Quantum Information Entropy for a Hyperbolic Double Well Potential in the Fractional Schrödinger Equation.

In this study, we investigate the position and momentum Shannon entropy, denoted as Sx and Sp, respectively, in the context of the fractional Schrödinger equation (FSE) for a hyperbolic double well potential (HDWP). We explore various values of the fractional derivative represented by k in our analysis. Our findings reveal intriguing behavior concerning the localization properties of the position entropy density, ρs(x), and the momentum entropy density, ρs(p), for low-lying states. Specifically, as the fractional derivative k decreases, ρs(x) becomes more localized, whereas ρs(p) becomes more delocalized. Moreover, we observe that as the derivative k decreases, the position entropy Sx decreases, while the momentum entropy Sp increases. In particular, the sum of these entropies consistently increases with decreasing fractional derivative k. It is noteworthy that, despite the increase in position Shannon entropy Sx and the decrease in momentum Shannon entropy Sp with an increase in the depth u of the HDWP, the Beckner-Bialynicki-Birula-Mycielski (BBM) inequality relation remains satisfied. Furthermore, we examine the Fisher entropy and its dependence on the depth u of the HDWP and the fractional derivative k. Our results indicate that the Fisher entropy increases as the depth u of the HDWP is increased and the fractional derivative k is decreased.

Triaging women with human papillomavirus infection and normal cytology or low-grade dyskaryosis: evidence from 10-year follow up of the ARTISTIC trial cohort.

OBJECTIVES: To estimate long-term cervical intraepithelial neoplasia grade 3 (CIN3) risks associated with different triage strategies for human papillomavirus positive (HPV+) women with a view to reducing unnecessary referrals. DESIGN: The ARTISTIC trial cohort was recruited in Manchester in 2001-03 and was followed up for CIN3 and cancer notification through national registration until December 2015. RESULTS: The 10-year cumulative risk of CIN3+ was much higher for women with HPV16/18 infection (19.4%, 95% CI 15.8-23.8% with borderline/low-grade cytology and 10.7%, 95% CI 8.3-13.9% with normal cytology) than for those with other HPV types (7.3%, 95% CI 5.4-9.7% with borderline/low-grade cytology and 3.2%, 95% CI 2.2-4.5% with normal cytology). Among the 379 women with normal to low-grade cytology and new HPV infection, the 10-year cumulative CIN3+ risk was 2.9% (95% CI 1.6-5.2%). CONCLUSIONS: The CIN3 risk is confined to women with persistent type-specific HPV so partial genotyping test assays identifying HPV16/18 as a minimum are essential for efficient risk stratification. Immediate referral to colposcopy for HPV+ women with borderline or low-grade cytology and referral after a year if still HPV+ with normal cytology may be unnecessary. Low-grade lesions can safely be retested to identify those with persistent HPV. Recall intervals of 1 year for HPV16/18 and 2 years for other high-risk HPVs are justified for women with normal cytology and might also be considered for women with borderline/low-grade cytology. The minimal risk of invasive cancer that has progressed beyond stage 1A must be weighed against the advantages for patients and the NHS of reducing the number of referrals to colposcopy. TWEETABLE ABSTRACT: Cervical screening would be better for women and cheaper for the NHS if women with HPV and normal to low-grade cytology were retested after a year or two when many infections will have cleared.

High constant incidence in twins and other relatives of women with breast cancer.

The incidence of breast cancer rises steeply between ages 25 and 50, and more slowly thereafter. In contrast, the incidence in the unaffected (contralateral) breast of women who have had breast cancer remains constant at about 0.7% per year for at least the next 20 years after diagnosis, irrespective of age at first diagnosis. The incidence in relatives of the patients seems to show a similar pattern. The incidence in a prospective study of monozygotic twins of patients was approximately constant at 1.3% per year (77 cases), again about 0.7% per breast. At ages older than a patient's age at diagnosis, her mother and sisters have an incidence of 0.3-0.4% per year. Above the index patient's age at diagnosis, the rate in relatives shows no temporal trend and is independent of the patient's age at diagnosis. A statistically simple explanation is that incidence in susceptible women increases to a high constant level by a predetermined age that varies between families, but this seems inconsistent with conventional models of carcinogenesis and susceptibility. The very high incidence in monozygotic twins of patients indicates that a high proportion, and perhaps the majority, of breast cancers arise in a susceptible minority of women.

That the effects of smoking should be measured in pack-years: misconceptions 4.

Lung cancer incidence in smokers is roughly proportional to dose rate (cigarettes per day) but increases much more rapidly with duration of smoking. The assumption that the incidence rate is proportional to total lifetime dose (the product of dose rate and duration) has been known to be wrong for many years, but total dose in pack-years is still often included, either alone or together, with more fundamental parameters such as dose rate, in regression analysis of epidemiological data. This is mathematically unnecessary and scientifically unhelpful.

Estimating the asbestos-related lung cancer burden from mesothelioma mortality.

BACKGROUND: Quantifying the asbestos-related lung cancer burden is difficult in the presence of this disease's multiple causes. We explore two methods to estimate this burden using mesothelioma deaths as a proxy for asbestos exposure. METHODS: From the follow-up of 55 asbestos cohorts, we estimated ratios of (i) absolute number of asbestos-related lung cancers to mesothelioma deaths; (ii) excess lung cancer relative risk (%) to mesothelioma mortality per 1000 non-asbestos-related deaths. RESULTS: Ratios varied by asbestos type; there were a mean 0.7 (95% confidence interval 0.5, 1.0) asbestos-related lung cancers per mesothelioma death in crocidolite cohorts (n=6 estimates), 6.1 (3.6, 10.5) in chrysotile (n=16), 4.0 (2.8, 5.9) in amosite (n=4) and 1.9 (1.4, 2.6) in mixed asbestos fibre cohorts (n=31). In a population with 2 mesothelioma deaths per 1000 deaths at ages 40-84 years (e.g., US men), the estimated lung cancer population attributable fraction due to mixed asbestos was estimated to be 4.0%. CONCLUSION: All types of asbestos fibres kill at least twice as many people through lung cancer than through mesothelioma, except for crocidolite. For chrysotile, widely consumed today, asbestos-related lung cancers cannot be robustly estimated from few mesothelioma deaths and the latter cannot be used to infer no excess risk of lung or other cancers.

That lung cancer incidence falls in ex-smokers: misconceptions 2.

Misconceptions and ill-founded theories can arise in all areas of science. However, the apparent accessibility of many epidemiology findings and popular interest in the subject can lead to additional misunderstandings. The article below continues an occasional series of short editorials highlighting some current misinterpretations of epidemiological findings. Invited authors will be given wide scope in judging the prevalence of the misconception under discussion. We hope that this series will prove instructive to cancer researchers in other disciplines as well as to students of epidemiology. Adrian L Harris and Leo Kinlen.

Evaluation of variation in the phosphoinositide-3-kinase catalytic subunit alpha oncogene and breast cancer risk.

BACKGROUND: Somatic mutations in phosphoinositide-3-kinase catalytic subunit alpha (PIK3CA) are frequent in breast tumours and have been associated with oestrogen receptor (ER) expression, human epidermal growth factor receptor-2 overexpression, lymph node metastasis and poor survival. The goal of this study was to evaluate the association between inherited variation in this oncogene and risk of breast cancer. METHODS: A single-nucleotide polymorphism from the PIK3CA locus that was associated with breast cancer in a study of Caucasian breast cancer cases and controls from the Mayo Clinic (MCBCS) was genotyped in 5436 cases and 5280 controls from the Cancer Genetic Markers of Susceptibility (CGEMS) study and in 30 949 cases and 29 788 controls from the Breast Cancer Association Consortium (BCAC). RESULTS: Rs1607237 was significantly associated with a decreased risk of breast cancer in MCBCS, CGEMS and all studies of white Europeans combined (odds ratio (OR)=0.97, 95% confidence interval (CI) 0.95-0.99, P=4.6 × 10(-3)), but did not reach significance in the BCAC replication study alone (OR=0.98, 95% CI 0.96-1.01, P=0.139). CONCLUSION: Common germline variation in PIK3CA does not have a strong influence on the risk of breast cancer.

Optimal threshold for a positive hybrid capture 2 test for detection of human papillomavirus: data from the ARTISTIC trial.

We present data on the use of the Hybrid Capture 2 (HC2) test for the detection of high-risk human papillomavirus (HR HPV) with different thresholds for positivity within a primary screening setting and as a method of triage for low-grade cytology. In the ARTISTIC population-based trial, 18,386 women were screened by cytology and for HPV. Cervical intraepithelial neoplasia lesions of grade two and higher (CIN2+ lesions) were identified for 453 women within 30 months of an abnormal baseline sample. When a relative light unit/cutoff (RLU/Co) ratio of > or = 1 was used as the threshold for considering an HC2 result positive, 15.6% of results were positive, and the proportion of CIN2+ lesions in this group was 14.7%. The relative sensitivity for CIN2+ lesion detection was 93.4%. When an RLU/Co ratio of > or = 2 was used as the threshold, there was a 2.5% reduction in positivity, with an increase in the proportion of CIN2+ lesions detected. The relative sensitivity decreased slightly, to 90.3%. Among women with low-grade cytology, HPV prevalences were 43.7% and 40.3% at RLU/Co ratios of > or = 1 and > or = 2, respectively. The proportions of CIN2+ lesions detected were 17.3% and 18.0%, with relative sensitivities of 87.7% at an RLU/Co ratio of > or = 1 and 84.2% at an RLU/Co ratio of > or = 2. At an RLU/Co ratio of > or = 1, 68.3% of HC2-positive results were confirmed by the Roche line blot assay, compared to 77.2% of those at an RLU/Co ratio of > or = 2. Fewer HC2-positive results were confirmed for 35- to 64-year-olds (50.3% at an RLU/Co ratio of > or = 1 and 63.2% at an RLU/Co ratio of > 2) than for 20- to 34-year-olds (78.7% at an RLU/Co ratio of > or = 1 and 83.7% at an RLU/Co ratio of > 2). If the HC2 test is used for routine screening as an initial test or as a method of triage for low-grade cytology, we would suggest increasing the threshold for positivity from the RLU/Co ratio of > or = 1, recommended by the manufacturer, to an RLU/Co ratio of > or = 2, since this study has shown that a beneficial balance between relative sensitivity and the proportion of CIN2+ lesions detected is achieved at this threshold.

Occupational, domestic and environmental mesothelioma risks in the British population: a case-control study.

We obtained lifetime occupational and residential histories by telephone interview with 622 mesothelioma patients (512 men, 110 women) and 1420 population controls. Odds ratios (ORs) were converted to lifetime risk (LR) estimates for Britons born in the 1940s. Male ORs (95% confidence interval (CI)) relative to low-risk occupations for >10 years of exposure before the age of 30 years were 50.0 (25.8-96.8) for carpenters (LR 1 in 17), 17.1 (10.3-28.3) for plumbers, electricians and painters, 7.0 (3.2-15.2) for other construction workers, 15.3 (9.0-26.2) for other recognised high-risk occupations and 5.2 (3.1-8.5) in other industries where asbestos may be encountered. The LR was similar in apparently unexposed men and women (approximately 1 in 1000), and this was approximately doubled in exposed workers' relatives (OR 2.0, 95% CI 1.3-3.2). No other environmental hazards were identified. In all, 14% of male and 62% of female cases were not attributable to occupational or domestic asbestos exposure. Approximately half of the male cases were construction workers, and only four had worked for more than 5 years in asbestos product manufacture.

Runs of homozygosity and testicular cancer risk.

BACKGROUND: Testicular germ cell tumour (TGCT) is highly heritable but > 50% of the genetic risk remains unexplained. Epidemiological observation of greater relative risk to brothers of men with TGCT compared to sons has long alluded to recessively acting TGCT genetic susceptibility factors, but to date none have been reported. Runs of homozygosity (RoH) are a signature indicating underlying recessively acting alleles and have been associated with increased risk of other cancer types. OBJECTIVE: To examine whether RoH are associated with TGCT risk. METHODS: We performed a genome-wide RoH analysis using GWAS data from 3206 TGCT cases and 7422 controls uniformly genotyped using the OncoArray platform. RESULTS: Global measures of homozygosity were not significantly different between cases and controls, and the frequency of individual consensus RoH was not significantly different between cases and controls, after correction for multiple testing. RoH at three regions, 11p13-11p14.3, 5q14.1-5q22.3 and 13q14.11-13q.14.13, were, however, nominally statistically significant at p < 0.01. Intriguingly, RoH200 at 11p13-11p14.3 encompasses Wilms tumour 1 (WT1), a recognized cancer susceptibility gene with roles in sex determination and developmental transcriptional regulation, processes repeatedly implicated in TGCT aetiology. DISCUSSION AND CONCLUSION: Overall, our data do not support a major role in the risk of TGCT for recessively acting alleles acting through homozygosity, as measured by RoH in outbred populations of cases and controls.

Prevalence of type-specific HPV infection by age and grade of cervical cytology: data from the ARTISTIC trial.

Human papillomavirus (HPV) infection causes cervical cancer and premalignant dysplasia. Type-specific HPV prevalence data provide a basis for assessing the impact of HPV vaccination programmes on cervical cytology. We report high-risk HPV (HR-HPV) type-specific prevalence data in relation to cervical cytology for 24,510 women (age range: 20-64; mean age 40.2 years) recruited into the ARTISTIC trial, which is being conducted within the routine NHS Cervical Screening Programme in Greater Manchester. The most common HR-HPV types were HPV16, 18, 31, 51 and 52, which accounted for 60% of all HR-HPV types detected. There was a marked decline in the prevalence of HR-HPV infection with age, but the proportion due to each HPV type did not vary greatly with age. Multiple infections were common below the age of 30 years but less so between age 30 and 64 years. Catch-up vaccination of this sexually active cohort would be expected to reduce the number of women with moderate or worse cytology by 45%, but the number with borderline or mild cytology would fall by only 7%, giving an overall reduction of 12% in the number of women with abnormal cytology and 27% in the number with any HR-HPV infection. In the absence of broader cross-protection, the large majority of low-grade and many high-grade abnormalities may still occur in sexually active vaccinated women.

The BOADICEA model of genetic susceptibility to breast and ovarian cancers: updates and extensions.

Multiple genetic loci confer susceptibility to breast and ovarian cancers. We have previously developed a model (BOADICEA) under which susceptibility to breast cancer is explained by mutations in BRCA1 and BRCA2, as well as by the joint multiplicative effects of many genes (polygenic component). We have now updated BOADICEA using additional family data from two UK population-based studies of breast cancer and family data from BRCA1 and BRCA2 carriers identified by 22 population-based studies of breast or ovarian cancer. The combined data set includes 2785 families (301 BRCA1 positive and 236 BRCA2 positive). Incidences were smoothed using locally weighted regression techniques to avoid large variations between adjacent intervals. A birth cohort effect on the cancer risks was implemented, whereby each individual was assumed to develop cancer according to calendar period-specific incidences. The fitted model predicts that the average breast cancer risks in carriers increase in more recent birth cohorts. For example, the average cumulative breast cancer risk to age 70 years among BRCA1 carriers is 50% for women born in 1920-1929 and 58% among women born after 1950. The model was further extended to take into account the risks of male breast, prostate and pancreatic cancer, and to allow for the risk of multiple cancers. BOADICEA can be used to predict carrier probabilities and cancer risks to individuals with any family history, and has been implemented in a user-friendly Web-based program (http://www.srl.cam.ac.uk/genepi/boadicea/boadicea_home.html).

Persisting risk of nickel related lung cancer and nasal cancer among Clydach refiners.

OBJECTIVE: To evaluate the risk of lung cancer and nasal cancer among workers employed at the Clydach nickel refinery, South Wales since 1930 by combining data from the two most recently published papers on this cohort. METHODS: Observed and expected numbers of cancer deaths were extracted for workers who had a minimum of five years service and were employed for the first time between 1902 and 1992. Standardised mortality ratios (SMR) were calculated for subgroups according to year of employment, time since first employment, and process work. RESULTS: A persisting excess of respiratory cancer was found for workers employed in the period 1930-92, with a lung cancer SMR of 133 (95% CI 103 to 172) and a SMR for nasal cancer of 870 (95% CI 105 to 3141). The lung cancer excess was most clearly seen 20 years or more after first employment and seemed to be confined to process workers. There was no indication of a further reduction in risk since 1930. CONCLUSION: The extreme nickel related cancer hazard at the refinery before 1920 was greatly reduced during subsequent years. Some of the carcinogenic exposures seem to have remained after 1930, producing an elevated risk of nasal cancer and a 30% excess of lung cancer in the workforce. There was evidence of a persisting risk among process workers first employed since 1953.

Breast and ovarian cancer risks to carriers of the BRCA1 5382insC and 185delAG and BRCA2 6174delT mutations: a combined analysis of 22 population based studies.

A recent report estimated the breast cancer risks in carriers of the three Ashkenazi founder mutations to be higher than previously published estimates derived from population based studies. In an attempt to confirm this, the breast and ovarian cancer risks associated with the three Ashkenazi founder mutations were estimated using families included in a previous meta-analysis of populatrion based studies. The estimated breast cancer risks for each of the founder BRCA1 and BRCA2 mutations were similar to the corresponding estimates based on all BRCA1 or BRCA2 mutations in the meta-analysis. These estimates appear to be consistent with the observed prevalence of the mutations in the Ashkenazi Jewish population.

Models for respiratory cancer in nickel refinery workers.

Lung and nasal sinus cancer death rates among employees of a nickel refinery in South Wales were examined from the standpoint of quantifying the relationship between exposure and the risk of these two cancers. Areas in the refinery associated with high risk were identified by using a matched case-control approach, and a simple index of exposure for each man was constructed accordingly based on the duration of time spent in these areas. The dependence of relative risk and absolute excess risk for lung and nasal sinus cancers on age at first employment, calendar period of first employment, time since first employment, and duration of exposure in high-risk areas was then analyzed. The relative risk for nasal sinus cancer increased sharply with increasing age at first exposure but remained roughly constant throughout the period of follow-up, while that for lung cancer was independent of age at first exposure and dropped sharply with increasing time since first employment. The implications and limitations of these analyses are discussed in relation to the multistage theory of carcinogenesis and occupational risk assessment.

Prevalence of human papillomavirus in cervical cancer: a worldwide perspective. International biological study on cervical cancer (IBSCC) Study Group.

BACKGROUND: Epidemiologic studies have shown that the association of genital human papillomavirus (HPV) with cervical cancer is strong, independent of other risk factors, and consistent in several countries. There are more than 20 different cancer-associated HPV types, but little is known about their geographic variation. PURPOSE: Our aim was to determine whether the association between HPV infection and cervical cancer is consistent worldwide and to investigate geographic variation in the distribution of HPV types. METHODS: More than 1000 specimens from sequential patients with invasive cervical cancer were collected and stored frozen at 32 hospitals in 22 countries. Slides from all patients were submitted for central histologic review to confirm the diagnosis and to assess histologic characteristics. We used polymerase chain reaction-based assays capable of detecting more than 25 different HPV types. A generalized linear Poisson model was fitted to the data on viral type and geographic region to assess geographic heterogeneity. RESULTS: HPV DNA was detected in 93% of the tumors, with no significant variation in HPV positivity among countries. HPV 16 was present in 50% of the specimens, HPV 18 in 14%, HPV 45 in 8%, and HPV 31 in 5%. HPV 16 was the predominant type in all countries except Indonesia, where HPV 18 was more common. There was significant geographic variation in the prevalence of some less common virus types. A clustering of HPV 45 was apparent in western Africa, while HPV 39 and HPV 59 were almost entirely confined to Central and South America. In squamous cell tumors, HPV 16 predominated (51% of such specimens), but HPV 18 predominated in adenocarcinomas (56% of such tumors) and adenosquamous tumors (39% of such tumors). CONCLUSIONS: Our results confirm the role of genital HPVs, which are transmitted sexually, as the central etiologic factor in cervical cancer worldwide. They also suggest that most genital HPVs are associated with cancer, at least occasionally. IMPLICATION: The demonstration that more than 20 different genital HPV types are associated with cervical cancer has important implications for cervical cancer-prevention strategies that include the development of vaccines targeted to genital HPVs.

Prevalence of BRCA1 and BRCA2 gene mutations in patients with early-onset breast cancer.

BACKGROUND: Mutations in the BRCA1 and BRCA2 genes are found in most families with cases of both breast and ovarian cancer or with many cases of early-onset breast cancer. However, in an outbred population, the prevalence of BRCA1 and BRCA2 mutations in patients with breast cancer who were unselected for a family history of this disease has not been determined. METHODS: Mutations in the BRCA1 and BRCA2 genes were detected in blood samples from two population-based series of young patients with breast cancer from Britain. RESULTS: Mutations were detected in 15 (5.9%) of 254 women diagnosed with breast cancer before age 36 years (nine [3.5%] in BRCA1 and six [2.4%] in BRCA2) and in 15 (4.1%) of 363 women diagnosed from ages 36 through 45 years (seven [1.9%] in BRCA1 and eight [2.2%] in BRCA2). Eleven percent (six of 55) of patients with a first-degree relative who developed ovarian cancer or breast cancer by age 60 years were mutation carriers, compared with 45% (five of 11) of patients with two or more affected first- or second-degree relatives. The standardized incidence ratio for breast cancer in mothers and sisters was 365 (five observed and 1.37 expected) for 30 mutation carriers and 199 (64 observed and 32.13 expected) for 587 noncarriers. If we assume recent penetrance estimates, the respective proportions of BRCA1 and BRCA2 mutation carriers are 3.1% and 3.0%, respectively, of patients with breast cancer who are younger than age 50 years, 0.49% and 0.84% of patients with breast cancer who are age 50 years or older, and 0.11% and 0.12% of women in the general population. CONCLUSIONS: Mutations in the BRCA1 and BRCA2 genes make approximately equal contributions to early-onset breast cancer in Britain and account for a small proportion of the familial risk of breast cancer.

Multifactorial analysis of differences between sporadic breast cancers and cancers involving BRCA1 and BRCA2 mutations.

BACKGROUND: We have previously demonstrated that breast cancers associated with inherited BRCA1 and BRCA2 gene mutations differ from each other in their histopathologic appearances and that each of these types differs from breast cancers in patients unselected for family history (i.e., sporadic cancers). We have now conducted a more detailed examination of cytologic and architectural features of these tumors. METHODS: Specimens of tumor tissue (5-microm-thick sections) were examined independently by two pathologists, who were unaware of the case or control subject status, for the presence of cell mitosis, lymphocytic infiltration, continuous pushing margins, and solid sheets of cancer cells; cell nuclei, cell nucleoli, cell necrosis, and cell borders were also evaluated. The resulting data were combined with previously available information on tumor type and tumor grade and further evaluated by multifactorial analysis. All statistical tests are two-sided. RESULTS: Cancers associated with BRCA1 mutations exhibited higher mitotic counts (P = .001), a greater proportion of the tumor with a continuous pushing margin (P<.0001), and more lymphocytic infiltration (P = .002) than sporadic (i.e., control) cancers. Cancers associated with BRCA2 mutations exhibited a higher score for tubule formation (fewer tubules) (P = .0002), a higher proportion of the tumor perimeter with a continuous pushing margin (P<.0001), and a lower mitotic count (P = .003) than control cancers. CONCLUSIONS: Our study has identified key features of the histologic phenotypes of breast cancers in carriers of mutant BRCA1 and BRCA2 genes. This information may improve the classification of breast cancers in individuals with a family history of the disease and may ultimately aid in the clinical management of patients.