2.1

Setting, perspective, population, horizon

This study adopted a mixed public-private-payer perspective in the context of the German healthcare system. We modelled a population of initially 6-year old male individuals with one, two, to four permanent severe MIH-affected molars with a vital pulp. Molars were assumed to require restorative or surgical/orthodontic treatment, and were followed over the patient’s lifetime (TreeAge Pro 2013, TreeAge Software, Williamstown, MA, USA). Patient level costs were calculated, while effectiveness was calculated as mean value per molar (see below).

2.2

Comparators

Based on a recent systematic review, the study team, which involved preventive and restorative clinicians, orthodontists, and pediatric dentists, appraised the available options. These were different directly placed restorations, such as resin composite, amalgam, compomer, glass ionomer cement restorations or preformed metal crowns; different indirectly placed restorations, such as metal, ceramic or composite inlays/onlays/crowns; extraction and orthodontic alignment if needed . It was decided to assess three different strategies, based on two key questions: (a) Which options are supported by the majority of data, where uncertainty in survival is low enough to yield estimates with certain robustness, and where new studies are unlikely to completely change that estimate?, and (b) Which options are representative for other options and could serve as indicator strategies (like resin composite, which − within the chosen setting − have similar costs to amalgam, compomer or preformed metal crowns), i.e. modelling further and similar options would have only limited information gain?

The three options we eventually chose were (1) the removal of the tooth and orthodontic alignment of the second and third molar (Ex/Ortho); (2) the restoration of the tooth using resin composite (Comp); (3) the restoration of the tooth using an indirect restoration, specifically, a non-precious metal crown, after temporizing the tooth using a preformed metal crown (PMC/IR). It should, however, be noted that the choice of these options was not decided using a formal consensus process, with other comparators being available and possibly also valid. Also note that removing affected teeth and leaving a gap was not considered an option within the German healthcare, while in other settings such strategy might be acceptable.

2.3

Model and assumptions

A model following patients and molars over their lifetime was constructed. Three main pathways were possible:

• (1)

  Removal and alignment with or without active orthodontic treatment (Ex/Ortho). It was assumed that the patient had an Angle class I molar relationship without orthodontic treatment need. In our base-case scenario, it was assumed that the tooth was scheduled for extraction at the optimal age. Based on a recent systematic review , the assumed optimal age was 9.5 years for maxillary molars and 11 years for mandibular molars, with mean chances of spontaneous alignment being 83% and 63% (see Table 1 ). This age was increased to 14 years, assuming no spontaneous alignment at this age any longer, to model a worst case for this strategy. The MIH molar was temporized using a preformed metal crown (PMC), the chance of failure of PMCs was derived from a systematic review . After tooth removal, the sound second and third molar were assumed to be orthodontically aligned if needed, with space closure to be attempted from distal, which requires minimum anchorage. For this alignment, orthodontists can choose between a number of treatment modalities. A multi-bracket appliance, a transpalatal arch and/or a lingual arch and a reverse pull headgear (extraoral anchorage appliance) could be used for the mesialization of the second permanent molar (see below). Alternatively, the mesialization would be achieved by the use of a multi-bracket appliance, a transpalatal arch and/or a lingual arch and temporary anchorage devices (bone anchorage) as part of a mesialslider. These scenarios were assumed to be both representative for the reality within German healthcare; the first scenario for patients unwilling to pay any out of pocket costs, the second scenario for patients topping up their public health insurance treatment privately out of their own pockets (see below). Each scenario was modelled for missing 1, 2, 3 or 4 MIH-affected molars, with the position of the missing teeth (maxilla, mandible, or both) also being taken into consideration. Note that the second molar was assumed to be subject to caries increment after alignment into the first molar position. The caries increment was assumed to be constant over the patient’s lifetime, with 0.11 teeth being affected per year, as reported by a life course study from New Zealand . If carious lesions occurred, a resin composite restoration was assumed to be placed; this restoration was assumed to have a relatively limited surface extent, with the annual failure hazard being derived from a long-term cohort study from Denmark . Restored molars could experience restorative and non-restorative complications. Restorative complications led to repair of the restoration (possible once), replacement using resin composite (possible once), or replacement using non-precious metal crowns (in case repair or renewal were not possible any longer). The hazard of failure of repaired or renewed resin composites was derived from published studies in the field, as was the hazard of failure of crowns (see Table 1 ). In case of pulpal complications, root-canal treatment was assumed to be performed, followed by placement of a crown (as was expected after endodontic treatment). The hazard of failure of such therapy was derived from studies in the field ( Table 1 ). In follow-up health states, molars 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). If molars extraction was required, tooth replacement was assumed to utilize 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) or technical complications (like abutment or implant fracture); these were derived from systematic reviews. In case of implant removal, it was assumed that re-implantation would be attempted in 50% of the cases.

  Table 1

  Parameters used for effectiveness estimation.

  Health state	Reference	Transition probability per year	Triangular distribution	Allocation to	Allocation probability
  Spontaneous alignment maxillary molar at age 9.5 years	Eichenberger et al.	–	0.8;1.0;1.2	No orthodontic therapy Orthodontic therapy	0.82 0.18
  Spontaneous alignment mandibular molar at age 11 years	Eichenberger et al.	–	0.7;1.0;1.3	No orthodontic therapy Orthodontic therapy	0.63 0.37
  Aligned second molar	Broadbent et al.	0.011	0.1;1.0;3.0	Caries → composite	1.00
  Composite on MIH molar	Elhennawy and Schwendicke	0.0436y −0.113	0.5;1.0;1.5	Repair Re-replacement RCT Extraction	0.42 0.43 0.08 0.07
  Repaired composite	Kanzow et al.	RR = 3.4 relative to newly placed composite	0.9;1.0;1.6	Replaced composite RCT Extraction	0.85 0.10 0.05
  Replaced composite	Kanzow et al.	RR = 1.4 relative to newly placed composite	0.7;1.0;1.7	Crown RCT Extraction	0.85 0.08 0.07
  Preformed metal crown	Elhennawy and Schwendicke	0.013	0.1;1.0;2.3	Crown or PMC RCT Extraction	0.85 0.08 0.07
  Crown	Burke and Lucarotti	0.076	0.7;1.0;1.7	Re-cementation RCT Re-new Extraction	0.25 0.25 0.13 0.12
  RCT	Ricucci et al. ; Schwendicke and Stolpe	0.0232y −0.823	–	Non-surgical re-RCT Extraction	0.50 0.50
  Non-surgical re-RCT	Ng et al.	0.059	0.3;1.0;2.0	Surgical re-RCT Extraction	0.80 0.20
  Surgical re-RCT	Torabinejad et al.	0.080	0.5;1.0;2.0	Extraction	1.00
  Implant loss	Jung et al.	0.032	0.5;1.0;1.7	Renewal Removal	0.5 0.5
  Implant crown failure or loss	Jung et al.	0.047	0.6;1.0;1.8	Renewal Re-cementation	0.4 0.6

• (2)

  If MIH molars were retained and restored using resin composite (Comp), they followed the identical pathway as described for the second molar in pathway 1. However, the hazard of complications was adjusted to reflect the significantly increased risk of restorative or pulpal complications in MIH molars . In case of crown placement or root-canal treatment being required (assumed to lead to crown placement), the hazard of failure of MIH molars was no longer assumed to differ compared with non-MIH teeth.

• (3)

  If MIH molars were retained and restored using indirect restorations, the assumption of temporization being required between age 6 and 18 was made, as indirect restorations would not be placed commonly in early childhood, but late adolescence. Temporization was assumed using a preformed metal crown (PMC/IR).

The constructed model is illustrated in Figure 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 sensitivity analyses.

Transition diagram.

2.4

Health outcomes and measurement of effectiveness

The health outcome was tooth retention years; that is, the mean time a tooth was retained in a patient’s mouth. This was chosen as other possibly relevant measures, like experienced episodes of pain or provided number of re-treatments, could not be modelled due to scarcity of data. Similarly, quality of life data for MIH teeth were not available and could not be used to inform outcomes.

Transition probabilities to allow teeth to move from one health state to another (i.e. risks of complications and associated re-treatments) were estimated as described above, and are summarized in Table 1 . Note that for extracted MIH molars, the second and third molars were aligned to close the resulting gap. Tooth retention years were thus calculated for the first molar until removal, and for the second molar after alignment.

2.5

Resources and costs

Cost calculations were based on the German public and private dental fee catalogues, BEMA and GOZ , as described elsewhere . German dentists use fee items to claim for reimbursement for treatments. As most patients are members of the statutory insurance, for most procedures and patients items are drawn from the public catalogue BEMA. The catalogue is a detailed list of items, their definition and assigned fees, which can be charged. Procedures drawn from BEMA are usually fully (most conservative or surgical treatments) or partially (prosthetic treatments) covered and re-imbursed by the statutory insurance. For few treatments (composites, non-surgical re-root-canal treatment, implants, bone anchorage and mesialsliders), fees are derived from the private catalogue GOZ, which similarly lists items, with the difference being that more items are available, and that these can be charged at different factors. The most often used factor is 2.3, i.e. the basic fee is multiplied to reach the eventual fee, which is then paid privately by patients out of their own pocket (in case they have an additional private insurance, these costs might be reimbursed). We used the factor of 2.3 for our estimation of GOZ items. A small proportion (11%) of Germans are not members of the public insurance. For them, all items would be drawn from GOZ.

Within the analysis, the aim was to reflect the usual cost mix within German healthcare taking a mixed public-private payer’s perspective. Thus, costs for most procedures were estimated using BEMA, and if not-available there, GOZ was used. As for orthodontic treatment, costs vary significantly between a strict public and a public-private payer’s perspective. As mentioned above, both options are likely to occur within German healthcare. To reflect the resulting uncertainty, probabilistic sensitivity analyses (see below) were performed. Note that estimates do not fully apply to solely privately insured patients.

Given the lack of primary data, opportunity costs of patients’ time in treatment were not accounted for.

2.6

Discounting, currency and price date

Future costs were discounted at 3% per annum . Discounting accounts for time preference, i.e. opportunities lost or gained by spending money now instead of later, or experiencing health now instead of later. Discount rates were varied between 0 and 5% to explore the impact of higher or lower discounting. Costs were estimated in 2016 Euro.

2.7

Analytical methods

Monte-Carlo microsimulations were performed for analysis, with 1000 independent individuals (teeth) being followed over the average expected life-time of patients in annual cycles.

First, incremental-cost-effectiveness ratios (ICER) were used to express cost differences per gained or lost effectiveness when comparing the least costly with the most effective treatment option. Positive ICERs indicate additional costs per additional effectiveness, while negative ICERs indicate additional costs per effectiveness loss. Strategies which had higher effectiveness, but also higher costs (i.e. a positive ICER) compared with the least costly option were considered undominated, while strategies with additional costs but no additional effectiveness were considered dominated.

Second and to introduce parameter uncertainty, we sampled transition probabilities randomly from a triangular or uniform distribution of parameters ( Tables 1 and 2 ) .

Third, using estimates for costs (c, in Euro) 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 alternative intervention is considered more cost-effective than the comparator despite possibly being more costly . The net-benefit approach was used to calculate the probability of a strategy being acceptable regarding its cost-effectiveness for payers with different willingness-to-pay ceiling thresholds.

Lastly, univariate sensitivity analyses were performed to explore the impact of uncertainty and heterogeneity.