2122. Assessment and comparison of likely density distributions in the cases of thickness measurement of skin tumours by ultrasound examination and histological analysis

Indre Drulyte1, Tomas Ruzgas2, Renaldas Raisutis3, Skaidra Valiukeviciene4

1, 3Prof. K. Baršauskas Ultrasound Research Institute, Kaunas University of Technology, Kaunas, Lithuania

2Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences,
Kaunas University of Technology, Kaunas, Lithuania

3Department of Electrical Power systems, Faculty of Electrical and Electronics Engineering,
Kaunas University of Technology, Kaunas, Lithuania

4Department of Skin and Venereal Diseases, Lithuanian University of Health Sciences, Kaunas, Lithuania

1Corresponding author

E-mail: 1drulyte.indre@inbox.lt, 2tomas.ruzgas@ktu.lt, 3renaldas.raisutis@ktu.lt, 4skaidra.valiukeviciene@lsmuni.lt

Received 9 May 2016; received in revised form 14 June 2016; accepted 21 June 2016

DOI https://doi.org/10.21595/jve.2016.17183

Abstract. Ultrasonic diagnostic methods are used to estimate the structural changes and to measure parameters of lesions of the human tissue. Nowadays, the special algorithms of medical data analysis are able to perform diagnosis and monitor the progress of treatment, efficiency of treatment methods, also to estimate the health status and to make prognosis of the diseases evolution. The aim of the presented research is to check the goodness of fit test for thicknesses of the skin tumours measured in two different ways (ultrasound examination and histological analysis) and to compare the compatibility of likely density of histological thicknesses distribution of the skin tumours and density of Normal distribution. As a result, the study has showed that thicknesses of the skin tumours measured by ultrasonic method are strongly similar to histological values, which means that the density of ultrasonic thicknesses distribution and density of Normal distribution are closely interconnected. Therefore, the obtained results show the sufficient level of reliability in the case of application of non-invasive ultrasonic thickness measurement comparing with reference invasive technique based on biopsy and histological thickness evaluation.

Keywords: skin tumour, thickness measurement, goodness of fit test, kernel method, nonparametric density estimator, Monte Carlo method.


[1]        Ruzgas T., Drulytė I. Kernel density estimators for Gaussian mixture models. Lithuanian Journal of Statistics (Lietuvos Statistikos Darbai), Lithuanian Statistical Association, Vilnius, Vol. 52, Issue 1, 2013, p. 14‑21.

[2]        Policy Implications of Medical Information Systems. Report by the US Congress Office of Technology Assessment, http://digital.library.unt.edu/ark:/67531/metadc39374/, 1977.

[3]        Ministry of Health of the Republic of Lithuania, http://sam.lrv.lt/en/.

[4]        Esfandiari N., Babavalian M. R., Moghadam A. M., Tabar V. K. Knowledge discovery in medicine: current issue and future trend. Expert Systems with Applications, Elsevier, Vol. 41, Issue 9, 2014, p. 4434‑4463.

[5]        Bellazzi R., Zupan B. Predictive data mining in clinical medicine: current issues and guidelines. International Journal of Medical Informatics, Elsevier, Vol. 77, Issue 2, 2008, p. 81‑97.

[6]        Houston A. L., Chen H., Hubbard S. M., Schatz B. R., Ng T. D., Sewell R. R., Tolle K. M. Medical data mining on the internet: research on a cancer information system. Artificial Intelligence Review, Springer, Vol. 13, Issue 5, 1999, p. 437‑466.

[7]        Silver M., Sakata T., Su H. C., Herman C., Dolins S. B., O’Shea M. J. Case study: how to apply data mining techniques in a healthcare data warehouse. Journal of Healthcare Information Management, Wiley, Vol. 15, Issue 2, 2001, p. 155‑164.

[8]        Lalayants M., Epstein I., Auslander G. K., Chan W. C. H., Fouché C., Giles R., Joubert L., Rosenne H., Vertigan A. International social work. Sage Journals, Vol. 56, Issue 6, 2013, p. 775‑797.

[9]        Wasan S., Bhatnagar V., Kaur H. The impact of data mining techniques on medical diagnostics. Data Science Journal, Ubiquity Press, Vol. 5, 2006, p. 119‑126.

[10]     Cios K. J., Moore G. W. Uniqueness of medical data mining. Artificial Intelligence in Medicine, Elsevier, Vol. 26, Issues 1‑2, 2002, p. 1‑24.

[11]     Jones M. C., Marron J. S., Sheather S. J. A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, Vol. 91, 1996, p. 401‑407.

[12]     Marron J. S., Wand M. P. Exact mean integrated squared error. Annals of Statistics, Vol. 20, 1992, p. 712‑736.

[13]      Silverman B. W. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 1986.

[14]     Bashtannyk D. M., Hyndman R. J. Bandwidth Selection for Kernel Conditional Density Estimation. Technical Report, Department of Econometrics and Business Statistics, Monash University, 1998.

[15]     Jones M. C. Potential for automatic bandwidth choice in variations of kernel density estimation. Statistics and Probability Letters, Vol. 13, 1992, p. 351‑356.

[16]     Zhang X., King M. L., Hyndman R. J. Bandwidth selection for multivariate kernel density estimation using MCMC. Computational Statistics and Data Analysis, Vol. 50, 2004, p. 3009‑3031.

[17]     Smailyte G., Jasilionis D., Kaceniene A., Krilaviciute A., Ambrozaitiene D., Stankuniene V. Suicides among cancer patients in Lithuania: a population-based census-linked study. Cancer Epidemiology, Elsevier, Vol. 37, Issue 5, 2013, p. 714‑718.

[18]     Sant M., Allemani C., Santaquilani M., Knijn A., Marchesi F., Capocaccia R. EUROCARE‑4. Survival of cancer patients diagnosed in 1995-1999. Results and commentary. European Journal of Cancer, Elsevier, Vol. 45, 2009, p. 931‑991.

[19]     Braun R. P., Saurat J. H., French L. E. Dermoscopy of pigmented lesions: a valuable tool in the diagnosis of melanoma. Swiss Medical Weekly, Vol. 134, Issues 7‑8, 2004, p. 83‑90.

[20]     Gershenwald J. E., Soong S. J., Balch C. M. 2010 TNM staging system for cutaneous melanoma and beyond. Annals of Surgical Oncology, Springer, Vol. 17, Issue 6, 2010, p. 1475‑1477.

[21]     Scott D. W. Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley, New York, 1992.

[22]     Fix E., Hodges J. L. Discriminatory Analysis – Nonparametric Discrimination: Consistency Properties. Report No. 21-49-004, US Air Force School of Aviation Medicine, Random Field, Texas, 1951.

[23]     Silverman B. W., Jones M. C. E. Fix and J. L. Hodges (1951): an important contribution to nonparametric discriminant analysis and density estimation. International Statistical Review, Vol. 57, Issue 3, 1989, p. 233‑247.

[24]     Rosenblatt M. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, Vol. 27, 1956, p. 832‑837.

[25]     Parzen E. On the estimation of probability density and mode. The Annals of Mathematical Statistics, Vol. 33, 1962, p. 1065‑1076.

[26]     Cencov N. N. Estimation of unknown density function from observations. SSSR Academy of Sciences, Vol. 147, 1962, p. 45‑48.

[27]     Watson G. S., Leadbetter M. R. On the estimation of the probability density II. The Annals of Mathematical Statistics, Vol. 34, 1963, p. 480‑491.

[28]     Loftsgaarden D. O., Quesenberry C. P. A nonparametric estimate of a multivariate density function. The Annals of Mathematical Statistics, Vol. 36, Issue 3, 1965, p. 1049‑1051.

[29]     Schwartz S. C. Estimation of probability density by an orthogonal series. The Annals of Mathematical Statistics, Vol. 38, Issue 4, 1967, p. 1261‑1265.

[30]     Epanechnikov V. A. Nonparametric estimates of a multivariate probability density. Theoretical Probability Applications, Vol. 14, 1969, p. 153‑158.

[31]     Tarter M., Kronmal R. On multivariate density estimates based on orthogonal expansions. The Annals of Mathematical Statistics, Vol. 41, Issue 2, 1970, p. 718‑722.

[32]     Kimeldorf G., Wahba G. Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and Applications, Vol. 33, 1971, p. 82‑95.

[33]     Cacoullos T. Estimation of a multivariate density. Annals of the Institute of Statistical Mathematics, Vol. 18, Issue 1, 1966, p. 179‑189.

[34]     Scott D. W., Tapia R. A., Thompson J. R. Multivariate Density Estimation by Discrete Maximum Penalized-Likelihood Methods. Graphical Representation of Multivariate Data. Academic Press, New York, 1978.

[35]     Silverman B. W. Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. The Annals of Statistics, Vol. 6, 1978, p. 177‑184.

[36]     Fukunaga K. Introduction to Statistical Pattern Recognition. Academic Press, New York, 1972.

[37]     Gasser T., Müller H. G., Mammitzsch V. Kernels for nonparametric curve estimation. Journal of the Royal Statistical Society, Vol. 47, 1985, p. 238‑252.

[38]     Marron J. S., Nolan D. Canonical kernels for density estimations. Statistics and Probability Letters, Vol. 7, Issue 3, 1988, p. 195‑199.

[39]     Sacks J., Ylvisaker D. Asymptotically optimum kernels for density estimation at a point. The Annals of Statistics, Vol. 9, 1981, p. 334‑346.

[40]     Tapia R. A., Thompson J. R. Nonparametric Probability Density Estimation. Johns Hopkins Series in the Mathematical Sciences. Johns Hopkins University Press, Baltimore and London, 1978.

[41]     Hall P. Kernel estimation of a distribution function. Communications in Statistics. Theory and Methods, Vol. 14, 1985, p. 605‑620.

[42]     Wand M. P., Jones M. C. Kernel Smoothing. Chapman and Hall, London, 1995.

[43]     Hansen B. E. Lecture Notes on Nonparametrics. University of Wisconsin, 2009, www.ssc.wisc.edu/~bhansen/718/NonParametrics1.pdf

[44]     Jasaitiene D., Valiukeviciene S., Linkeviciute G., Raisutis R., Jasiuniene E., Kazys R. Principles of high-frequency ultrasonography for investigation of skin pathology. Journal of the European Academy of Dermatology and Venereology, 2011, p. 375‑382.

[45]     Kučinskienė V., Samulėnienė D., Gineikienė A., Raišutis R., Kažys R., Valiukevičienė S. Preoperative assessment of skin tumor thickness and structure using 14-MHz ultrasound. Medicina (B Aires), 2014, p. 150‑155.

[46]     Rudzkis R., Bakshaev A. Goodness of fit tests based on kernel density estimators. Informatica, Vol. 24, Issue 3, 2013, p. 447‑460.

Cite this article

Drulyte Indre, Ruzgas Tomas, Raisutis Renaldas, Valiukeviciene Skaidra Assessment and comparison of likely density distributions in the cases of thickness measurement of skin tumours by ultrasound examination and histological analysis. Journal of Vibroengineering, Vol. 18, Issue 5, 2016, p. 3279‑3291.


© JVE International Ltd. Journal of Vibroengineering. Aug 2016, Vol. 18, Issue 5. ISSN 1392-8716