An identity on order statistics of a set of random variables.

When an n × 1 random vector X = (X1, …, Xn ) T has a sign-invariant distribution, Strait [J. Multivariate Anal. 4 (1974) 494-496] proved that the expectations of max(0, X1, X1 + X2, …, X1 + Xn ) and max(0, X1, …, Xn ) are equal. In this note we assume a weaker condition that (X1, X2, …, Xn ) and (-X1, X2, …, Xn ) are equal in distribution and prove a more general result that the expectations of Lr (0, X1, X1 + X2, …, X1 + Xn ) and Lr (0, X1, …, Xn ) are equal, where Lr (0, X1, …, Xn ) is the rth order statistic of 0, X1, …, Xn for r = 1, …, n + 1.

Assessing the risk of ovarian malignancy in asymptomatic women with abnormal CA 125 and transvaginal ultrasound scans in the prostate, lung, colorectal, and ovarian screening trial.

OBJECTIVE: To estimate the risk of ovarian malignancy among asymptomatic women with abnormal transvaginal ultrasound scans or CA 125 and to provide guidance to physicians managing these women. METHODS: A cohort of women from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial with abnormal ovarian results at the initial (T0) and subsequent (T1+) screens were analyzed to estimate which findings were associated with high risk of ovarian cancer. Cancer risks more than 10% were designated as high and risks of 3% or less were designated as low. RESULTS: For the T0 screen, two high-risk categories were identified: CA 125 of 70 or more with negative transvaginal ultrasound scan (positive predictive value [PPV] 15.9%, CI 14.7-17.7%); and positive for both CA 125 and transvaginal ultrasound scan (PPV 25.0%, CI 23.3-27.3%). For T1+ screens, three high-risk categories were identified: negative transvaginal ultrasound scan with change in CA 125 of 45 or more (PPV 29.0%, CI 28.3-30.3%); increase in size of cyst 6 cm or more with negative CA 125 (PPV 13.3%, CI 10.5-18.0%); and positive for both tests (PPV 42.9%, CI 40.0-46.0%). High-risk criteria for T0 provide a sensitivity of 60%, specificity of 96.2%, PPV of 19.7%, and a negative predictive value (NPV) of 99.3%. T1+ criteria yielded a sensitivity of 85.3%, specificity of 95.6%, PPV of 29.6%, and NPV of 99.7%. CONCLUSIONS: High-risk categories for predicting risk of cancer in women with abnormal CA 125, transvaginal ultrasound scan, or both at initial and subsequent screens have been identified. The large number of women in this study, the 4-year complete follow-up, and small number of invasive cancers in the low-risk categories provide guidance for clinical decisions regarding need for surgery in these women. LEVEL OF EVIDENCE: II.

Longitudinal evaluation of CA-125 velocity and prediction of ovarian cancer.

OBJECTIVE: To determine whether CA-125 velocity is a statistically significant predictor of ovarian cancer and develop a classification rule to screen for ovarian cancer. METHODS: In the ovarian component of the PLCO cancer screening trial, 28,038 women aged 55-74 had at least two CA-125 screening tests. Ovarian cancer was diagnosed in 72 (0.26%) women. A multiple logistic regression model was developed to evaluate CA-125 velocity and other related covariates as predictors of ovarian cancer. Predictive accuracy was assessed by the concordance index and measures of discrimination and calibration while the fit of the model was assessed by the Hosmer and Lemeshow's goodness-of-fit χ(2)test. RESULTS: CA-125 velocity decreased as the number of CA-125 measurements increased but was unaffected by age at baseline screen and family history of ovarian cancer. The average velocity (19.749U/ml per month) of the cancer group was more than 500 times the average velocity (0.035U/ml per month) of the non-cancer group. CONCLUSION: Among six covariates used in the model, CA-125 velocity and time intervals between baseline and second to last screening test and between last two screening tests were statistically significant predictors of ovarian cancer. The chance of having ovarian cancer increased as velocity increased, and the chance decreased when the time intervals between baseline and the second to last screening test and between last two screening tests of an individual increased.

Effect of screening on ovarian cancer mortality: the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Randomized Controlled Trial.

CONTEXT: Screening for ovarian cancer with cancer antigen 125 (CA-125) and transvaginal ultrasound has an unknown effect on mortality. OBJECTIVE: To evaluate the effect of screening for ovarian cancer on mortality in the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial. DESIGN, SETTING, AND PARTICIPANTS: Randomized controlled trial of 78,216 women aged 55 to 74 years assigned to undergo either annual screening (n = 39,105) or usual care (n = 39,111) at 10 screening centers across the United States between November 1993 and July 2001. Intervention The intervention group was offered annual screening with CA-125 for 6 years and transvaginal ultrasound for 4 years. Participants and their health care practitioners received the screening test results and managed evaluation of abnormal results. The usual care group was not offered annual screening with CA-125 for 6 years or transvaginal ultrasound but received their usual medical care. Participants were followed up for a maximum of 13 years (median [range], 12.4 years [10.9-13.0 years]) for cancer diagnoses and death until February 28, 2010. MAIN OUTCOME MEASURES: Mortality from ovarian cancer, including primary peritoneal and fallopian tube cancers. Secondary outcomes included ovarian cancer incidence and complications associated with screening examinations and diagnostic procedures. RESULTS: Ovarian cancer was diagnosed in 212 women (5.7 per 10,000 person-years) in the intervention group and 176 (4.7 per 10,000 person-years) in the usual care group (rate ratio [RR], 1.21; 95% confidence interval [CI], 0.99-1.48). There were 118 deaths caused by ovarian cancer (3.1 per 10,000 person-years) in the intervention group and 100 deaths (2.6 per 10,000 person-years) in the usual care group (mortality RR, 1.18; 95% CI, 0.82-1.71). Of 3285 women with false-positive results, 1080 underwent surgical follow-up; of whom, 163 women experienced at least 1 serious complication (15%). There were 2924 deaths due to other causes (excluding ovarian, colorectal, and lung cancer) (76.6 per 10,000 person-years) in the intervention group and 2914 deaths (76.2 per 10,000 person-years) in the usual care group (RR, 1.01; 95% CI, 0.96-1.06). CONCLUSIONS: Among women in the general US population, simultaneous screening with CA-125 and transvaginal ultrasound compared with usual care did not reduce ovarian cancer mortality. Diagnostic evaluation following a false-positive screening test result was associated with complications. Trial Registration clinicaltrials.gov Identifier: NCT00002540.

[Temperature dependent Raman spectra and micro-structure study of cuspidine in solid and liquid phases].

Cuspidine plays an important role in conventional metallurgical continuous casting mould flux. An UV laser source was used to record its ambient and high temperature Raman spectra (temperature range: 298-1 723 K) combined with a charge coupled device (CCD) detector. Both increasing and decreasing processes as well as characteristic spectra and shifts in wavenumber were observed. Micro-structure of cuspidine in liquid state is not unitary and different from that in solid state, suggesting multi clusters coexisting. Density functional theory (DFT) simulation method was applied to calculate its wavenumbers of Raman active vibrations by introducing the crystal spatial configuration model of cuspidine. Thus the experimental vibrational wavenumbers of the characteristic peaks could be assigned. This will help study physical and chemical behavior of cuspidine in continuous casting mould flux and provide an unique in-situ method under varying temperature with Raman spectroscopic technique.

Cumulative incidence of false-positive results in repeated, multimodal cancer screening.

PURPOSE: Multiple cancer screening tests have been advocated for the general population; however, clinicians and patients are not always well-informed of screening burdens. We sought to determine the cumulative risk of a false-positive screening result and the resulting risk of a diagnostic procedure for an individual participating in a multimodal cancer screening program. METHODS: Data were analyzed from the intervention arm of the ongoing Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial, a randomized controlled trial to determine the effects of prostate, lung, colorectal, and ovarian cancer screening on disease-specific mortality. The 68,436 participants, aged 55 to 74 years, were randomized to screening or usual care. Women received serial serum tests to detect cancer antigen 125 (CA-125), transvaginal sonograms, posteroanterior-view chest radiographs, and flexible sigmoidoscopies. Men received serial chest radiographs, flexible sigmoidoscopies, digital rectal examinations, and serum prostate-specific antigen tests. Fourteen screening examinations for each sex were possible during the 3-year screening period. RESULTS: After 14 tests, the cumulative risk of having at least 1 false-positive screening test is 60.4% (95% CI, 59.8%-61.0%) for men, and 48.8% (95% CI, 48.1%-49.4%) for women. The cumulative risk after 14 tests of undergoing an invasive diagnostic procedure prompted by a false-positive test is 28.5% (CI, 27.8%-29.3%) for men and 22.1% (95% CI, 21.4%-22.7%) for women. CONCLUSIONS: For an individual in a multimodal cancer screening trial, the risk of a false-positive finding is about 50% or greater by the 14th test. Physicians should educate patients about the likelihood of false positives and resulting diagnostic interventions when counseling about cancer screening.

Results from four rounds of ovarian cancer screening in a randomized trial.

OBJECTIVE: To test whether annual screening with transvaginal ultrasonography and CA 125 reduces ovarian cancer mortality. METHODS: Data from the first four annual screens, denoted T0-T3, are reported. A CA 125 value at or above 35 units/mL or an abnormality on transvaginal ultrasonography was considered a positive screen. Diagnostic follow-up of positive screens was performed at the discretion of participants' physicians. Diagnostic procedures and cancers were tracked and verified through medical records. RESULTS: Among 34,261 screening arm women without prior oophorectomy, compliance with screening ranged from 83.1% (T0) to 77.6% (T3). Screen positivity rates declined slightly with transvaginal ultrasonography, from 4.6 at T0 to 2.9-3.4 at T1-T3; CA 125 positivity rates (range 1.4-1.8%) showed no time trend. Eighty-nine invasive ovarian or peritoneal cancers were diagnosed; 60 were screen detected. The positive predictive value (PPV) and cancer yield per 10,000 women screened on the combination of tests were similar across screening rounds (range 1.0-1.3% for PPV and 4.7-6.2 for yield); however, the biopsy (surgery) rate among screen positives decreased from 34% at T0 to 15-20% at T1-T3. The overall ratio of surgeries to screen-detected cancers was 19.5:1. Seventy-two percent of screen-detected cases were late stage (III/IV). CONCLUSION: Through four screening rounds, the ratio of surgeries to screen-detected cancers was high, and most cases were late stage. However, the effect of screening on mortality is as yet unknown. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov, www.clinicaltrials.gov, NCT00002540 LEVEL OF EVIDENCE: II.

The epidemiology of CA-125 in women without evidence of ovarian cancer in the Prostate, Lung, Colorectal and Ovarian Cancer (PLCO) Screening Trial.

OBJECTIVE: To determine the epidemiology of CA-125 in women without ovarian cancer. METHODS: We analyzed demographic, medical and lifestyle characteristics related to CA-125, measured using the Centocor CA-125II RIA assay, among 25,608 multi-ethnic U.S. women aged 55-74 years enrolled in a cancer screening trial and found to have no evidence of ovarian cancer. RESULTS: Mean CA-125 level was 11.9 U/ml (SD 8.3); median 10.0 U/ml, interquartile range 8.0-14.0. High levels, using the clinical cut point of >or=35 U/ml, were associated with increased age (p<0.001) and former smoking (p<0.021), while hysterectomy and obesity were protective (p<0.001). Mean levels were higher with increasing age (p<0.001), ever use of hormone therapy (p<0.001), former smoking (p<0.017) and history of breast cancer (p<0.002), but lower (p<0.001) with non-White status, previous hysterectomy, current smoking, and obesity. Current hormone therapy use was not associated with CA-125 in women without a uterus. CONCLUSION: In post-menopausal women without ovarian cancer, CA-125 level is influenced by a number of factors, including race/ethnicity, age, hysterectomy, smoking history and obesity.

Estimating the cumulative risk of a false-positive test in a repeated screening program.

The goal of screening tests for a chronic disease such as cancer is early detection and treatment with a consequent reduction in mortality from the disease. Screening tests, however, might produce false positive and false-negative results. With an increasing number of screening tests, it is clear that the risk of a false-positive screen, a finding with potentially significant emotional, financial, and health costs, also increases. Elmore et al. (1998, New England Journal of Medicine 338, 1089-1096), Christiansen et al. (2000, Journal of the National Cancer Institute 92, 1657-1666), and Gelfand and Wang (2000, Statistics in Medicine 19, 1865-1879) investigated this problem under the somewhat unrealistic assumption that the choice of making the decision to drop out at the kth screen does not depend upon the results of the earlier k - 1 screens. In this article we obtain sufficient and necessary conditions for their assumption to hold and use one of them to provide a method for testing the validity of the assumption. A new model which does not depend on their assumption is introduced. The maximum likelihood estimator of the cumulative risk of receiving a false-positive screen under the new model is derived and its asymptotic normality is proved. The extension of the new model by incorporating covariate information is also considered. We apply our testing method and the new model to data from the breast cancer screening trial of the Health Insurance Plan of Greater New York.

Modelling and analysing exchangeable binary data with random cluster sizes.

Correlated binary data occur very frequently in cluster sample surveys, dependent repeated cancer screening, teratological experiments, ophthalmologic and otolaryngologic studies, and other clinical trials. The standard methods to analyse these data include the use of beta-binomial models and generalized estimating equations with third and fourth moments specified by 'working matrices'. However, in many applications it is reasonable to assume that the data from the same cluster are exchangeable. When all sampled clusters have equal sizes, Bowman and George introduced maximum likelihood estimates (MLEs) of the population parameters such as the marginal means, moments, and correlations of order two and higher. They also extended their approach to sampled clusters with unequal sizes. It seems that their extension has a gap. This paper points out the source of this gap and shows that estimates introduced by Bowman and George are not the MLEs of the parameters which are used to identify the joint distribution of correlated binary data. We show that the MLEs of the population parameters have no closed form in general and should be calculated by numerical methods. We apply our results and a generalized estimating equation procedure to a data set from a double-blind randomized clinical trial comparing two antibiotics, cefaclor and amoxicillin, used for the treatment of acute otitis media. To see the performance of the MLEs with small or moderate sample sizes, several simulation studies are also conducted.