Prediction of Malignant Breast Lesions from MRI Features

Rationale and Objectives

Dynamic contrast-enhanced magnetic resonance imaging is a clinical imaging modality for the detection and diagnosis of breast lesions. Analytic methods were compared for diagnostic feature selection and the performance of lesion classification to differentiate between malignant and benign lesions in patients.

Materials and Methods

The study included 43 malignant and 28 benign histologically proved lesions. Eight morphologic parameters, 10 gray-level co-occurrence matrix texture features, and 14 Laws texture features were obtained using automated lesion segmentation and quantitative feature extraction. Artificial neural network (ANN) and logistic regression analysis were compared for the selection of the best predictors of malignant lesions among the normalized features.

Results

Using ANN, the final four selected features were compactness, energy, homogeneity, and Law_LS, with an area under the receiver-operating characteristic curve (AUC) of 0.82 and accuracy of 0.76. The diagnostic performance of these four features computed on the basis of logistic regression yielded an AUC of 0.80 (95% confidence interval [CI], 0.688–0.905), similar to that of ANN. The analysis also showed that the odds of a malignant lesion decreased by 48% (95% CI, 25%–92%) for every increase of 1 standard deviation in the Law_LS feature, adjusted for differences in compactness, energy, and homogeneity. Using logistic regression with z -score transformation, a model composed of compactness, normalized radial length entropy, and gray-level sum average was selected, and it had the highest overall accuracy, 0.75, among all models, with an AUC of 0.77 (95% CI, 0.660–0.880). When logistic modeling of transformations using the Box-Cox method was performed, the most parsimonious model with predictors compactness and Law_LS had an AUC of 0.79 (95% CI, 0.672–0.898).

Conclusion

The diagnostic performance of models selected by ANN and logistic regression was similar. The analytic methods were found to be roughly equivalent in terms of predictive ability when a small number of variables were chosen. The robust ANN methodology uses a sophisticated nonlinear model, while logistic regression analysis provides insightful information to enhance the interpretation of the model features.

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a clinical imaging modality for the detection and diagnosis of breast lesions. Computer algorithms have been used for automated lesion segmentation , with statistical analysis techniques applied to select an optimal set of features to achieve the highest diagnostic accuracy . Breast MRI has demonstrated high sensitivity (>95%), with specificity of approximately 67% reported by meta analysis . To address the challenge of accuracy and efficiency in the interpretation of breast MRI, a computer-aided diagnosis (CAD) system that can automatically analyze lesion features to differentiate between malignant and benign lesions would be very useful.

The general approach of breast CAD to predict a dichotomous outcome, malignant versus benign, involves applying computer algorithms for tumor characterization and then developing models using techniques including linear discriminate analysis , logistic regression analysis , and artificial neural networks (ANNs) for classifying a lesion as either malignant or benign. Because of inherent differences in these techniques, it is of interest to compare the diagnostic performance of analytic methods. In a review of 28 studies comparing ANN with other statistical approaches, Sargent found that ANN outperformed regression analysis in 36% of cases, ANN was outperformed by regression analysis in 14% of cases, and similar results were obtained in 50% of cases. The advantages of ANN for predicting a dichotomous outcome include a requirement of less formal statistical training, an ability to implicitly detect complex nonlinear relationships between dependent and predictor variables, consideration of all possible interactions between predictor variables, and the availability of multiple training algorithms. Disadvantages include the “black box” nature of the ANN procedure, a greater computational burden, the tendency for overfitting, and the empirical nature of model development . Logistic regression is superior for examining possible causal relationships between independent and dependent variables and understanding the effects of predictors on outcome variables . In summary, there is no universal approach to select models for data classification; the evaluation of tasks on a case-by-case basis is necessary.

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Materials and methods

Malignant and Benign Lesion Database

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ANN for Diagnostic Feature Selection

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Logistic Regression Model

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logit(p)=loge(p1−p). logit

(

)

log

(

−

)

The logistic regression model enables the prediction of the probability of a malignant breast lesion in relation to m lesion features, from an equation of the form

loge(p1−p)=β0+β1x1+β2x2+β3x3+⋯+βmxm, log

(

−

)

⋯

where β 0 is the intercept term, and β 1 , β 2 , β 3 ,…, β m are the coefficients in the model associated with the m lesion features. It is assumed that the lesion features are linearly related to the log odds of the response. For a continuous lesion feature, the odds ratio for malignant versus benign lesions can be estimated as the exponentiation of the associated coefficient in the model .

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Evaluation of ANN Models Using Logistic Regression

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Logistic Regression Analysis for Diagnostic Feature Selection

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Results

ANN Diagnostic Feature Selection and Evaluation

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Table 1

Diagnostic Evaluation of Models Selected Using the ANN Technique

Model Imaging Descriptors ¶ Method Accuracy ∗ (%) Sensitivity † (%) Specificity ‡ (%) PPV § NPV || Estimated AUC 95% CI A Morphology (three selected from eight): volume, NRL entropy, compactness ANN 77 88 61 0.78 0.77 0.80 Logistic regression 76 93 50 0.74 0.82 0.80 0.686–0.912 B GLCM (three selected from 10): energy, gray-level sum average, homogeneity ANN 73 84 57 0.75 0.70 0.81 Logistic regression 68 86 39 0.69 0.65 0.77 0.660–0.880 C Laws (only one selected from 14): Law_LS ANN 65 84 36 0.67 0.59 0.70 Logistic regression 65 86 32 0.66 0.60 0.70 0.573–0.819 D Combining all seven selected features: volume, NRL entropy, compactness, energy, gray-level sum average, homogeneity, Law_LS ANN 79 81 75 0.83 0.72 0.87 Logistic regression 80 86 71 0.82 0.77 0.86 0.772–0.949 E Final (four selected from seven): compactness, energy, homogeneity, Law_LS ANN 76 84 64 0.78 0.72 0.82 Logistic regression 72 86 50 0.73 0.70 0.80 0.688–0.905

ANN, artificial neural network; AUC, area under the receiver-operating characteristic curve; CI, confidence interval; GLCM, gray-level co-occurrence matrix; NPV, negative predictive value; NRL, normalized radial length; PPV, positive predictive value. For each model, the corresponding logistic regression equation also was applied to data from the full cohort ( n = 71; 43 malignant, 28 benign).

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logit(p)=0.69+1.69compactness−0.61energy+0.24homogeneity−0.73Law_LS. logit

(

)

0.69

1.69

compactness

−

0.61

energy

0.24

homogeneity

−

0.73

Law

Law_LS was the most predictive variable in the model (Wald statistic, P = .028). The P value of the Hosmer-Lemeshow test was .76, indicating a reasonably good fit of the model to the data. However, the adjusted R 2 value for the model was 0.30, indicating that only 30% of the total variation in values could be explained by the predictor features in the model . The estimated odds ratio for Law_LS was calculated as the exponentiation of the associated estimated coefficient, exp(−0.73) = 0.48. Thus the odds of a malignant lesion decreased by 48% (95% CI, 25%–92%) for every increase of 1 SD in the Law_LS feature, adjusted for differences in compactness, energy, and homogeneity. For example, comparing a lesion with Law_LS of 0.19, 1 SD above the mean of 0.13 for the set of 71 lesions, to a lesion with Law_LS of 0.25, 2 SDs above the mean, the odds of the second lesion being malignant are about half those of the first lesion, assuming they have similar values for compactness, energy, and homogeneity.

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Diagnostic Feature Selection Using Logistic Regression Analysis

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Table 2

Diagnostic Evaluation of Models Selected Using Logistic Regression of Feature z Scores With Fourfold Cross-Validation and Applied to Data From the Full Cohort ( n = 71; 43 Malignant, 28 Benign)

Training Cohort Model With Highest AUC for Corresponding Validation Cohort # Likelihood Ratio χ 2 P Accuracy ∗ (%) Sensitivity † (%) Specificity ‡ (%) PPV § NPV || Estimated AUC ¶ 95% CI 1 Compactness, NRL entropy, energy 13.54 0.0036 73 95 39 0.71 0.85 0.75 0.626–0.879 2 Compactness, NRL entropy, gray-level sum average 17.86 0.0005 75 91 50 0.74 0.78 0.77 0.660–0.880 3, 4 Compactness, NRL entropy, Law_LW 19.16 0.0003 72 86 50 0.73 0.70 0.80 0.690–0.908

AUC, area under the receiver-operating characteristic curve; CI, confidence interval; NPV, negative predictive value; NRL, normalized radial length; PPV, positive predictive value.

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logit(p)=0.66+1.28compactness−0.66NRLentropy+0.72gray-levelsum average. logit

(

)

0.66

1.28

compactness

−

0.66

NRL

entropy

0.72

gray-level

sum average

Gray-level sum average was the most predictive variable in the model (Wald statistic, P = .016). For this variable, the estimated odd ratio was exp(0.72) = 2.1 (95% CI, 1.14–3.68); thus, the odds of a malignant lesion increased by 2.1 for every increase of 1 SD in the gray-level sum average feature, adjusted for differences in compactness and NRL entropy. For example, comparing a lesion with gray-level sum average of 27.6, the mean for the 71 lesions, to a lesion with feature value of 34.2, 1 SD above the mean, the odds of the second lesion being malignant are over twice that of the first lesion, assuming they have similar values for compactness and NRL entropy.

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logit(p)=−5.650+0.666(ln compactness)−266.50[(Law_LS0.1)−1]/(1/0.1). logit

(

)

−

5.650

0.666

(

ln compactness

)

−

266.50

[

(

Law

0.1

)

−

]

(

0.1

)

For the natural log of compactness, the estimated odds ratio was exp(0.666) = 1.9, indicating that the odds of a malignant lesion increased by 1.9 (95% CI, 1.20–3.56) for every increase of 1 unit in the natural log of the morphologic feature compactness, adjusted for differences in the Laws feature Law_LS. For example, comparing a lesion with natural log of compactness of 3.0, 1 SD above the mean of 1.6 for the set of 71 lesions, to that of a lesion with natural log of compactness of 4.5, 2 SDs above the mean, the second lesion would be nearly twice as likely to be malignant as the first lesion, assuming equal values for Law_LS.

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Discussion

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References

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Prediction of Malignant Breast Lesions from MRI Features

Rationale and Objectives

Materials and Methods

Results

Conclusion

Materials and methods

Malignant and Benign Lesion Database

ANN for Diagnostic Feature Selection

Logistic Regression Model

Evaluation of ANN Models Using Logistic Regression

Logistic Regression Analysis for Diagnostic Feature Selection

Results

ANN Diagnostic Feature Selection and Evaluation

Diagnostic Feature Selection Using Logistic Regression Analysis

Discussion

References

Further Reading

Atlas of Brain Function

Breast Mass Segmentation in Mammography Using Plane Fitting and Dynamic Programming

Computed Radiography-based Mammography with 50-μm Pixel Size