Mathematically optimal decisions in forensic age assessment

Forensic age estimation generally involves considerable amounts of uncertainty. Forensic age indicators such as teeth or skeleton images predict age only approximately, and this is likely to remain true even for future forensic age indicators. Thus, forensic age assessment should aim to make the best possible decisions under uncertainty. In this paper, we apply mathematical theory to make statistically optimal decisions to age assessment. Such an application is fairly straightforward assuming there is a standardized procedure for obtaining age indicator information from individuals, assuming we have data from the application of this procedure to a group of persons with known ages, and assuming the starting point for each individual is a probability distribution describing prior knowledge about the persons age. The main problem is then to obtain such a prior. Our analysis indicates that individual priors rather than a common prior for all persons may be necessary. We suggest that caseworkers, based on individual case information, may select a prior from a menu of priors. We show how information may then be collected over time to gradually increase the robustness of the decision procedure. We also show how replacing individual prior distributions for age with individual prior odds for being above an age limit cannot be recommended as a general method. Our theoretical framework is applied to data where the maturity of the distal femur and the third molar is observed using MRI. As part of this analysis we observe a weak positive conditional correlation between maturity of the two body parts.

Bargaining under the Illusion of Transparency

This paper studies bargaining with noncommon priors where the buyer projects and exaggerates the probability that her private information may leak to the seller. Letting the buyer name her price first, raises the seller’s payoff above his payoff from posting a price. In seller-offer bargaining, projection implies a partial reversal of classic Coasian comparative static results. Weakening price commitment can benefit the seller and, as long as the relative speed at which imaginary information versus offers arrive does not converge to zero too quickly, frictionless bargaining converges to a fast haggling process which allows the seller to extract all surplus from trade. Bargaining under common prior transparency is instead slow and becomes equivalent to simply waiting. The comparative static predictions are consistent with experimental evidence. (JEL C78, D82)

Management of Hepatitis C Virus Genotype 4 Treatment Failure: A Real-World Single Center Experience

Background: Treatment failure with direct-acting antiviral (DAA) therapy is associated with worsening of liver disease especially in cirrhotic patients. Moreover, data on retreatment of HCV genotype 4 patients (G4) with DAA failure are still very limited, since they are under- represented in most clinical trials. Aims: To evaluate the efficacy of retreatment of Egyptian HCV G4 DAA failure patients based on the use of a new DAA class from currently available first- generation DAA regimens other than the patient had relapsed to. Methods: 29 Egyptian HCV G4 DAA failure patients were retreated by switch to a new DAA class from first- generation DAA regimens than the patient had relapsed to independent of RAS testing. 25 out of these 29 patients completed retreatment and 4 patients were lost for follow–up. Results: Among other risk factors, by logistic regression analysis, only older age, high CTP score and high base-line viral load were independent predictors of DAA failure among our cohort. Also SOF/RBV regimen was the most common prior DAA regimen associated with treatment failure (48.3%). All our DAA failure patients were cirrhotics that made prompt retreatment of them a rescue strategy to halt viral replication and disease progression. After retreatment, 22 (88%) of the 25 patients who completed retreatment achieved SVR12 and the remaining 3 (12%) failed. These 3 patients completed a second retreatment, one achieved SVR and the other 2 relapsed again (re-relapsers) Conclusion: The overall SVR rate (88%) demonstrated in this real –world study, clearly shows that, the retreatment policy of DAA failure patients by switch to – or addition of a new drug class independent of RAS testing is a good retreatment option, that may be of importance for many areas of the world with no or difficult access to RAS testing or second-generation rescue regimens.

Feasible joint posterior beliefs (through examples)

Through a sequence of examples, we survey the main results of "Feasible Joint Posterior Beliefs" [Arieli, Babichenko, Sandomirskiy, Tamuz 2021]. A group of agents share a common prior distribution regarding a binary state, and observe some information structure. What are the possible joint distributions of their posteriors? We discuss feasibility of product distributions, correlation of posteriors in feasible distributions, extreme feasible distributions and the characterization of feasibility in terms of a "no-trade" condition.

Characterization of Patients With Refractory or Unexplained Chronic Cough Participating in a Phase 2 Clinical Trial of the P2X3-Receptor Antagonist Gefapixant

Purpose This analysis assesses clinical characteristics of patients with refractory chronic cough (RCC) or unexplained chronic cough (UCC) enrolled in a phase 2 study to better understand this patient population. Methods Patients with RCC/UCC lasting for ≥ 1 year and cough severity visual analog scale (VAS) score of > 40 mm at screening were eligible. Demographics, clinical characteristics, and medical history were collected at baseline. Cough-related measures included cough severity VAS, Cough Severity Diary (CSD), Leicester Cough Questionnaire (LCQ), and a structured cough-trigger questionnaire. Medication history included all medications 30 days before screening and chronic cough treatments within 1 year before screening. Data were summarized using descriptive statistics. Results Patients (N = 253; female, 76%; mean age, 60 years) had severe (mean cough severity VAS, 57.5 mm) and long-lasting (median duration, 11 years) cough. The most burdensome self-reported aspects included psychological and social factors (LCQ) and cough frequency and intensity (CSD). Patient-reported triggers were consistent with cough hypersensitivity (e.g., 95% to 96% reported irritation or tickle in throat). Common reported comorbidities included gastroesophageal reflux disease (GERD; 56%), allergic rhinitis (47%), and asthma (30%); 12% of patients had been diagnosed with all 3 conditions. The most common prior medications included inhaled or oral steroids (21%), antihistamines (15%), and antacids (15%). Conclusion Patients with RCC/UCC had severe, long-lasting, and burdensome cough with clinical features of cough hypersensitivity. Many patients had been diagnosed with GERD, allergic rhinitis, and asthma but had a persistent cough despite treatment of these conditions. Trial registration: ClinicalTrials.gov, NCT02612610; registered November 20, 2015

Knowledge, Awareness and Probabilistic Beliefs

Bayesian game theory investigates strategic interaction of players with full awareness but incomplete information about their environment. We extend the analysis to players with incomplete awareness, who might not be able to reason about all contingencies in the first place. We develop three logical systems for knowledge, probabilistic beliefs and awareness, and characterize their axiom systems. Bayesian equilibrium is extended to games with incomplete awareness and we show that it is consistent with common prior and speculative trade, when common knowledge of rationality is violated.

Simple bets to elicit private signals

This paper introduces two simple betting mechanisms—top‐flop and threshold betting—to elicit unverifiable information from crowds. Agents are offered bets on the rating of an item about which they received a private signal versus that of a random item. We characterize conditions for the chosen bet to reveal the agents' private signal even if the underlying ratings are biased. We further provide microeconomic foundations of the ratings, which are endogenously determined by the actions of other agents in a game setting. Our mechanisms relax standard assumptions of the literature, such as common prior, and homogeneous and risk neutral agents.

Prior-Independent Optimal Auctions

Auctions are widely used in practice. Although auctions are also extensively studied in the literature, most of the developments rely on the significant common prior assumption. We study the design of optimal prior-independent selling mechanisms: buyers do not have any information about their competitors, and the seller does not know the distribution of values but only knows a general class to which it belongs. Anchored on the canonical model of buyers with independent and identically distributed values, we analyze a competitive ratio objective in which the seller attempts to optimize the worst-case fraction of revenues garnered compared with those of an oracle with knowledge of the distribution. We characterize properties of optimal mechanisms and in turn establish fundamental impossibility results through upper bounds on the maximin ratio. By also deriving lower bounds on the maximin ratio, we are able to crisply characterize the optimal performance for a spectrum of families of distributions. In particular, our results imply that a second price auction is an optimal mechanism when the seller only knows that the distribution of buyers has a monotone nondecreasing hazard rate, and it guarantees at least 71.53% of oracle revenues against any distribution within this class. Furthermore, a second price auction is near optimal when the class of admissible distributions is that of those with nondecreasing virtual value function (a.k.a. regular). Under this class, it guarantees a fraction of 50% of oracle revenues, and no mechanism can guarantee more than 55.6%. This paper was accepted by Kalyan Talluri, revenue management and market analytics.

A variance shrinkage method improves arm-based Bayesian network meta-analysis

Network meta-analysis is a commonly used tool to combine direct and indirect evidence in systematic reviews of multiple treatments to improve estimation compared to traditional pairwise meta-analysis. Unlike the contrast-based network meta-analysis approach, which focuses on estimating relative effects such as odds ratios, the arm-based network meta-analysis approach can estimate absolute risks and other effects, which are arguably more informative in medicine and public health. However, the number of clinical studies involving each treatment is often small in a network meta-analysis, leading to unstable treatment-specific variance estimates in the arm-based network meta-analysis approach when using non- or weakly informative priors under an unequal variance assumption. Additional assumptions, such as equal (i.e. homogeneous) variances for all treatments, may be used to remedy this problem, but such assumptions may be inappropriately strong. This article introduces a variance shrinkage method for an arm-based network meta-analysis. Specifically, we assume different treatment variances share a common prior with unknown hyperparameters. This assumption is weaker than the homogeneous variance assumption and improves estimation by shrinking the variances in a data-dependent way. We illustrate the advantages of the variance shrinkage method by reanalyzing a network meta-analysis of organized inpatient care interventions for stroke. Finally, comprehensive simulations investigate the impact of different variance assumptions on statistical inference, and simulation results show that the variance shrinkage method provides better estimation for log odds ratios and absolute risks.