Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Incidence trends of colorectal cancer in the early 2000s in Italy. Figures from the IMPATTO study on colorectal cancer screening

We utilised the IMPATTO study's archives to describe the 2000-2008 colorectal cancer (CRC) incidence rate trends in Italy, once screening programmes based on the faecal immunochemical test were implemented in different areas. Data on CRCs diagnosed in Italy from 2000 to 2008 in subjects aged 40-79 years were collected by 23 cancer registries. Incidence rate trends were evaluated as a whole and by macro-area (North-Centre and South-Islands), presence of a screening programme, sex, ten-year age class, anatomic site, stage at diagnosis, and pattern of diagnosis (screen-detected, non-screen-detected). The annual percent change (APC) of incidence rate trends, with 95% confidence intervals (95%CI), were computed. The study included 46,857 CRCs diagnosed in subjects aged 40-79 years, of which 2,806 were screendetected. The incidence rates in the North-Centre were higher than in the South and on the Islands. During the study period, screening programmes had been implemented only in the North-Centre and had a significant effect on incidence rates, with an initial sharp increase in incidence, followed by a decrease that started in the 3rd-4th years of screening. These incidence rate trends were exclusively due to modifications in the rates of stage I cases. After screening programmes started, incidence increased in all anatomic sites, particularly in the distal colon. The differential figures introduced by the implementation of screening programmes warrant a continuous surveillance of CRC incidence and mortality trends to monitor the impact of screening at a national level

ITALIAN CANCER FIGURES - REPORT 2015: The burden of rare cancers in Italy = I TUMORI IN ITALIA - RAPPORTO 2015: I tumori rari in Italia

OBJECTIVES: This collaborative study, based on data collected by the network of Italian Cancer Registries (AIRTUM), describes the burden of rare cancers in Italy. Estimated number of new rare cancer cases yearly diagnosed (incidence), proportion of patients alive after diagnosis (survival), and estimated number of people still alive after a new cancer diagnosis (prevalence) are provided for about 200 different cancer entities. MATERIALS AND METHODS: Data herein presented were provided by AIRTUM population- based cancer registries (CRs), covering nowadays 52% of the Italian population. This monograph uses the AIRTUM database (January 2015), which includes all malignant cancer cases diagnosed between 1976 and 2010. All cases are coded according to the International Classification of Diseases for Oncology (ICD-O-3). Data underwent standard quality checks (described in the AIRTUM data management protocol) and were checked against rare-cancer specific quality indicators proposed and published by RARECARE and HAEMACARE (www.rarecarenet.eu; www.haemacare.eu). The definition and list of rare cancers proposed by the RARECAREnet "Information Network on Rare Cancers" project were adopted: rare cancers are entities (defined as a combination of topographical and morphological codes of the ICD-O-3) having an incidence rate of less than 6 per 100,000 per year in the European population. This monograph presents 198 rare cancers grouped in 14 major groups. Crude incidence rates were estimated as the number of all new cancers occurring in 2000-2010 divided by the overall population at risk, for males and females (also for gender-specific tumours).The proportion of rare cancers out of the total cancers (rare and common) by site was also calculated. Incidence rates by sex and age are reported. The expected number of new cases in 2015 in Italy was estimated assuming the incidence in Italy to be the same as in the AIRTUM area. One- and 5-year relative survival estimates of cases aged 0-99 years diagnosed between 2000 and 2008 in the AIRTUM database, and followed up to 31 December 2009, were calculated using complete cohort survival analysis. To estimate the observed prevalence in Italy, incidence and follow-up data from 11 CRs for the period 1992-2006 were used, with a prevalence index date of 1 January 2007. Observed prevalence in the general population was disentangled by time prior to the reference date (≤2 years, 2-5 years, ≤15 years). To calculate the complete prevalence proportion at 1 January 2007 in Italy, the 15-year observed prevalence was corrected by the completeness index, in order to account for those cancer survivors diagnosed before the cancer registry activity started. The completeness index by cancer and age was obtained by means of statistical regression models, using incidence and survival data available in the European RARECAREnet data. RESULTS: In total, 339,403 tumours were included in the incidence analysis. The annual incidence rate (IR) of all 198 rare cancers in the period 2000-2010 was 147 per 100,000 per year, corresponding to about 89,000 new diagnoses in Italy each year, accounting for 25% of all cancer. Five cancers, rare at European level, were not rare in Italy because their IR was higher than 6 per 100,000; these tumours were: diffuse large B-cell lymphoma and squamous cell carcinoma of larynx (whose IRs in Italy were 7 per 100,000), multiple myeloma (IR: 8 per 100,000), hepatocellular carcinoma (IR: 9 per 100,000) and carcinoma of thyroid gland (IR: 14 per 100,000). Among the remaining 193 rare cancers, more than two thirds (No. 139) had an annual IR <0.5 per 100,000, accounting for about 7,100 new cancers cases; for 25 cancer types, the IR ranged between 0.5 and 1 per 100,000, accounting for about 10,000 new diagnoses; while for 29 cancer types the IR was between 1 and 6 per 100,000, accounting for about 41,000 new cancer cases. Among all rare cancers diagnosed in Italy, 7% were rare haematological diseases (IR: 41 per 100,000), 18% were solid rare cancers. Among the latter, the rare epithelial tumours of the digestive system were the most common (23%, IR: 26 per 100,000), followed by epithelial tumours of head and neck (17%, IR: 19) and rare cancers of the female genital system (17%, IR: 17), endocrine tumours (13% including thyroid carcinomas and less than 1% with an IR of 0.4 excluding thyroid carcinomas), sarcomas (8%, IR: 9 per 100,000), central nervous system tumours and rare epithelial tumours of the thoracic cavity (5%with an IR equal to 6 and 5 per 100,000, respectively). The remaining (rare male genital tumours, IR: 4 per 100,000; tumours of eye, IR: 0.7 per 100,000; neuroendocrine tumours, IR: 4 per 100,000; embryonal tumours, IR: 0.4 per 100,000; rare skin tumours and malignant melanoma of mucosae, IR: 0.8 per 100,000) each constituted <4% of all solid rare cancers. Patients with rare cancers were on average younger than those with common cancers. Essentially, all childhood cancers were rare, while after age 40 years, the common cancers (breast, prostate, colon, rectum, and lung) became increasingly more frequent. For 254,821 rare cancers diagnosed in 2000-2008, 5-year RS was on average 55%, lower than the corresponding figures for patients with common cancers (68%). RS was lower for rare cancers than for common cancers at 1 year and continued to diverge up to 3 years, while the gap remained constant from 3 to 5 years after diagnosis. For rare and common cancers, survival decreased with increasing age. Five-year RS was similar and high for both rare and common cancers up to 54 years; it decreased with age, especially after 54 years, with the elderly (75+ years) having a 37% and 20% lower survival than those aged 55-64 years for rare and common cancers, respectively. We estimated that about 900,000 people were alive in Italy with a previous diagnosis of a rare cancer in 2010 (prevalence). The highest prevalence was observed for rare haematological diseases (278 per 100,000) and rare tumours of the female genital system (265 per 100,000). Very low prevalence (<10 prt 100,000) was observed for rare epithelial skin cancers, for rare epithelial tumours of the digestive system and rare epithelial tumours of the thoracic cavity. COMMENTS: One in four cancers cases diagnosed in Italy is a rare cancer, in agreement with estimates of 24% calculated in Europe overall. In Italy, the group of all rare cancers combined, include 5 cancer types with an IR>6 per 100,000 in Italy, in particular thyroid cancer (IR: 14 per 100,000).The exclusion of thyroid carcinoma from rare cancers reduces the proportion of them in Italy in 2010 to 22%. Differences in incidence across population can be due to the different distribution of risk factors (whether environmental, lifestyle, occupational, or genetic), heterogeneous diagnostic intensity activity, as well as different diagnostic capacity; moreover heterogeneity in accuracy of registration may determine some minor differences in the account of rare cancers. Rare cancers had worse prognosis than common cancers at 1, 3, and 5 years from diagnosis. Differences between rare and common cancers were small 1 year after diagnosis, but survival for rare cancers declined more markedly thereafter, consistent with the idea that treatments for rare cancers are less effective than those for common cancers. However, differences in stage at diagnosis could not be excluded, as 1- and 3-year RS for rare cancers was lower than the corresponding figures for common cancers. Moreover, rare cancers include many cancer entities with a bad prognosis (5-year RS <50%): cancer of head and neck, oesophagus, small intestine, ovary, brain, biliary tract, liver, pleura, multiple myeloma, acute myeloid and lymphatic leukaemia; in contrast, most common cancer cases are breast, prostate, and colorectal cancers, which have a good prognosis. The high prevalence observed for rare haematological diseases and rare tumours of the female genital system is due to their high incidence (the majority of haematological diseases are rare and gynaecological cancers added up to fairly high incidence rates) and relatively good prognosis. The low prevalence of rare epithelial tumours of the digestive system was due to the low survival rates of the majority of tumours included in this group (oesophagus, stomach, small intestine, pancreas, and liver), regardless of the high incidence rate of rare epithelial cancers of these sites. This AIRTUM study confirms that rare cancers are a major public health problem in Italy and provides quantitative estimations, for the first time in Italy, to a problem long known to exist. This monograph provides detailed epidemiologic indicators for almost 200 rare cancers, the majority of which (72%) are very rare (IR<0.5 per 100,000). These data are of major interest for different stakeholders. Health care planners can find useful information herein to properly plan and think of how to reorganise health care services. Researchers now have numbers to design clinical trials considering alternative study designs and statistical approaches. Population-based cancer registries with good quality data are the best source of information to describe the rare cancer burden in a population

Non-central moderate deviations for compound fractional Poisson processes

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about non-central moderate deviations when the weak convergence is towards a non-Gaussian distribution. In this paper we study noncentral moderate deviations for compound fractional Poisson processes with light-tailed jumps

Large deviation results on some estimators for stationary Gaussian processes

In this paper, we present large deviation results for estimators of some unknown parameters concerning stationary Gaussian processes. We deal with both maximum likelihood estimators and posterior distributions; moreover, we illustrate the differences between short-range- and long-range-dependent processes. As a typical feature the rate functions for maximum likelihood estimators and posterior distributions are given in terms of the same relative entropy and the roles of the two probability measures in the relative entropy are exchanged. We define a sort of relative entropy with respect to the sampling process which in the i.i.d. case corresponds to the relative entropy with respect to the common law of each single sample. In view of potential applications in risk theory we prove large deviation results for estimators of the logarithmic asymptotic decay rate of the tail of the supremum of a random walk with stationary Gaussian increments. Finally, we present results for compound renewal processes with stationary Gaussian distributed rewards, independent of i.i.d.Weibull distributed renewal times

Non-central moderate deviations for compound fractional Poisson processes

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about non-central moderate deviations when the weak convergence is towards a non-Gaussian distribution. In this paper we study non-central moderate deviations for compound fractional Poisson processes with light-tailed jumps

Censored Exponential Data: Large Deviations for MLEs and Posterior Distributions

In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models

Censured Exponential data: large deviations for MLEs and posterior distributions

In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models

Mixtures of conjugate prior distributions and large deviations for level crossing probabilities

In this paper we present asymptotic estimates of level crossing probabilities from a Bayesian point of view, based on large deviations. For the Bayesian analysis we choose a finite mixture of conjugate prior distributions to model the uncertainty on the unknown parameters of the two classes of stochastic processes considered: the Brownian motion and the compound Poisson process with upward jumps and negative drift. The estimates of level crossing probabilities are derived as a consequence of large deviation principles for posterior distributions