The original restoration was assumed to involve four surfaces.

• •

  The patient was assumed to be 40 years old at baseline, which increases the horizon of the simulation.

Transition diagram.

¹ Re-Repair was only possible in a sensitivity analysis. ² Number of repeated replacements was varied in sensitivity analysis. ³ Crown was only placed after root-canal treatment in case no crown was present.

2.4

Health outcome measure

The health outcome measure was tooth retention years, i.e. the mean time a tooth was retained in a patients’ mouth. This was determined by the tooth experiencing complications, the risk of which is modelled via transition probabilities, which allow teeth to move from one health state to another (i.e. risks of complications and associated re-treatments).

Transition probabilities for repaired versus new/replaced restorations were estimated based on a rapid systematic review of the literature (see Appendix).

Based on the included five studies (8 publications) , we estimated the risk of complications in repaired relative to those in new/replaced composite or amalgam restorations. While some studies were controlled , i.e. had randomly assigned restorations to repair or replacement, some were cohort studies . For these, we took care to only compare risk of complications in repaired versus new/replaced restorations if they were performed on similar patients (age range, source population) under similar conditions (setting, operators). Note that in this case, indication bias is nevertheless likely, as placement of amalgam might be more frequent in certain (demographic, socio-economic) populations than placement of composite , which is why extensive sensitivity analyses were required to check the robustness of our findings. The relative risk of complications in repaired versus new/replaced restorations was estimated as sample-size weighted means and ranges of reported annual failure rates (AFR) (Appendix Table S3).

Risk of complications of new/replaced restorations were estimated from one large practice-based study , which had reported on large posterior amalgam and composite restorations. The AFR found in this study (1.7% for composite and 2.4% for amalgam after 12 years) were validated by comparing them with findings from systematic reviews and other practice based studies , which found AFRs ranging from 1.1% to 2.2% for composite, and 2.1–3.0% for amalgam in posterior permanent teeth, i.e. of similar magnitude (see Appendix). The uncertainty of this estimate was reflected by randomly sampling between a triangular distribution between the minimum and maximum of these values. It should be born in mind that some of these studies evaluated both replaced and newly placed restorations, and not only replacements.

To allow the risk of complications in both repair and replacement to vary time-dependently (i.e. to reflect that risk of restorations failure is not constant with time), reported Kaplan-Meier curves were transformed into hazard functions. Risk of complications in follow-up states had been estimated for previous studies, mainly using systematic reviews, with full detail of estimation being described elsewhere .

2.5

Resources and costs

German healthcare is characterized by a two-tiered insurance system. Cost calculations were based on the German public and private dental fee catalogues, BEMA and GOZ providing an estimation of costs from the payers perspective, as described in the Appendix. Given the lack of primary data, opportunity costs of patients’ time in treatment were not accounted for. Costs were estimated in 2015 Euro.

2.6

Discounting

Future costs and effectiveness were discounted at 3% per annum, as recommended by German authorities . Discounting accounts for opportunities forgone if spending money now instead of later, or gaining health benefits later instead of now . Discount rates were varied between 0 and 5% in a sensitivity analysis.

2.7

Analytical methods

Analysis was performed using Monte Carlo micro simulations, with 1000 independent individuals (teeth) being followed over the average expected life-time of patients in annual cycles. To introduce parameter uncertainty, we randomly sampled transition probabilities from a triangular distribution of parameters, as outlined above , with 100 random samples being drawn for each population of individuals/teeth.

Strategies were ranked according to their costs, and incremental-cost-effectiveness ratios (ICERs) used to express cost differences per gain or loss of effectiveness when comparing repair versus complete replacement. A positive ICER thus indicates additional costs per additional effectiveness (such a strategy is considered to be undominated), while negative ICERs indicate higher costs at lower effectiveness (such strategy is considered to be dominated by the alternative).

Using estimates for costs (c, in €) and effectiveness (e, in years), the net benefit of each strategy combination was calculated using the formula

with λ denoting the ceiling threshold of willingness-to-pay, i.e. the additional costs a decision maker is willing to bear for gaining an additional unit of effectiveness . If λ > Δc/Δe, an intervention is considered more cost-effective compared to the alternative despite possibly being more costly . We used the net-benefit approach to calculate the probability of a detection strategy being acceptable regarding its cost-effectiveness for payers with different willingness-to-pay ceiling thresholds. A number of univariate sensitivity analyses were performed to explore the impact of uncertainty and heterogeneity. Details regarding the input variables for these analyses can be found in the Appendix (Appendix Table S4).

2.1

Setting, perspective, population, horizon

This study adopted a mixed public-private-payer perspective in the context of the German healthcare setting. We modelled a population of 1000 60-year old females with one permanent molar with a vital non-painful pulp and a three-surfaced composite or amalgam restoration in need of repair or replacement. The tooth was followed over the patient’s lifetime. The resulting time horizon was 26 years. To avoid clustering effects and simplify modelling and interpretation of findings, only one restoration per mouth was simulated. Restoration surface numbers and the time horizon were varied in sensitivity analyses (see below).

2.2

Comparators

We compared restoration repair versus complete replacement:

• •

  Restoration repair was defined as mending a number of possible complications like tooth (cusp) or restoration fracture, partial restoration loss, secondary caries, or aesthetic reasons. Such mending was performed by partially replacing the original restoration with adhesively placed composite resin and assumed to involve only one surface. Note that we did not assume repair to be provided according to any specific standard. Also note that performing any further conditioning procedures, like application of silane or silica coating, might increase costs of repair, but could also affect effectiveness .

• •

  Complete replacement of the partially defective amalgam and composite restorations was defined as completely removing and replacing the failed restoration either with amalgam or adhesively placed resin composite (depending on the initial, failed restoration) and increasing the restoration surface by +1.

2.3

Model and assumptions

A Markov model was used for this study (TreeAge Pro 2013, TreeAge Software, Williamstown, MA, USA).

Complications of both repaired and replaced restorations were assumed to lead to

• •

  Restorative re-treatments like re-replacement or re-repair (possible reasons might be fracture, including partial loss of restoration and tooth fracture with or without retention loss, secondary caries, or primary caries).

• •

  Repaired restorations could not be repaired again, but needed complete restoration replacement.

• •

  Complete restoration replacement was assumed to generate an additional restoration surface and increased the risk of restorative failure and re-treatment by 1.4 .

• •

  We assumed a direct (composite, amalgam) restoration to have a maximum of five surfaces, therefore limiting the number of re-replacements.

• •

  A full-metal crown was placed if replacements were not possible any longer.

• •

  Endodontic treatment, i.e. root-canal treatment (assuming the treatment of a vital pulp including instrumentation and obturation), followed by placement of a crown (as could be expected after endodontic treatment in extensively restored teeth).

• •

  Extraction for non-mendable complications.

The proportions of the different re-treatments were derived from a large, practice-based study, which had followed repaired and replaced restorations placed by the same operator in the same population of patients (Appendix Table S1):

• •

  In follow-up health states, teeth were again assumed to experience restorative complications (e.g. crown de-cementation, fracture or secondary caries, leading to re-cementation or renewal of crowns, or extractions) or endodontic complications (leading to non-surgical primary or secondary root-canal treatment or surgical re-treatment, i.e. apisectomy, or extraction).

• •

  We assumed 50% of extracted teeth to be replaced using implant-supported single crowns. Implants were assumed to experience restorative complications (requiring re-cementation or renewal of crowns) as well as biologic (e.g. peri-implantitis, possibly with subsequent implant loss) or technical complications (like abutment or implant fracture).

The constructed model is shown in a simplified form in Fig. 1 . Model validation was performed internally by varying key parameters to check their impact on the results, by evaluating different model structures, and by performing the following univariate sensitivity analyses:

• •

  Repairs were assumed to be possible twice, not only once.

• •

  Complete replacement did not add an additional surface to the restoration, but was only possible twice before crown placement was required.

• •

  Between 0% and 100% of removed teeth were replaced using implant-supported crowns.

• •

  The original restoration was assumed to involve four surfaces.

• •

  The patient was assumed to be 40 years old at baseline, which increases the horizon of the simulation.

Transition diagram.

¹ Re-Repair was only possible in a sensitivity analysis. ² Number of repeated replacements was varied in sensitivity analysis. ³ Crown was only placed after root-canal treatment in case no crown was present.

2.4

Health outcome measure

The health outcome measure was tooth retention years, i.e. the mean time a tooth was retained in a patients’ mouth. This was determined by the tooth experiencing complications, the risk of which is modelled via transition probabilities, which allow teeth to move from one health state to another (i.e. risks of complications and associated re-treatments).

Transition probabilities for repaired versus new/replaced restorations were estimated based on a rapid systematic review of the literature (see Appendix).

Based on the included five studies (8 publications) , we estimated the risk of complications in repaired relative to those in new/replaced composite or amalgam restorations. While some studies were controlled , i.e. had randomly assigned restorations to repair or replacement, some were cohort studies . For these, we took care to only compare risk of complications in repaired versus new/replaced restorations if they were performed on similar patients (age range, source population) under similar conditions (setting, operators). Note that in this case, indication bias is nevertheless likely, as placement of amalgam might be more frequent in certain (demographic, socio-economic) populations than placement of composite , which is why extensive sensitivity analyses were required to check the robustness of our findings. The relative risk of complications in repaired versus new/replaced restorations was estimated as sample-size weighted means and ranges of reported annual failure rates (AFR) (Appendix Table S3).

Risk of complications of new/replaced restorations were estimated from one large practice-based study , which had reported on large posterior amalgam and composite restorations. The AFR found in this study (1.7% for composite and 2.4% for amalgam after 12 years) were validated by comparing them with findings from systematic reviews and other practice based studies , which found AFRs ranging from 1.1% to 2.2% for composite, and 2.1–3.0% for amalgam in posterior permanent teeth, i.e. of similar magnitude (see Appendix). The uncertainty of this estimate was reflected by randomly sampling between a triangular distribution between the minimum and maximum of these values. It should be born in mind that some of these studies evaluated both replaced and newly placed restorations, and not only replacements.

To allow the risk of complications in both repair and replacement to vary time-dependently (i.e. to reflect that risk of restorations failure is not constant with time), reported Kaplan-Meier curves were transformed into hazard functions. Risk of complications in follow-up states had been estimated for previous studies, mainly using systematic reviews, with full detail of estimation being described elsewhere .

2.5

Resources and costs

German healthcare is characterized by a two-tiered insurance system. Cost calculations were based on the German public and private dental fee catalogues, BEMA and GOZ providing an estimation of costs from the payers perspective, as described in the Appendix. Given the lack of primary data, opportunity costs of patients’ time in treatment were not accounted for. Costs were estimated in 2015 Euro.

2.6

Discounting

Future costs and effectiveness were discounted at 3% per annum, as recommended by German authorities . Discounting accounts for opportunities forgone if spending money now instead of later, or gaining health benefits later instead of now . Discount rates were varied between 0 and 5% in a sensitivity analysis.

2.7

Analytical methods

Analysis was performed using Monte Carlo micro simulations, with 1000 independent individuals (teeth) being followed over the average expected life-time of patients in annual cycles. To introduce parameter uncertainty, we randomly sampled transition probabilities from a triangular distribution of parameters, as outlined above , with 100 random samples being drawn for each population of individuals/teeth.

Strategies were ranked according to their costs, and incremental-cost-effectiveness ratios (ICERs) used to express cost differences per gain or loss of effectiveness when comparing repair versus complete replacement. A positive ICER thus indicates additional costs per additional effectiveness (such a strategy is considered to be undominated), while negative ICERs indicate higher costs at lower effectiveness (such strategy is considered to be dominated by the alternative).

Using estimates for costs (c, in €) and effectiveness (e, in years), the net benefit of each strategy combination was calculated using the formula

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