**Reducing False Positives in a Computer-Aided Diagnosis Scheme for Detecting Breast Microcalcificacions: A Quantitative Study with Generalized Additive Models**

Javier Roca-Pardiñas1, María J. Lado1, Pablo G. Tahoces2 and Carmen Cadarso Suárez2 *1University of Vigo 2University of Santiago de Compostela Spain* 

#### **1. Introduction**

458 Cancer Prevention – From Mechanisms to Translational Benefits

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Breast cancer continues to be one of the most usual cancers in the world (Siegel et al., 2011). The primary signs that indicate the presence of breast cancer are masses and microcalcifications. Masses can be defined as three-dimensional structures demonstrating convex outward borders, usually evident on two orthogonal views. Microcalcifications are relevant radiologic signs of irregular shape, varying size, and located in an inhomogeneous background of parenchymal tissues. While individual microcalcifications are not, in most cases, clinically significant, clustered microcalcifications appear in 30%-50% of breast cancers (Murphy & DeSchryver, 1978). Moreover, the distribution of the calcification should be specified as grouped, linear, segmental, regional, or diffuse.

It has been demonstrated that an early diagnosis of breast cancer can dramatically reduce the mortality rates. Mammography continues to be the most effective technique for an early detection of the disease, and it is recommended every 1-2 year for women aged between 40-50 years old, and every year for women over 50 years of age. Furthermore, mammography screening should not only be based on age and family history of breast cancer, but also on breast density, among other factors (Schousboe et al., 2011). In fact, mammographic sensitivity for breast cancer can significantly decrease with increasing breast density (Mandelson et al., 2000).

It also deserves comment that radiologists do not detect all the breast cancers present in the mammograms. In fact, the cancers missed at mammographic screening can be categorized into different groups, such as screening errors; minimal sign present; radiographically occult; or radiographically occult at diagnosis (Van Dijck et al., 1993). To minimize the percentage of missed cancers, an independent double reading of mammograms can be an interesting option for increasing the number of breast cancers that are detected at screening mammography (Duijm et al., 2007).

of variable participating in the reduction of false positives. To perform this task, nonlinear classifiers were used, and the methodology was evaluated employing empirical ROC. Results yielded an improvement in sensitivity close to 3%, while the average number of false positive

<sup>461</sup> Reducing False Positives in a Computer-Aided Diagnosis Scheme for Detecting Breast Microcalcificacions: A Quantitative Study with Generalized Additive Models

One of the limitations present in this previous work was that no factors were used in the study. Factors can be defined as categorical variables, such as, for example, type of breast tissue (fatty or dense), than can clearly affect the diagnosis of clusters of microcalcifications, as stated before (Mandelson et al., 2000), and should be taken in consideration, because the response of a continuous covariate may vary across groups defined by levels of a given factor. This indicates that the continuous covariates can behave different in absence/presence of several

To overcome the limitations imposed by the absence of factors in GAMs, the second work (Lado et al., 2008) introduced in the analysis factors and their interactions with continuous variables in the reduction step. The results obtained showed an increase in the sensitivity

In this work, we propose a new approach to reduce false clustered microcalcifications, employing GAMs and GLMs, which is based on the extraction of several features from the detected clusters, corresponding to both fatty and dense mammograms, and the automated study to discover different behaviours and influences among the covariates (microcalfication

The software programs employed to perform the analysis were developed using R (http: //www.r-project.org/), an open source software idiom for statistical computing and graphics, which is being used by an increasing number of researchers. Moreover, the R language is distributed under the GNU project, and can run on a wide variety of UNIX, Windows and MacOSX platforms. It is mainly characterized by its core functionality and its high extensibility via the packages, which can be easily downloaded and installed from the

Results show an increase of the sensitivity of the automated system, this leading to a better diagnosis of the disease, not confusing the radiologists by indicating normal areas as

The paper is organized as follows: Section 1 gives a detailed introduction about the breast cancer problem, the automated detection employing CAD systems, and the limitations in detection derived from the use of several features, as well as several solutions and methods employed to perform this task; Section 2 gives an overview about the GLMs and GAMs and the interactions among variables; Section 3 presents the database employed, as well as the CAD system developed for detecting microcalcifications. The database of selected features and the study employing GAMS are presented in Section 4. Section 5 shows and discusses the results obtained. Finally, Section 6 provides the main conclusions of the work. An Appendix also presents the source code developed in R language for performing the GAM analysis.

In this work, we are interested in predicting the presence or absence of a lesion, using a regression model for binary response. Explicitly, let *Y* be a binary (0/1) response variable, and **X** = (*X*1,..., *Xq*) the q-vector of the associated continuous covariates. In this framework,

suspicious regions, thus reducing the number of biopsies to be performed.

from more than 2%, while the false positive rate was drastically reduced to the half.

detections was reduced in 0.5 per image.

features) present in the analysis.

CRAN family of Internet sites.

**2. Generalized additive models**

factors, this producing the corresponding factor-by-curve effects.

In the last decades, digital mammography has emerged as a promising technique that offers the possibility of a second-opinion consultation, or computer-aided detection (CAD) schemes to assist radiologists in the detection of radiological features that could point to those different pathologies (Banik et al., 2011; Hupse & Karssemeijer, 2009 ; Lado et al., 2001).

Nowadays, utility of CAD systems has been already demonstrated, and there are several computerized systems dedicated to detection and diagnosis tasks approved by the Food and Drug Administration (FDA), such as Second Look (CADx Medical Systems, Inc) (approved in 2002), MammoReader (Intelligent Systems Software, Inc) (approved in 2002), or the Kodak Mammography CAD Engine (Eastman Kodak Company) (approved in 2004).

It is clear that, in order to automatically detect lesions, it could be very useful to learn from the radiologists' experience, as well as to quantify the different image features employed by the clinicians to perform their diagnosis. Even although a computer system will never reach the specialists knowledge level, its ability to detect and classify abnormalities can be improved analyzing the existing differences between the human observer and the computer (Kuprinski & Nishikawa, 1997). It becomes necessary to understand both the medical image contents and the process developed by radiologists for analyzing the information. Given the difficult task of interpreting mammograms by radiologists, the CAD mammographic systems are addressed to limited goals, such as the detection and classification of masses and microcalcifications.

It must be indicated that CAD systems, dedicated to detect abnormalities not only in the breast but also in other medical fields (Doi, 2007), produce suspicious areas that should be identified as lesions or false detections, in order to avoid confusing the clinicians when analyzing the areas detected by the computer. Because of this, a significant stage in nearly all the CAD schemes consists in reducing the number of false positives, by the application of different algorithms and diverse statistical methods(Lado et al., 2006; Tourassi et al., 2005).

There are several models, usually employed by the CAD systems in any field to reduce false detections, such as linear discriminant analysis (LDA) (Yoshida et al., 2002), neural networks (Park et al., 2011), or generalized additive models (GAMs) (Lado et al., 2006). However, reduction of false positives can be a difficult task if an inadequate method or algorithm is selected, this leading to incorrect results, by rejecting correct detections while keeping false positives. Because of this, researchers should pay much attention to the reduction of false positives step.

One of the most important aspects to be considered when the diagnostic imaging systems are analyzed is the evaluation of their diagnostic performance. To perform this task, receiver operating characteristic (ROC) curves are the method usually selected, since they indicate the trade-off between sensitivity and specificity, available from a diagnostic system describing the inherent discrimination capability of these systems (Metz, 1986).

The method of ROC curves can be generalized for the diagnostic performance of both the human observers and the CAD systems. In fact, a large amount of automated systems dedicated to the early detection and diagnosis cancer are frequently evaluated employing ROC methodology, not only in the field of breast lesions (Obuchowski, 2005), but also in nearly any type of cancer or disease (Keotan et al., 2002; Li et al., 2005).

In previous works (Lado et al., 2006; 2008) GAMs were applied to the reduction of false positives in CAD systems dedicated to the detection of microcalcifications. In the first work (Lado et al., 2006), the main goal was to overcome the limitations imposed by LDA in the type of variable participating in the reduction of false positives. To perform this task, nonlinear classifiers were used, and the methodology was evaluated employing empirical ROC. Results yielded an improvement in sensitivity close to 3%, while the average number of false positive detections was reduced in 0.5 per image.

One of the limitations present in this previous work was that no factors were used in the study. Factors can be defined as categorical variables, such as, for example, type of breast tissue (fatty or dense), than can clearly affect the diagnosis of clusters of microcalcifications, as stated before (Mandelson et al., 2000), and should be taken in consideration, because the response of a continuous covariate may vary across groups defined by levels of a given factor. This indicates that the continuous covariates can behave different in absence/presence of several factors, this producing the corresponding factor-by-curve effects.

To overcome the limitations imposed by the absence of factors in GAMs, the second work (Lado et al., 2008) introduced in the analysis factors and their interactions with continuous variables in the reduction step. The results obtained showed an increase in the sensitivity from more than 2%, while the false positive rate was drastically reduced to the half.

In this work, we propose a new approach to reduce false clustered microcalcifications, employing GAMs and GLMs, which is based on the extraction of several features from the detected clusters, corresponding to both fatty and dense mammograms, and the automated study to discover different behaviours and influences among the covariates (microcalfication features) present in the analysis.

The software programs employed to perform the analysis were developed using R (http: //www.r-project.org/), an open source software idiom for statistical computing and graphics, which is being used by an increasing number of researchers. Moreover, the R language is distributed under the GNU project, and can run on a wide variety of UNIX, Windows and MacOSX platforms. It is mainly characterized by its core functionality and its high extensibility via the packages, which can be easily downloaded and installed from the CRAN family of Internet sites.

Results show an increase of the sensitivity of the automated system, this leading to a better diagnosis of the disease, not confusing the radiologists by indicating normal areas as suspicious regions, thus reducing the number of biopsies to be performed.

The paper is organized as follows: Section 1 gives a detailed introduction about the breast cancer problem, the automated detection employing CAD systems, and the limitations in detection derived from the use of several features, as well as several solutions and methods employed to perform this task; Section 2 gives an overview about the GLMs and GAMs and the interactions among variables; Section 3 presents the database employed, as well as the CAD system developed for detecting microcalcifications. The database of selected features and the study employing GAMS are presented in Section 4. Section 5 shows and discusses the results obtained. Finally, Section 6 provides the main conclusions of the work. An Appendix also presents the source code developed in R language for performing the GAM analysis.
