We present the true stages machinery and illustrate its applications to descriptive set theory. We use this machinery to provide new proofs of the Hausdorff–Kuratowski and Wadge theorems on the structure of $\mathbf {\Delta }^0_\xi $, Louveau and Saint Raymond’s separation theorem, and Louveau’s separation theorem.

Health economic evaluations are comparative analyses of alternative courses of action in terms of their costs and consequences. The Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement, published in 2013, was created to ensure health economic evaluations are identifiable, interpretable, and useful for decision making. It was intended as guidance to help authors report accurately which health interventions were being compared and in what context, how the evaluation was undertaken, what the findings were, and other details that may aid readers and reviewers in interpretation and use of the study. The new CHEERS 2022 statement replaces previous CHEERS reporting guidance. It reflects the need for guidance that can be more easily applied to all types of health economic evaluation, new methods and developments in the field, as well as the increased role of stakeholder involvement including patients and the public. It is also broadly applicable to any form of intervention intended to improve the health of individuals or the population, whether simple or complex, and without regard to context (such as health care, public health, education, social care, etc.). This summary article presents the new CHEERS 2022 28-item checklist and recommendations for each item. The CHEERS 2022 statement is primarily intended for researchers reporting economic evaluations for peer-reviewed journals, as well as the peer reviewers and editors assessing them for publication. However, we anticipate familiarity with reporting requirements will be useful for analysts when planning studies. It may also be useful for health technology assessment bodies seeking guidance on reporting, as there is an increasing emphasis on transparency in decision making.

We define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it distinguishes between whether the simplest Scott sentence is $\Sigma _{\alpha }$ , $\Pi _{\alpha }$ , or $\mathrm {d-}\Sigma _{\alpha }$ . We give a complete classification of the possible Scott complexities, including an example of a structure whose simplest Scott sentence is $\Sigma _{\lambda + 1}$ for $\lambda $ a limit ordinal. This answers a question left open by A. Miller.

We also construct examples of computable structures of high Scott rank with Scott complexities $\Sigma _{\omega _1^{CK}+1}$ and $\mathrm {d-}\Sigma _{\omega _1^{CK}+1}$ . There are three other possible Scott complexities for a computable structure of high Scott rank: $\Pi _{\omega _1^{CK}}$ , $\Pi _{\omega _1^{CK}+1}$ , $\Sigma _{\omega _1^{CK}+1}$ . Examples of these were already known. Our examples are computable structures of Scott rank $\omega _1^{CK}+1$ which, after naming finitely many constants, have Scott rank $\omega _1^{CK}$ . The existence of such structures was an open question.

A problem is a multivalued function from a set of instances to a set of solutions. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness property if every computable instance of the problem admits a solution relative to which the property holds. For example, cone avoidance is the ability, given a noncomputable set A and a computable instance of a problem ${\mathsf {P}}$ , to find a solution relative to which A is still noncomputable.

In this article, we compare relativized versions of computability-theoretic notions of preservation which have been studied in reverse mathematics, and prove that the ones which were not already separated by natural statements in the literature actually coincide. In particular, we prove that it is equivalent to admit avoidance of one cone, of $\omega $ cones, of one hyperimmunity or of one non- $\Sigma ^{0}_1$ definition. We also prove that the hierarchies of preservation of hyperimmunity and non- $\Sigma ^{0}_1$ definitions coincide. On the other hand, none of these notions coincide in a nonrelativized setting.

We review the current knowledge concerning strong jump-traceability. We cover the known results relating strong jump-traceability to randomness, and those relating it to degree theory. We also discuss the techniques used in working with strongly jump-traceable sets. We end with a section of open questions.

We show that a Δ02 Turing degree computes solutions to all computable instances of the finite intersection principle if and only if it computes a 1-generic degree. We also investigate finite and infinite variants of the principle.

We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15] (also Problem 5.5.19 in [34]). We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.

Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

Economic evaluations of health interventions pose a particular challenge for reporting. There is also a need to consolidate and update existing guidelines and promote their use in a user friendly manner. The Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement is an attempt to consolidate and update previous health economic evaluation guidelines efforts into one current, useful reporting guidance. The primary audiences for the CHEERS statement are researchers reporting economic evaluations and the editors and peer reviewers assessing them for publication.

The need for new reporting guidance was identified by a survey of medical editors. A list of possible items based on a systematic review was created. A two round, modified Delphi panel consisting of representatives from academia, clinical practice, industry, government, and the editorial community was conducted. Out of 44 candidate items, 24 items and accompanying recommendations were developed. The recommendations are contained in a user friendly, 24 item checklist. A copy of the statement, accompanying checklist, and this report can be found on the ISPOR Health Economic Evaluations Publication Guidelines Task Force website (www.ispor.org/TaskForces/EconomicPubGuidelines.asp).

We hope CHEERS will lead to better reporting, and ultimately, better health decisions. To facilitate dissemination and uptake, the CHEERS statement is being co-published across 10 health economics and medical journals. We encourage other journals and groups, to endorse CHEERS. The author team plans to review the checklist for an update in five years.

Objective: The Israeli National Health Insurance Law stipulates a National List of Health Services (NLHS) to which all residents are entitled from their HMOs. This list has been updated annually for almost a decade using a structured review and decision-making process. Although this process has been described in detail in previous papers, none of these have fully addressed legitimacy and fairness. We examine the legitimacy and fairness of the process of updating the NLHS in Israel.

Methods: We assessed the priority-setting process for compliance with the four conditions of accountability for reasonableness outlined by Daniels and Sabin (relevance, publicity, appeals, and enforcement). These conditions emphasize transparency and stakeholder engagement in democratic deliberation.

Results: Our analysis suggests that the Israeli process for updating the NLHS does not fulfill the appeals and enforcement conditions, and only partially follows the publicity and relevance conditions, outlined in the accountability for reasonableness framework. The main obstacles for achieving these goals may relate to the large number of technologies assessed each year within a short time frame, the lack of personnel engaged in health technology assessment, and the desire for early adoption of new technologies.

Conclusions: The process of updating the NLHS in Israel is unique and not without merit. Changes in the priority-setting process should be made to increase its acceptability among the different stakeholders.

Objectives: The diffusion of cost-utility analyses (CUAs) through the medical literature was examined, documenting visible patterns and determining how they correspond with expectations about the diffusion of process innovations.

Methods: This study used 539 CUAs from a registry. It includes data elements comprising year of publication, the research center in which the study was performed, the clinical area covered by the CUA, and the specific journal. Finally, each paper was assigned to a journal type that could be one of the three categories: health services research, general medicine, or clinical specialty.

Results: When the average number of publications is plotted against time, the plot reveals an S-shaped curve. It appears that, whereas CUAs initially were published more frequently in general medical or health services research journals, there was a clear increase in the diffusion of CUA into subspecialty journals over time. The concentration ratio for research centers as measured by the Herfindhal–Hirschman Index decreased over time.

Conclusions: The spread of CUA through the medical literature follows patterns identified for the diffusion of other new technologies and processes. Future research should focus on what impact this spread has had on the practice of medicine and formulation of health policy.

Objectives: New medical technologies have been identified as the leading cause of increasing health-care expenditures. Adoption of a new technology is one of the most important decisions in medical centers. The objectives of this study were to map and describe the function of hospital decision-makers within the area of new technology assessment and adoption, and to examine relevant considerations, sources of information, and decision-making processes in the adoption of a new technology.

Methods: A questionnaire was mailed to hospital executives and referred to (i) the considerations for and against adoption of a new technology, (ii) the decision-making process, (iii) information sources used in the decision-making process.

Results: The most frequent criteria favoring adoption included increased cost-effectiveness, increased efficacy, and decrease in complication rates. An increase in complication rates or side effects and decreased efficacy were the top ranked criteria against adoption. The final decision-making responsibility varied among technologies; the medical director frequently made the final decision when a new device was involved, but this responsibility decreased when a new drug or a new procedure was considered. Participation in scientific meetings, opinions of local experts, medical journals, and Food and Drug Administration clearance documents were the most important information sources used in the decision-making process. However, these were not necessarily the optimal sources of information. Significant barriers in adoption decision-making are lack of timely data regarding the safety of the new technology, its cost-effectiveness, and efficacy.

Conclusion: To improve the adoption decisions, hospitals must develop criteria upon which the decision-making will be based.

Objectives: This preliminary study had two objectives: a) charting the considerations relevant to decisions about acquisition of new medical technology at the hospital level; and b) creating a basis for the development of a research tool that will examine the function of the Israeli health system in assessment of new medical technologies.

Methods: A comprehensive literature review and in-depth interviews with decision makers at different levels allowed formulation of criteria considered by decision makers when they decide to purchase and use (or disallow the use) of new medical technology. The resulting questionnaire was sent to medical center directors, along with a letter explaining the goals of the study. The questionnaire included 31 possible considerations for decision making concerning the acquisition of new medical technology by medical centers. The interviewees were asked to indicate the relevance of each consideration in the decision-making process.

Results: The most relevant criteria for the adoption of new technologies related to the need for a large capital investment, clinical efficacy of the technology as well as its influence on side effects and complication rates, and a formal approval by the Ministry of Health. Most interviewees stated that pressures exerted by the industry, by patients, or by senior physicians in the hospital are less relevant to decision making. Very small and usually not statistically significant differences in the ranking of hospital directors were found according to the hospitals' ownership, size, or location.

Conclusions: The present study is a basis for a future study that will map and describe the function of hospital decision makers within the area of new technology assessment and the decision-making process in the adoption of new healthcare technologies.

Objectives: The study evaluated the extent to which quality-adjusted life-years (QALYs) and healthy-years equivalents (HYEs) were used in cost-utility studies over the past 20 years (1981–2000) as well as possible changes in the quality of journals reporting cost-utility studies.

Methods: Cost-utility studies were identified through an electronic search. For each study the journal name, date of publication, article's language and research origin, and the journal's impact factor were recorded.

Results: The number of published cost-utility studies increased in the last 20 years but has leveled off in 1997. Most studies were performed in the United States and were published in English. All studies except one used QALYs as an outcome measure. The mean journal's impact factor has changed slightly over the years.

Conclusions: Cost-utility studies would possibly gain more popularity if they were used as a vehicle in the decision-making process regarding healthcare budgets and were more visible in the scientific literature.