Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Costs and Effectiveness of Treatment Alternatives for Proximal Caries Lesions

OBJECTIVES: Invasive therapy of proximal caries lesions initiates a cascade of re-treatment cycles with increasing loss of dental hard tissue. Non- and micro-invasive treatment aim at delaying this cascade and may thus reduce both the health and economic burden of such lesions. This study compared the costs and effectiveness of alternative treatments of proximal caries lesions. METHODS: A Markov-process model was used to simulate the events following the treatment of a proximal posterior lesion (E2/D1) in a 20-year-old patient in Germany. We compared three interventions (non-invasive; micro-invasive using resin infiltration; invasive using composite restoration). We calculated the risk of complications of initial and possible follow-up treatments and modelled time-dependent non-linear transition probabilities. Costs were calculated based on item-fee catalogues in Germany. Monte-Carlo-microsimulations were performed to compare cost-effectiveness of non- versus micro-invasive treatment and to analyse lifetime costs of all three treatments. RESULTS: Micro-invasive treatment was both more costly and more effective than non-invasive therapy, with ceiling-value-thresholds for willingness-to-pay between 16.73 € for E2 and 1.57 € for D1 lesions. Invasive treatment was the most costly strategy. Calculated costs and effectiveness were sensitive to lesion stage, patient's age, discounting rate and assumed initial treatment costs. CONCLUSIONS: Non- and micro-invasive treatments have lower long-term costs than invasive therapy of proximal lesions. Micro-invasive therapy had the highest cost-effectiveness for treating D1 lesions in young patients. Decision makers with a willingness-to-pay over 16.73 € and 1.57 € for E2 and D1 lesions, respectively, will find micro-invasive treatment more cost-effective than non-invasive therapy

State-transition diagram.

<p>A Markov-model was used to simulate non-, micro- or invasive treatment of proximal E2 or D1 lesions. Non- and micro-invasively treated E2 lesions remained in their state (circled arrows) or progressed to D1 lesions according to their transition probabilities (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone-0086992-t001" target="_blank">Table 1</a>). Translation to the next state accrued costs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone-0086992-t002" target="_blank">Table 2</a>). If D1 lesions progressed further, restoration with composite was simulated. Invasively treated lesions were restored using composite regardless of their stage. Restorations were assumed to fail either due to endodontic complications, requiring endodontic (re-)treatment, or due to restorative complications, requiring repair, recementation or re-restoration. Teeth could always translate to extraction (depending on allocation probabilities or if no further options remained). Missing teeth were replaced in 80% of simulations. Replacement was performed using implant-retained single crowns.</p

Cost estimation.

1<p>Costs for dental diagnostics (items 01, 8, Ä925) not included.</p>2<p>Two-surface restoration assumed.</p>3<p>Treatment of three root canals per tooth assumed.</p><p>For each course of treatment, costs were calculated by quantification of item-fees from public or private item-catalogues (for details see Supporting Information). Within the base-case scenario, non-invasive treatment accrued costs of 1/12 item-fee for fluoridation, since we assumed that all posterior interdental areas would be fluoridated. Within the high-costs scenario, non-invasive treatment generated full costs for topical fluoridation, and a higher fee-multiplicator (×3.5) was used for factorable items of the initial therapy to reflect cost-variability. Future costs were discounted with 3% per annum.</p

Transition probabilities (p) used within the model.

<p>Teeth were allocated to their initial health state (I) depending on the treatment strategy and the lesion stage (left column). For non- and micro-invasively treated lesions, transition probabilities per 6-monthly cycle depended on patient’s age (α) and were calculated using hazard functions (middle column). For all follow-up states (F), transition probabilities depended on the time spent in the health state (e.g. the time since a crown had been placed), with three time plateaus being modelled (<2, 2–5, >5 years). To introduce joint parameter uncertainty, a triangular distribution of parameters between their 95% Confidence Intervals (CI) was assumed. For hazard functions, 95% CI (given in brackets) were used within scenario analyses. To simplify the table, we only present the range of follow-up transition probabilities used within the model. Full details (time-dependent mean and 95% CI probabilities) can be found within the Supporting Information. If transition occurred, teeth were allocated to follow-up states according to allocation probabilities (right columns).</p

Cost-effectiveness of strategies in different scenarios.

1<p>Input data regarding effectiveness within scenarios taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone-0086992-t001" target="_blank">Table 1</a>.</p>2<p>Calculated to highest ranked strategy. Negative values indicate additional costs per effectiveness loss; positive values indicate additional costs per effectiveness gain. Strategies were either dominated (d) or undominated (u) by the first-ranked strategy.</p>3<p>Base-case: 20-year-old-patient with 58.25 years to live <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone.0086992-Statistisches1" target="_blank">[19]</a>; replacement of 80% of removed teeth assumed <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone.0086992-BarmerGEK1" target="_blank">[26]</a>; 3% discounting rate <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone.0086992-IQWIG1" target="_blank">[18]</a>, triangular distribution of probabilities between 95% CI assumed.</p>4<p>Best-case: Highest evidence-based effectiveness of micro-invasive treatment assumed.</p>5<p>Worst-case: Lowest evidence-based effectiveness of micro-invasive treatment assumed.</p>6<p>Years to live: 63.5 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone.0086992-Statistisches1" target="_blank">[19]</a>.</p>7<p>Years to live: 39.0 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086992#pone.0086992-Statistisches1" target="_blank">[19]</a>.</p><p>Mean costs (c, €) and effectiveness (e, % of unrestored lesions), ranking of strategies as well as incremental cost-effectiveness ratios (ICERs) were calculated. Ranking was performed according to costs (strategies with higher costs were ranked lower). Cost-effectiveness analyses were performed separately for lesions of different stages (E2 or D1). Besides the base-case analysis, we performed best- and worst-case sensitivity analyses to explore effects of uncertainty resulting from current evidence. Within these analyses, we varied the transition probabilities of micro-invasively treated lesions based on the 95% CI of calculated Risk Ratios of our meta-analysis. We additionally explored the effects of the patient’s age as well as used discount rates and applied distribution of probabilities for random sampling on the cost-effectiveness estimates.</p

Lifetime costs of different treatment strategies.

<p>4a: Costs were analysed within the base-case scenario (20-year old patient, life expectancy 58.25 years, discount rate 3% per year, initial treatment costs for non-, micro- and invasive treatment 0.54 €, 84.99 € and 92.66 €, respectively). Costs for invasively treated lesions were not influenced by lesion stage. Since E2 lesions had lower transition probabilities than D1 lesions, lifetime costs for non- or micro-invasively treated E2 lesions were reduced compared to D1 lesions. Due to reduced efficacy of non-invasive treatment for D1 lesions, the cost-advantage of non-invasive compared to micro-invasive treatment was considerably reduced for these lesions. Invasive treatment was the most expensive option for both E2 and D1 lesions. 4b: Lifetime costs within the high-cost scenario. Non-invasive was assumed to accrue costs of 9.84 € for topical fluoridation each cycle, followed by costs for follow-up treatments. Micro-invasive treatment initially generated costs of 129.33 €, followed by regular costs for topical fluoridation and all follow-up treatments. Invasive treatment was assumed to initially generate costs of 130.19 €, followed by costs for follow-up treatment. Within this scenario, micro-invasive treatment was the least costly treatment for both E2 and D1 lesions.</p