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Introduction: This study aimed to study the trend, histologic pattern, geographical distribution, and characteristics of nasopharyngeal carcinoma (NPC) and nasopharyngeal neoplasms (NPN) from 2003 to 2017 in Iran. Materials and Methods: The Ministry of Health and Medical Education collected NPN cases from the corresponding university in each province and stored them in Iran National Cancer Registry (INCR) database. The Joinpoint program calculated the average annual percent change (AAPC) and its 95% confidence interval (CI). The jump model minimized the interfering effect of INCR transformation. Results: 3653 NPN cases were reported between 2003-2010 and 2014-2017, with a mean age of 49.04 ± 18.31 years and a male-to-female ratio of 2.15. The age-standardized incidence rate (ASIR) per 100,000 person-years was 0.30 for females and 0.68 for males in 2017. Although the ASIR/100,000 of NPN raised from 0.35 to 0.49 during 2003-2017, the trend was constant with an AAPC of -2% (95% CI: - 4.8% to 0.9%). The age-specific incidence rate was highest in the older than 70 population (1.56/100,000). NPC formed 77.1% of NPNs and showed a constant pattern (AAPC CI: -5.7% to 0.2%), in contrast to the significant increase of non-keratinizing squamous cell carcinoma (AAPC CI: 2.3% to 24.5%). Conclusions: Nasopharynx cancer is rare in Iran, and NPC incidence remained constant from 2003 to 2017, unlike previously reported rising trend. However, non-keratinizing squamous cell carcinoma exhibited a significant increase, and future studies are needed to examine the role of the Epstein-Barr virus on this growth rate. [ABSTRACT FROM AUTHOR]

Describing the non-stationarity of mixed stochastic jump processes presents a formidable challenge. This study employs a mixed compound Poisson process by Markov switching model (CPMSM) to address the issue of overdispersed data of random jumps. The Poisson rate is governed by a continuous-time Markov chain in this model. By assuming independence of the compound Poisson process and jump sizes, we present a generalized algorithm to estimate the parameters of CPMSM and try to predict the future behavior of this stochastic system. To investigate the potential application of this model and the accuracy of our algorithm, we provide a numerical simulation example in the context of the auto insurance payout scenario. The results suggest that CPMSM is an effective method of describing jump behavior controlled by random counts with mode switching via a Markov chain. Furthermore, we demonstrate a specific application of this model in identifying seismicity levels of Greek earthquake data and identify four hidden states. Finally, we compare its fitting effectiveness with the ETAS model using two public earthquake datasets in Japan and Iran. [ABSTRACT FROM AUTHOR]