In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions. Copyright Springer-Verlag 2004Boot strap, Distance between fuzzy numbers, Fuzzy random variables, Large Smaple Theory,
We developed a semi-automated tool to assess mammographic density (MD), a phenotype risk marker for breast cancer (BC), in full-field digital images and evaluated its performance testing its reproducibility, comparing our MD estimates with those obtained by visual inspection and using Cumulus, verifying their association with factors that influence MD, and studying the association between MD measures and subsequent BC risk.Three radiologists assessed MD using DM-Scan, the new tool, on 655 processed images (craniocaudal view) obtained in two screening centers. Reproducibility was explored computing pair-wise concordance correlation coefficients (CCC). The agreement between DM-Scan estimates and visual assessment (semi-quantitative scale, 6 categories) was quantified computing weighted kappa statistics (quadratic weights). DM-Scan and Cumulus readings were compared using CCC. Variation of DM-Scan measures by age, body mass index (BMI) and other MD modifiers was tested in regression mixed models with mammographic device as a random-effect term.The association between DM-Scan measures and subsequent BC was estimated in a case–control study. All BC cases in screening attendants (2007–2010) at a center with full-field digital mammography were matched by age and screening year with healthy controls (127 pairs). DM-Scan was used to blindly assess MD in available mammograms (112 cases/119 controls). Unconditional logistic models were fitted, including age, menopausal status and BMI as confounders.DM-Scan estimates were very reliable (pairwise CCC: 0.921, 0.928 and 0.916). They showed a reasonable agreement with visual MD assessment (weighted kappa ranging 0.79-0.81). DM-Scan and Cumulus measures were highly concordant (CCC ranging 0.80-0.84), but ours tended to be higher (4%-5% on average). As expected, DM-Scan estimates varied with age, BMI, parity and family history of BC. Finally, DM-Scan measures were significantly associated with BC (p-trend=0.005). Taking MD<7% as reference, OR per categories of MD were: OR7%-17%=1.32 (95% CI=0.59-2.99), OR17%-28%=2.28 (95% CI=1.03-5.04) and OR>=29%=3.10 (95% CI=1.35-7.14). Our results confirm that DM-Scan is a reliable tool to assess MD in full-field digital mammograms.Electronic supplementary materialThe online version of this article (doi:10.1186/2193-1801-2-242) contains supplementary material, which is available to authorized users.
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