Univariate Margin Research Articles

Trivariate copula to design coastal structures

Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by climate change. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The simplified Defra method that is currently used in particular for European coastal structures makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a single factor. These schematic correlations do not, however, represent all the complexity of the reality because of the use of this single factor. That may lead to damaging errors in coastal structure design. The aim of this paper is therefore to remedy the lack of robustness of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution functions to their univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method. In order to integrate extreme events, we also resort to the notion of tail dependence. The optimal copula parameter is estimated through the analysis of the tail dependence coefficient, the likelihood method and the mean error. The most robust copulas for our practical case with applications in Saint-Malo and Le Havre (in northern France) are the Clayton copula and the survival Gumbel copula. The originality of this paper is the creation of a new and robust trivariate copula with an analysis of the sensitivity to the method of construction and to the choice of the copula. Firstly, we select the best fitting of the bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years. We finally conclude that the choice of the bivariate copula is more important for the accuracy of the trivariate copula than its own construction.

Significance of p53, p27, Ki-67, E-cadherin, and HER2 expression in upper urinary tract urothelial carcinoma

BackgroundThe study investigated the expression and the clinicopathological significance of p53, p27, Ki-67, E-cadherin, and HER2 in upper urinary tract urothelial carcinomas (UTUC) from Tunisian patients. We performed a retrospective study of 66 UTUC. Main clinicopathological features were reported. The expression of p53, p27, Ki-67, E-cadherin, and HER2 was investigated by immunohistochemistry on whole tissue section.ResultsExpression of p53, Ki-67, p27, E-cadherin, and HERE2 was reported in 36.4%, 69.7%, 90.9%, 100%, and 0% of cases, respectively. p53 expression was associated with stage (p = 0.001), positive surgical margin (p = 0.005), and shorter recurrence-free survival (RFS; Log Rank test, p = 0.026). Ki-67 and p27 expression was associated with stage (p < 0.001 and p = 0.001, respectively) and grade (p < 0.001 and p = 0.001, respectively). Using Kaplan-Meier test, the positive surgical margin was associated with shorter RFS compared to free surgical margin (Log Rank test, p = 0.031). Moreover, in univariate Cox regression analysis, surgical margin (p = 0.041; HR 0.325, 95% CI 0.110–0.956) and p53 expression (p = 0.035; HR 0.328, 95% CI 0.116–0.925) were the significant factors associated with RFS.ConclusionsTogether, our findings suggest that positive surgical margin and p53 expression were potential prognostic factors of UTUC since both were associated with shorter RFS in Tunisian patients.

Can serum cytokeratin 19 fragments predict postoperative early progression in patients with upper urinary tract urothelial carcinoma?

557 Background: Current guidelines do not yet provide recommendations for any serum tumor markers in patients with upper tract urothelial carcinoma (UTUC) who received nephroureterectomy (NU). The criteria for adjuvant chemotherapy is also controversial. Previous studies have shown that serum cytokeratin levels (sCK) were correlated with depth of tumor invasion and metastases in patients with bladder cancer. We found that preoperative sCK was correlated with cancer specific survival(CSS) after NU. In this study we evaluated whether postoperative sCK (poCK) could predict early progression in patients who received NU. Methods: 160 patients with UTUC underwent NU from December 2003 to 2014 at our institution. The median age at diagnosis was 73 years (41-89). poCK19 had been measured in 112 patients within 8 weeks after NU. Patients were divided into two groups, a high-group and a low-group based on poCK19 levels (a cut-off value of 3.5 ng/mL). CSS and progression-free survival (PFS) were measured by Kaplan–Meier curves and log–rank test. Multivariate analysis was carried out using the Cox hazards model. Results: Of 112 patients ≤pT1 was 39 (34%), pT2 in 26 (23%), pT3 in 40 (35%), and pT4 in 7 (8%). The 5-year (5y) CSS rate was 86% and the 5yPFS rate was 60%. There were 24 (21%) patients in the high-group and 88 (79%) in the low-group. During the median follow-up period of 34.0 (1-152) months, 39 patients (35%) died. The 5yCSS rate of the high-group was 51%, which is significantly lower than the low-group (86%) (p&lt;0.001). The 1yPFS of the high-group was 66%, which was significantly lower than that of the low-group (86%) (p&lt;0.001). On univariate analysis, positive margin (HR4.0, p&lt;0.001) and poCK19 (HR3.9, p&lt;0.001) were the significant factors for 1yPFS. On multivariate analysis, poCK19 (HR5.3 95%CI (1.8-15.7), p=0.002) and positive margin (HR 4.6 95%CI (1.1-18.9), p=0.032) were also independent factors for 1yPFS. Conclusions: Our study suggests that postoperative sCK19 could predict early progression in patients with UTUC who received NU. Adjuvant chemotherapy might be indicated for patients with high postoperative sCK19 levels independent of pathological findings.

Serum cytokeratin 19 fragments: A novel preoperative prognostic marker in patients with upper urinary tract urothelial carcinoma.

412 Background: Current guidelines do not yet provide any recommendations for any serum tumor markers in patients with upper tract urothelial carcinoma (UTUC). Even today radiological images cannot diagnose muscle invasion correctly. Previous studies have shown that serum cytokeratin levels were correlated with depth of tumor invasion and metastases in patients with bladder cancer. In this study we evaluated whether preoperative serum cytokeratin 19 fragment levels (sCK19) could be a prognostic marker for survival in patients who received nephroureterectomy (NU). Methods: 160 cases with UTUC underwent NU from December 2003 to 2014 at our institution. The median age was 73 years. Preoperative sCK19 was measured in 138 cases. The patients were divided into two groups, high sCK19 group (HG) and low group (LG) based on sCK19 (a cut-off value: 3.5 ng/mL). Cancer-specific survival (CSS) and progression-free survival (PFS) were measured by Kaplan–Meier curves and statistical analysis was performed by the log–rank test. Multivariate analysis was carried out using the Cox proportional hazards model. Results: Of 138 cases ≤pT1 was 54 (39%), pT2 in 31 (22%), pT3 in 45 (32%) and pT4 in 8 (5%). 37 cases (23%) were the HG and 101 (78%) were the LG. sCK19 were significantly correlated with pT (rs 0.213, p=0.013, Spearman rank correlation). The median follow-up time was 34.0 months. In all cases the 5-year CSS was 78% and PFS was 60%. The 5-year CSS of the HG (57%) was significantly lower than the LG (86%) (p=0.001). The 5-year PFS of the HG (36%) was significantly lower than that of the LG (67%) (p&lt;0.001). On univariate analysis, pT stage, lymphovascular invasion, positive margin (PM) and sCK19 were the significant factors for CSS. On multivariate analysis, sCK19 (HR4.2, p=0.001) and PM (HR2.9, p=0.001) were the independent poor prognostic factors. Conclusions: Preoperative sCK19 was the prognostic factor for the patients with UTUC. Systemic chemotherapy should be considered before NU in patients with high preoperative sCK19 levels independent of radiological findings.

Recurrence outcomes after omission of postoperative radiotherapy following breast-conserving surgery for ductal carcinoma in situ of the breast: a multicenter, retrospective study in Korea (KROG 16-02)

To evaluate the loco-regional recurrence (LRR) rate after breast-conserving surgery without postoperative radiotherapy (RT) for ductal carcinoma in situ (DCIS) of the breast. Between 2000 and 2010, 311 DCIS patients from 9 institutions were analyzed retrospectively. The median age was 47 (range, 20-82). The median tumor size was 7mm (range, 0.01-76). Margin width was <1cm in 85 patients (27.3%), and nuclear grade was high in 37 patients (11.9%). Two hundred and three patients (65.3%) received tamoxifen. With a median follow-up of 74months (range, 5-189), there were 11 local recurrences (invasive carcinoma in 6 and DCIS in 5) and 1 regional recurrence. The 7-year LRR rate was 3.8%. On univariate analysis, age and margin width were significant risk factors influencing LRR (p=0.017 and 0.014, respectively). When age and margin width were combined among 211 patients whose margin width were available, the 7-year LRR rates were as follows (p<0.001): (1) 0% in patients with age >50years and any margin width status (n=64), (2) 1.2% in age ≤50years and margin width ≥1cm (n=93), (3) 13.1% in age ≤50years and margin width <1cm (n=54). The LRR rate was very low in selected DCIS patients treated with breast-conserving surgery without postoperative RT. However, adjuvant RT should be considered for those with age ≤50years and margin width <1cm.

Patterns of failure after radical cystectomy for pT3-4 bladder cancer: Implications for adjuvant radiation therapy.

370 Background: In patients with muscle-invasive bladder cancer, local-regional failure (LF) has been reported to occur in up to 20% of patients following radical cystectomy. The goals of this study were to describe patterns of LF, as well as assess factors associated with LF in a cohort of patients with pT3-4 bladder cancer. This information may have implications towards the use of adjuvant radiation therapy. Methods: Patients with pathologic T3-4 N0-1 bladder cancer were examined from an institutional radical cystectomy database. Preoperative demographics and pathologic characteristics were examined. Outcomes included overall survival and LF. Local-regional failures were defined using follow-up imaging reports and scans, and the locations of LF were characterized. Variables were tested by univariate and multivariable analysis for association with LF and overall survival. Results: 334 patients had pT3-4 and N0-1 disease after radical cystectomy and bilateral pelvic lymph node dissection. Of these, 46% received perioperative chemotherapy. The median age was 71 and median follow up was 11 months. On univariate analysis, margin status, pT stage, pN stage, and gender were all associated with LF (p &lt; 0.05), however, on multivariable analysis, only pT and pN stage were significantly associated with LF (p &lt; 0.01). Three strata of risk were defined, including low-risk patients with pT3N0 disease, intermediate-risk patients with pT3N1 or pT4N0 disease, and high-risk patients with pT4N1 disease, who had 2-year incidence of LF of 12%, 33%, and 72%, respectively. The most common sites of pelvic relapse included the external/internal iliac LNs and obturator LN regions. Notably, 34% of patients with LF had local-regional only disease at the time of recurrence. Conclusions: Patients with pT4 or N1 disease have a 2-year risk of LF that exceeds 30%. These patients may be the most likely to benefit from local adjuvant therapies.

Abstract P1-16-01: Effect of margin width on local recurrence in invasive lobular carcinoma treated with multimodality therapy

Abstract Background: Recent consensus guideline on margins for breast conserving surgery recommends the use of no ink on tumor as the standard for an adequate margin. Current recommendation extends to invasive lobular carcinoma (ILC), however the data in this subset is limited by small numbers. In the present analysis we sought to evaluate the influence of margin status on outcomes in ILC and mixed tumors. Methods: We performed retrospective cohort study and reviewed 809 eligible patients diagnosed with ILC (337 with pure ILC; 472 with mixed ILC) with Stage I –III treated at Dana Farber/Brigham and Women’s Cancer Center (DFBWCC) between May 1997 and Dec 2007. Clinico-pathologic data was extracted following the Clinical Research Information Systems (CRIS) Database procedures and manually reviewed to confirm inclusion and details of margin status. Margin status was defined using the last ASCO/ASTRO/SSA consensus guidelines criteria. Analysis results were considered to be statistically significant when the two-tailed p-value was &amp;lt;0.05. Results: Breast conservation was performed in 399 patients (49%). Margin status at the initial attempt for breast conservation was defined as follows: 180 (45%) negative, 64 (16%) positive, 71 (18%) ≤ 1mm margin, and 84 (21%) close margins (&amp;gt; 1 and &amp;lt; 3 mm). Following initial lumpectomy, 102 (25%) patients underwent additional surgery (96 re-excisions and 6 mastectomies) and residual invasive disease was found in 40 patients. Whole-breast radiation therapy was performed in 376 patients (96%). In multivariate models adjusted for classic clinico-pathologic factors, tumor size (HR= 1.8 95% CI 1.0 to 3.3, p=0.05), multifocality (HR= 2.0 95% CI 1.1 to 3.6, p= 0.02) and ILC subtype (HR= 2.0 95% CI 1.0 to 3.7, p=0.04) were correlated with positive margins, while year of diagnosis, age and pre-surgical MRI findings were not statistically significant. With 72 months median follow-up, 12 ipsilateral breast cancers (3.1%), 5 other locoregional (1.2%) and 15 distant (3.8%) recurrences were observed after definitive breast conserving therapy. The incidence of locoregional recurrence (LRR) was 4.3% and similar for ILC and mixed ILC (p=0.76). In univariate analysis positive surgical margin was associated with LRR (HR=5.1, p= 0.03) and disease-free survival (DFS) (HR=8.9, p≤ .001), but due to limited number of cases and events this could not be adjusted for other clinico-pathologic prognostic factors in a mulitvariate model. Close surgical margins, margins within 1mm and multifocality were not associated with increased LRR or worse DFS. Re-excision did not impact on DFS for patients with close margin (p= 0.57) and within 1 mm margin (p= 0.85). By contrast, significant improvement of DFS following re-excision was observed in patients with positive margin (p= 0.01). Conclusions: Following lumpectomy, local recurrence rates for ILC patients with close surgical margin and ≤ 1mm margin are low and equivalent to those in patients with negative margins. This study supports the validity of using no ink on tumor as the standard for an adequate margin for patients diagnosed with pure or mixed ILC treated with multimodality therapy. Citation Format: Yasuaki Sagara, William T Barry, Ines Vaz-Luis, Fatih Aydogan, Jane E Brock, Eric P Winer, Mehra Golshan, Otto Metzger-Filho. Effect of margin width on local recurrence in invasive lobular carcinoma treated with multimodality therapy [abstract]. In: Proceedings of the Thirty-Seventh Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2014 Dec 9-13; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2015;75(9 Suppl):Abstract nr P1-16-01.

Conditionalization of Copula-Based Models

Copula models are becoming increasingly popular in engineering and financial applications. They provide a flexible way of constructing joint distributions with arbitrary one-dimensional margins and a wide variety of dependence structures. This paper studies different types of conditionalization of copula-based models. We conditionalize these models in the usual way on point values but also propose a different type of conditionalization on a new margin. This new type of conditionalization is motivated by experience with a model built for application in modeling risk in civil aviation. Changing one margin in a copula model is very easy; however, it is not equivalent to conditionalizing on a new margin. For this purpose, the technique presented by Holland and Wang [Holland PW, Wang YJ (1987) Dependence function for continuous bivariate densities. Commun. Statist. Theory Methods 16(3):867–876], called marginal replacement, is used. The main result of this paper allows a simplified way of conditionalizing on more than one univariate margin in a normal copula model.

Univariate Decision Tree Induction using Maximum Margin Classification

In many pattern recognition applications, first decision trees are used due to their simplicity and easily interpretable nature. In this paper, we propose a new decision tree learning algorithm called univariate margin tree where, for each continuous attribute, the best split is found using convex optimization. Our simulation results on 47 data sets show that the novel margin tree classifier performs at least as good as C4.5 and linear discriminant tree (LDT) with a similar time complexity. For two-class data sets, it generates significantly smaller trees than C4.5 and LDT without sacrificing from accuracy, and generates significantly more accurate trees than C4.5 and LDT for multiclass data sets with one-vs-rest methodology.

Negative binomial time series models based on expectation thinning operators

The study of count data time series has been active in the past decade, mainly in theory and model construction. There are different ways to construct time series models with a geometric autocorrelation function, and a given univariate margin such as negative binomial. In this paper, we investigate negative binomial time series models based on the binomial thinning and two other expectation thinning operators, and show how they differ in conditional variance or heteroscedasticity. Since the model construction is in terms of probability generating functions, typically, the relevant conditional probability mass functions do not have explicit forms. In order to do simulations, likelihood inference, graphical diagnostics and prediction, we use a numerical method for inversion of characteristic functions. We illustrate the numerical methods and compare the various negative binomial time series models for a real data example.

Breast conservation: factors predictive of residual disease following reoperation for narrow surgical margins.

Abstract Abstract #5152 Introduction:&amp;#x2028; Ensuring pathologically tumor free surgical margins reduces local recurrence rates following breast conserving surgery for breast cancer or DCIS. There is no general agreement regarding the definition of a clear margin but units with an agreed policy report reduced local recurrence rates. In our unit all patients with a surgical clearance of &amp;lt;5mm are offered further surgery either by mastectomy or by re-excision. We have examined factors that may predict residual disease in re-excised tissues.&amp;#x2028; Method:&amp;#x2028; All attempted breast conserving operations between 01/01/2004 to 31/09/2007 were identified from a dedicated database. Patient age, presentation (symptomatic or screening), surgeon (any of 4 surgeons), weight of tissue removed, tumour size, grade, presence of lymphovascular invasion (LVI) and the closest radial margin (categorised as involved, &amp;lt;2mm, 2-5mm) were examined.&amp;#x2028; Results:&amp;#x2028; Breast conservation was attempted in 605 women (mean age 60; 297 symptomatic, 308 screening). Further surgery was performed in 166 (27.4%) women, including 89 (14.7%) mastectomies. Median tumour size was 20mm (range 0-109). Residual disease was found in 83(50%) of re excisions (66/111 with involved margins, 16/40 for non involved margins up to 2mm, and 1/15 for margins over 2mm). On univariate analysis excision margin (OR=0.33, p=0.000) and total tumor size (OR=4.0 p=0.045 for the smallest size quartile versus the largest) were associated with residual disease. On multivariate analysis only tumor margin remained predictive (OR for &amp;lt;2mm vs involved: 0.46, p=0.043; OR for 2-5mm vs involved: 0.05, p=0.004).&amp;#x2028; Conclusion:&amp;#x2028; In a unit with an aggressive re-excision policy, involved or close surgical margins predict the presence of residual disease in re-excision specimens. A margin of greater than 2mm reduces the risk of residual disease to 1/20 of that seen with microscopically involved margins. This study supports a 2mm minimum radial margin policy when attempting breast conservation for breast malignancy. Citation Information: Cancer Res 2009;69(2 Suppl):Abstract nr 5152.

Clear cell sarcoma of tendons and aponeuroses: An analysis of 75 cases

9572 Background: Clear cell sarcoma (CCS) of tendons and aponeuroses is a rare malignant tumor that occurs most commonly in the extremities of young adults. Because of the rarity of the disease (1% of all soft tissue sarcomas), most reports about CCS have dealt with a few cases during a long time period. We conducted a multi-institutional study of CCS to clarify the clinical findings and prognostic factors of CCS treated during the era of modern multidisciplinary treatment. Methods: The records of 75 consecutive patients with histologically confirmed CCS treated at the JMOG affiliated institutions between 1980 and 2004 (follow-up; average 44 months) were reviewed. There were 41 men and 34 women with an average age of 36 years (range, 10–71 years). 65 tumors were in the extremities (foot 22, hand 13, thigh 9, others 21) and 10 were in the trunk. The tumor size ranged from 1 to 11 cm (mean, 4 cm). 52 patients presented with localized disease (M0) and 23 with metastatic disease (M1). Results: Surgical excision of the primary tumor was performed in 71 patients (limb-sparing surgery; 56, amputation; 15). Microscopic surgical margin was negative in 60 and positive in 11. 56 patients received chemotherapy (30 with measurable disease) and 17 had radiotherapy. Local recurrence occurred in 16 patients and 48 patients developed metastasis. The 5-year overall survival rate was 47% (M0; 55%, M1; 20%). On univariate analysis, sex (p=0.02), size (p=0.001), depth (p=0.002), TNM stage (p=0.001), IRS group (p=0.001) and surgical margin (p=0.04) were prognostic factors. On multivariate analysis, size (p=0.02) remained to be a significant prognostic factor. Objective response to chemotherapy was observed in 8 (27%) patients. In the group of M0 patients, those who received adjuvant chemotherapy had better prognosis (5-year survival, 65%) than those without chemotherapy (5-year survival, 23%)(p=0.03). Conclusions: The results support the contention that early diagnosis and initial excision with negative surgical margin are essential for favorable outcome of CCS. The role of chemotherapy for CCS should be further investigated. No significant financial relationships to disclose.

On Reduction of Finite-Sample Variance by Extended Latin Hypercube Sampling

McKay, Conover and Beckman introduced Latin hypercube sampling (LHS) for reducing the variance of Monte Carlo simulations. LHS is a method for stratifying a univariate margin. We consider an extension of LHS to stratify an m-variate margin with orthogonal arrays, after Owen and Tang. We define extended Latin hypercube sampling of strength m (henceforth denoted by ELHS(m)), such that ELHS(1) reduces to LHS. Using the results obtained by Owen, we first derive an explicit formula for the finite-sample variance of ELHS(m). Based on this formula, we give a sufficient condition for variance reduction by ELHS(m), generalizing similar results from McKay et al. for m = 1. Actually, our sufficient condition for m = 1 contains the sufficient condition of McKay et al. and thus strengthens their result.