Epsilon Best Arm Identification in Spectral Bandits

We propose an analysis of Probably Approximately Correct (PAC) identification of an ϵ-best arm in graph bandit models with Gaussian distributions. We consider finite but potentially very large bandit models where the set of arms is endowed with a graph structure, and we assume that the arms' expectations μ are smooth with respect to this graph. Our goal is to identify an arm whose expectation is at most ϵ below the largest of all means. We focus on the fixed-confidence setting: given a risk parameter δ, we consider sequential strategies that yield an ϵ-optimal arm with probability at least 1-δ. All such strategies use at least T*(μ)log(1/δ) samples, where R is the smoothness parameter. We identify the complexity term T*(μ) as the solution of a min-max problem for which we give a game-theoretic analysis and an approximation procedure. This procedure is the key element required by the asymptotically optimal Track-and-Stop strategy.

Indicators for Risk of Airborne Transmission in Shared Indoor Environments and their application to COVID-19 Outbreaks

Some infectious diseases, including COVID-19, can be transmitted via aerosols that are emitted by an infectious person and inhaled by susceptible individuals. Although physical distancing effectively reduces short-range airborne transmission, many infections have occurred when sharing room air despite maintaining distancing. We propose two simple parameters as indicators of infection risk for this situation. They combine the key factors that control airborne disease transmission indoors: virus-containing aerosol generation rate, breathing flow rate, masking and its quality, ventilation and air cleaning rates, number of occupants, and duration of exposure. COVID-19 outbreaks show a clear trend in relation to these parameters that is consistent with an airborne infection model, supporting the importance of airborne transmission for these outbreaks. The observed trends of outbreak size vs. risk parameters allow us to recommend values of the parameters to minimize COVID-19 indoor infection risk. All of the pre-pandemic spaces are in a regime where they are highly sensitive to mitigation efforts. Measles outbreaks occur at much lower risk parameter values than COVID-19, while tuberculosis outbreaks are observed at much higher risk parameter values. Since both diseases are accepted as airborne, the fact that COVID-19 is less contagious than measles does not rule out airborne transmission. It is important that future outbreak reports include ventilation information, to allow expanding our knowledge of the circumstances conducive to airborne transmission of different diseases.

Hematopoietic Cell Transplantation Donor Selection Reimagined: KIR-KIR Ligand Interactions and a Formalized Donor Risk Index Effective at Predicting Survival

Background When selecting a human leukocyte antigen (HLA) matched unrelated donor (URD) for hematopoietic cell transplantation (HCT) it is generally accepted that donor age, sex, ABO blood group and viral serologic status should be considered. However, the inter-relationship among these variables is not well established and a consensus on how strongly to consider each variable has not been reached. Selection of the optimal donor gets more complicated as new donor recipient pair (DRP) selection parameters, including killer immunoglobulin-like receptors (KIR) haplotypes are included. In this study we seek to develop a logic-based method to reduce the inconsistencies in donor selection in the HLA matched HCT. Methods VCU IRB approval was obtained for a retrospective review of eligible subjects who were adults with known KIR genotyping receiving HLA-A, B, C & DRB1 allelically matched URD HCT for hematologic malignancy between 2014 and 2017. Donor recipient pairs were selected based on donor age, sex match, CMV sero-status match, and ABO compatibility when possible; KIR genotype was not considered in DRP selection. KIR-KIR ligand interactions were calculated for each DR pair and interaction unit values were ascribed as follows; -1, when the donor possessed an inhibitory KIR (iKIR) and the recipient the corresponding HLA; +1, when the donor possessed iKIR and recipient lacked corresponding HLA (mKIR score, missing ligand). A novel inhibitory-missing KIR (IM-KIR) score was calculated for each HLA matched DRP by summing the interaction values as in equation 1. IM KIR Score = |iKIR| + |mKIRL| ………. [1] Univariate and multivariate analysis using Cox regression methods were utilized to evaluate donor parameters associated with overall survival. Weights of each donor risk variable (age, sex, CMV & ABO match) contribution were ascribed and summed up to determine donor risk parameter. Donor risk parameters and reciprocal-IM-KIR were finally combined into a donor risk index. Receiver operating characteristic curve- area under the curve (ROC-AUC) analysis was utilized to compare indices. Results Ninety-eight DRP with known HLA & KIR genotyping were studied. Median follow up at the time of analysis was 583 days. A higher IM-KIR score describes a DRP with increased iKIR-KIR ligand interactions and missing KIR ligand interactions; which was associated with a favorable survival after HCT, HR of 0.44 (95%CI: 0.26 to 0.73; P=0.002). Further analyses were performed using a reciprocal of this score. Univariate analysis of overall survival for donor age, sex match, ABO compatibility and CMV status were all statistically insignificant (p>0.05). However, the donor risk parameter was predictive of mortality with a hazard ratio (HR) of 2.76 (95% CI: 1.22-6.18, p=0.014). Covariate analysis of the donor risk parameter and reciprocal IM-KIR score were both predictive of survival independent of each other with HR 2.41 (1.05-5.54, p=0.038) and 2.35 (1.18-4.70, p=0.016) respectively. Combining the two into a donor risk index was predictive of survival with a HR of 2.38 (1.44-3.92, p=0.001). ROC-AUC comparison of survival for IM-KIR score and donor risk parameter showed statistically significant AUCs of 0.63 and 0.67 respectively. Further, the combined donor risk index shows improved sensitivity and specificity over the donor risk parameter with AUCs of 0.72 and 0.67 respectively. Conclusions A novel KIR-HLA interaction score, the IM-KIR score independently predicts survival in HLA matched DRP, as does a formalized donor risk parameter which includes non-HLA donor characteristics. Moreover, the addition of IM-KIR score to the donor risk parameter enhanced the specificity and sensitivity of predicting survival in these patients. If validated in a larger exploration and validation cohort this method of donor selection may improve the donor selection process, decreasing variability in clinical outcomes and improve overall survival. Disclosures No relevant conflicts of interest to declare.

Modelling of tri-parameter bidding integrating cost, time and risk: a stochastic approach

Purpose This paper aims to propose a new tri-parameter bidding model integrating cost, time and risk. The key value of the model is that it remains within the framework of the competitive bidding system while controlling the risk resulting from float loss. Design/methodology/approach The model utilizes stochastic scheduling to quantify the float loss impact at the project level. Prospective bidders are evaluated based on their total combined bid (TCB) including cost, time and risk. The risk parameter is calculated as the relative risk between the bidder’s schedule and the client’s baseline schedule. Findings The results confirmed that choosing the contractor based on the lowest price and time reduces the available float and increases the schedule risks. The probability of completing the project on time dropped from 46 per cent for the baseline schedule to 19 per cent for the bidder with the most compressed schedule. The selected bidder, using the proposed model, has the lowest TCB of cost, time and risk. Results show that adding the risk parameter in the evaluation changed the ranking of the bidders. Research limitations/implications The model does not discuss all project risks that the contractor retains. It focuses on schedule risks that result from shortening project duration. The model focuses on solving the problem with price plus time bidding method by addressing the schedule risk issue. Other criteria, such as sustainability, are not considered. Practical implications The proposed model encourages contractors to pay more attention to the time parameter and the schedule risks resulting from aggressive reduction in project duration. Originality/value Problems arose, in the current complex construction industry, as owners rely solely on price as the award criterion. Recently, the bi-parameter bidding system, A + B, introduced the time parameter to the awarding criteria. However, reducing the project duration by compressing the schedule consumes the float of non-critical activities, which reduces the schedule flexibility of a project. The proposed model allows clients to evaluate potential bidders objectively. Rather than evaluating the bidders based on price, in the conventional low bid system, or based on price and time, as in the A + B system, the bidders are evaluated based on three parameters: price, time and risk.