SUMMARY There are many practical problems where the observed data are not drawn directly from the density g of real interest, but rather from another distribution derived from g by the application of an integral operator. The estimation of g then entails both statistical and numerical difficulties. A natural statistical approach is by maximum likelihood, conveniently implemented using the EM algorithm, but this provides unsatisfactory reconstructions of g. In this paper, we modify the maximum likelihood–EM approach by introducing a simple smoothing step at each EM iteration. In our experience, this algorithm converges in relatively few iterations to good estimates of g that do not depend on the choice of starting configuration. Some theoretical background is given that relates this smoothed EM algorithm to a maximum penalized likelihood approach. Two applications are considered in detail. The first is the classical stereology problem of determining particle size distributions from data collected on a plane section through a composite medium. The second concerns the recovery of the structure of a section of the human body from external observations obtained by positron emission tomography; for this problem, we also suggest several technical improvements on existing methodology.

Even within a low-income renter sample, Low Income Home Energy Assistance Program benefits seem to reach families at the highest social and medical risk with more food insecurity and higher rates of low birth-weight children. Nevertheless, after adjustment for differences in background risk, living in a household receiving the Low Income Home Energy Assistance Program is associated with less anthropometric evidence of undernutrition, no evidence of increased overweight, and lower odds of acute hospitalization from an emergency department visit among young children in low-income renter households compared with children in comparable households not receiving the Low Income Home Energy Assistance Program. The Low Income Home Energy Assistance Program in many states shuts down early each winter when their funding is exhausted. From a clinical perspective, pediatric health providers caring for children from impoverished families should consider encouraging families of these children to apply for the Low Income Home Energy Assistance Program early in the season before funding is depleted. From a public policy perspective, although this cross-sectional study design can only demonstrate associations and not causation, these findings suggest that, particularly as fuel costs and children's poverty rates increase, expanding the Low Income Home Energy Assistance Program funding and meeting the national Low Income Home Energy Assistance Program performance goal of increasing the percentage of recipient households with young children might potentially benefit such children's growth and health.

Medicine residents are aware of naloxone and willing to prescribe it to at-risk patients. Due to decreased applied knowledge and limited self-efficacy, few residents have prescribed naloxone in the past. In order to improve rates of physician prescribing, initiatives must help physicians better assess risk of overdose and improve prescribing self-efficacy.

In the United States, race-based disparities in cardiovascular disease care have proven to be pervasive, deadly, and expensive. African American/Black, Hispanic/Latinx, and Native/Indigenous American individuals are at an increased risk of cardiovascular disease and are less likely to receive high-quality, evidence-based medical care as compared with their White American counterparts. Although the United States population is diverse, the cardiovascular workforce that provides its much-needed care lacks diversity. The available data show that care provided by physicians from racially diverse backgrounds is associated with better quality, both for minoritized patients and for majority patients. Not only is cardiovascular workforce diversity associated with improvements in health care quality, but racial diversity among academic teams and research scientists is linked with research quality. We outline documented barriers to achieving workforce diversity and suggest evidence-based strategies to overcome these barriers. Key strategies to enhance racial diversity in cardiology include improving recruitment and retention of racially diverse members of the cardiology workforce and focusing on cardiovascular health equity for patients. This review draws attention to academic institutions, but the implications should be considered relevant for nonacademic and community settings as well.