Objectives: This study presents a trend analysis of Medication‐Related Osteonecrosis of the Jaw (MRONJ) using US National Inpatient Sample (NIS) data from 2016 to 2022, providing insights into its epidemiology, comorbidities, and economics. Methods: A retrospective cross‐sectional analysis was performed using US MRONJ hospital admissions. Prevalence rates were calculated relative to Bisphosphonate patient numbers in the United States and hospital‐based denominators. Statistical analyses included two‐sample proportion ( Z ) tests, Cochran–Armitage trend tests, Welch t ‐tests, and multivariable linear and ANOVA models with false discovery rate (FDR) correction for multiple comparisons, effect sizes, market basket analysis. Results: Cochran–Armitage trend tests revealed significant increasing trends in MRONJ prevalence across all denominators: total NIS hospitalizations ( p = 0.037), dental‐related hospitalizations ( p = 0.012), and bisphosphonate‐exposed patients ( p < 0.001). Females were more affected with MRONJ than males consistently across all years ( p = 0.188). Whites had the highest number of cases across all years ( p = 0.774). No region or income bracket stood out as highest or lowest. Medicare is the primary payer with 61%–80% of patients covered ( p = 0.497). The average age of patients is around 70 years across all years. The average length of stay in the hospital ranged from 4 to 8 days and the average daily charges ranged from $15,000 to $20,000. Hypertension is the most common co‐morbidity (except 2018). Conclusion: The study highlights the incidence of MRONJ, its demographic disparities, economics, and the need for enhanced prevention and cost‐effective management strategies.
We take up a British TV game in its final round. Three contestants choose an integer from 0 to 10000 independently. One of the contestants wins if the chosen numbers are distinct and the chosen number of the contestant is in between the other chosen numbers. The winning amount is the winning number in British pounds. In this paper, we discuss distributions on {0, 1, 2, ..., 10000} the contestants can use for selecting numbers. We show that the Uniform Distribution is optimal maximizing the probability of selections being distinct. We generalize the problem to the continuous case.