Brain tumors in children are life-threatening and deserve more research to improve patient care. In recentyears, multivariate analysis has been increasingly used in tumor classification (segmentation) and survival (outcome) assessment in childhood brain tumors. This paper reviewed the studies that applied multivariate analysis to tumor classification (segmentation) and survival (outcome) assessment in pediatric brain tumors. Large variations in the tumor classification results were observed in the studies of tumor classification (even in similar patient populations). Moderate error rate in the multivariate survival analysis model was also observed, which could lead to inaccurate survival estimates and misidentification of prognostic factors. To address these problems, this paper analyzed the data processing chains in these multivariate analyses in detail. It seems that optimizing and standardizing these data processing chains may improve tumor classification and survival analysis, reduce variations and errors in classification results and survival estimates. As multivariate analytic approaches, data processing technologies and imaging techniques advance in the Big Data era of the 21^st century, it is anticipated that the challenges in complex imaging data processing in tumor classification will be overcome and complex data processing will be revolutionized. This will make accurate automatic tumor classification/segmentation (for each tumor type and grade) possible to early detect and treat tumors, guide treatment planning, monitor tumor progression and treatment effects, together with advanced accurate survival assessment to guide life-saving rescue and recovery planning, revolutionize patient care, and truly benefit children with brain tumors.

Keywords: multivariate analysis, pediatric brain tumor, tumor classification, survival assessment

DWI, diffusion-weighted imaging; MRS, mr spectroscopy; PWI, perfusion-weighted imaging; SVM, support vector machine; LDA, linear discriminant analysis; kNN, k-nearest neighbour; ANN, artificial neural networks; KLD, kullback-leibler divergence; mBm, multi-fractional brownian motion; EM, expectation maximization; PNET, primitive neuroectodermal tumor; PTPSA, piecewise-triangular-prism-surface-area; MD, mean diffusivity; FA, fractional anisotropy; PCA, principal component analysis; mRMR, maximum-relevance minimum redundancy; DNET, dysembryoplastic neuroepithelial Tumor; DNT, dysembryoplastic neuroepithelial tumor; ADC, apparent diffusion coefficient; rADC, ADC tumor-to-normal-brain ratios; ROC, receiver operating characteristic; AUC, area under the roc curve; ATCT, apparent transient coefficient in tumor; OS, overall survival; PFS, progression-free survival; GTR, gross total resection; RT, radiation therapy

Brain and central nervous system tumors are the 2^nd most common tumors in children.¹ Compared with brain tumors in adults, the histological types of childhood brain tumors have a larger variety such as medulloblastomas, pilocytic astrocytomas and ependymomas, which increases the difficulty in tumor diagnosis and differentiation. Since brain tumors in children are life-threatening, they deserve more research to improve patient care.

MRI (including T1, T2, FLAIR and contrast-enhanced MRI) is the most important imaging technique for the visualization and assessment of pediatric brain tumors. However, conventional MRI technique is often inadequate in grading tumors or identifying the aggressive region of the tumor. Therefore, advanced MRI techniques (modalities) such as DWI (Diffusion Weighted Imaging), MRS (MR Spectroscopy) and PWI (Perfusion Weighted Imaging) are needed to help with tumor assessment, and are increasingly used in brain tumor diagnosis. DWI is based on water diffusion and the apparent diffusion coefficient (ADC) map that DWI generates provides information on the conditions of different brain tissues.² MRS provides information on the specific molecules’ concentration in the brain tissue which reflects the biochemical characteristics in that brain region. PWI provides information on vascular perfusion (blood flow in capillaries and larger vessels) of the brain. These imaging techniques are useful in classifying (typing) and grading brain tumors.³

Multivariate analysis is a statistical approach that assesses multiple variables simultaneously, which may be more advantageous than univariate analysis in characterizing the associations between data variables (e.g., variables associated with outcomes), classifying data into different categories (e.g., tumor types and grades) and generating new diagnostic tests. Multivariate analysis includes a number of analytic methods such as multivariate regression, principal components analysis (PCA), independent components analysis (ICA) and cluster analysis. Machine learning (statistical learning) is a group of multivariate analytic methods often used in data classification, pattern recognition and data mining.² Machine learning can be either supervised or unsupervised. In supervised learning, the classifications of data samples in the training set (to train the classification model or classifier) are known; while in unsupervised learning, the classifications of data samples in the training set are unknown. Examples of supervised learning methods include linear discriminate analysis (LDA), support vector machine (SVM), artificial neural networks (ANN) and random forests. Examples of unsupervised learning include cluster analysis and Hebbian learning neural networks.

Since tumor classification and patient survival assessment often have much larger number of data variables than the sample sizes, they are called high-dimensional problems. Multivariate analysis is suitable for such problems. Imaging analytic studies of brain tumors in adults have been developed for decades, but imaging research of brain tumors in children is relatively young.² In recentyears, multivariate analysis has been increasingly used in tumor classification (or segmentation) and survival (or outcome) assessment in childhood brain tumors. This paper reviewed the studies that applied multivariate analysis to tumor classification (segmentation) and survival (outcome) assessment in pediatric brain tumors.

Pubmed search was performed with keywords “multivariate MRI pediatric brain tumor”, “machine learning imaging brain tumor childhood” or “multivariate pediatric brain tumor”. The search yielded 41 articles, and articles were excluded if their subjects were not pediatric or the statistical methods used were not multivariate or the article was published before year 2000.

27 articles were selected in this review. Among them, 13 articles reported multivariate analysis methods applied to pediatric brain tumor classification (or segmentation).^3‒15 Table 1 provides a summary of these papers. The rest of the articles reported multivariate analysis (using Cox model) applied to survival (or outcome) evaluation in pediatric brain tumors,^16‒29 which are summarized in Table 2.

Multivariate analysis in pediatric brain tumor classification or segmentation

In the early years, multivariate methods such as LDA and belief networks were used in tumor classification (Table 1). Schneider et al. computed imaging parameters (ADC and metabolite ratio features from MRI, DWI and MRS), and used LDA as classifier to discriminate between four tumor groups (medulloblastoma, infiltrating glioma, ependymoma, and pilocytic astrocytoma).⁴ They found that combined ADC and metabolite ratio features (using water as an internal standard) could discriminate between these tumor groups.⁴ Reynolds et al. used tumor location information obtained from MRI to construct Bayesian belief networks, incorporated MRS information into the classifiers, and found that inclusion of a priori knowledge improved classification accuracy.⁵ Later, Davies et al. extracted multiple metabolite profiles from (short-TE PRESS) MRS, classified tumors (e.g., glial-cell vs. non-glial-cell tumors) with LDA and achieved high classification accuracies (>90%).⁷ Further, in a multi-national study (n=78), Vicente et al. computed metabolite concentrations from (short-TE PRESS) MRS data, classified tumors (e.g., medulloblastomas vs. ependymomas vs. pilocytic astrocytomas) with LDA, and achieved high classification accuracies (98%~100%).¹¹

Tumor segmentation allows quantitative (e.g., tumor volume) analysis, and automatic tumor segmentation was achieved by applying graph cut method to tumor image and using probabilistic boosting trees as classifier.⁶ In addition, Ahmed et al.⁸ and Iftekharuddin et al.,⁹ used shape, intensity and texture features extracted from MRI images for tumor segmentation and classification (sensitivity 100%, specificity 75%).⁹ For special brain tumors such as optic pathway gliomas, automatic tumor segmentation was achieved by using prior tumor location tissue characteristics and intensity information, and by classifying tumor into internal components.¹⁰

In recentyears, multivariate analysis methods such as SVM, cluster analysis and random forest have been applied to tumor classification (typing) and tumor grading. Using SVM classifier, Rodriguez Gutierrez et al. demonstrated that ADC histogram features generated high classification accuracy (95.8% of medulloblastomas, 96.9% of pilocytic astrocytomas, and 94.3% of ependymomas); and ADC textural features produced high tumor-subtype classification accuracy (89% of medulloblastoma subtypes).¹² With a large sample (n=74), Tantisatirapong et al. investigated two feature selection approaches (principal component analysis PCA, and the combination of max-relevance and min-redundancy (mRMR) and feedforward selection), and tumor classification with SVM classifier based on texture features (from MRI, DWI and DTI) yielded varied classification performance.¹³ In addition, Fetit et al. examined the classification performance of 6 classifiers with 2D and 3D texture features extracted MRI (T1, T2) and found that SVM and ANN had the highest overall classification accuracy (92%), and 3D texture features improved classification performance.¹⁴ In patients with pediatric posterior fossa ependymoma, tumor classification with cluster analysis revealed that tumor subgroups could be distinguished based on tumor centroid location, which was associated with prognostic and treatment factors.¹⁵ Further, in a recent study (n=76), Koob et al. classified tumors with random forest classifier, and found diagnostic accuracy 73.24% with DWI+PWI for tumor grading, and 55.76% with DWI+PWI+MRS for tumor typing.³ They also found that the best parameters for tumor grading and typing were ADC and rADC (ADC tumor-to-brain ratios), and multimodal MRI (MRI, DWI, PWI, MRS) could determine pediatric tumor grades (I, IV) and types (pilocytic astrocytomas and embryonal tumors).³

However, there are large variations in the tumor classification results among the studies (even in similar patient samples), e.g.,¹² vs.¹³;³ vs.¹¹;³ vs.¹²

Multivariate analysis in survival/outcome assessment in pediatric brain tumors

The majority of the studies listed in Table 2 used Kaplan-Meier method to estimate progression-free survival (PFS) and overall survival (OS), and applied multivariate Cox proportional hazards model to identification of prognostic factors. In patients with pilocytic astrocytomas (n=80), 5year PFS rate was 75%, and the 5year OS rates were 92-100%.¹⁶ In patients with low-grade gliomas (n=351), 10year PFS was 62% and OS was 90%.²⁰ However, in patients with malignant non-brainstem gliomas (n=39), 5year OS and PFS rates were 35% and 26% respectively, and the median PFS and OS were 12.2months and 21.3months respectively.¹⁷ In addition, in patients with brainstem gliomas (n=33), overall median survival was 11months with 1year survival rate 43.6%.²¹ Further, diffuse intrinsic pontine glioma has the worst prognosis. The median overall survival was 10months in patients with diffuse intrinsic pontine glioma (n=316) and in this large patient sample, the area under the ROC (Receiver Operating Characteristic) curve (AUC) for the final multivariate survival model was 0.68.²⁴

A number of prognostic factors such as tumor characteristics (type, grade, location, etc.), imaging features and treatment are associated with patients’ survival.^{17,19,20,23‒26} The AUC (0.68) of the final multivariate survival model for a large sample of patient with diffuse intrinsic pontine glioma (n>300)²⁴ indicates that the survival estimate and prognostic factor identification made by the multivariate survival model are far from perfect, and error may exist in the survival results.

Brain tumors in children are heterogeneous, and have imaging and histological features that are quite different from adults. Posterior fossa tumors are the most studied pediatric brain tumors. Multivariate approaches are powerful analytic tools suitable for high dimensional problems, and have been increasingly used in pediatric brain tumor classification (or segmentation) and patient survival (outcome) assessment.

Pediatric brain tumor classification/segmentation with multivariate analysis

The large variations in the classification results among the imaging studies (even in similar samples) may be explained by viewing the process of brain tumor classification as an image processing chain, and the final classification result (classification accuracy) as the imaging diagnostic accuracy. A number of factors along the tumor classification processing chain have impacts on the final result.

First, image selection for analysis: The most commonly used imaging data for tumor classification is MRI (T1, T2, FLAIR); DWI and MRS are often used; and PWI is sometimes used. Although the diagnostic values of advanced imaging modalities such as PWI and the optimal MR imaging protocol for tumor classification are still to be determined, studies have shown that metabolite ratios (from MRS) or ADC features (from DWI) alone could not discriminate the tumor groups, but combined ADC and metabolite ratio features could;⁴ further, the combination of DWI, MRS and PWI was good for tumor classification (accuracy 55.76 %), and the combination of DWI and PWI was good for tumor grade evaluation (accuracy 73.24%).³ More studies are needed to examine the diagnostic values of advanced MRI imaging modalities for each tumor type and grade, and explore the optimal MR imaging protocol for classification of pediatric brain tumors.

Second, feature extraction: Some imaging features such as shape, histogram, tumor location, ADC, metabolite concentration ratio and CBV (cerebral blood volume) can be obtained by straightforward standard computation. However, some imaging features such as texture features are not straightforward nor standard. They can be 2D or 3D, based on grey-level co-occurrence matrix or grey-level run-length matrix,¹⁴ or fractal dimension or multi-fractional Brownian motion.^8,9 Study has shown that computed with 2D texture features, 3D texture features improved tumor classification performance.¹⁴ In addition, it has been shown that multi-fractional Brownian motion-based texture features produced high tumor segmentation accuracy for T1 and FLAIR images and for T1-T2-FLAIR fused images (100%), and intensity features best for T2 images.⁸ Therefore, classification performance can be improved by standardizing (e.g., 3D texture features) and optimizing feature extraction.

Third, feature selection: Studies have investigated various feature selection approaches including: PCA, boosting, KLD (Kullback-Leibler divergence),⁸ entropy (entropy-MDL discretization);¹⁴ mRMR (maximum-relevance minimum redundancy) and feed forward methods,⁸ and expectation maximization for feature fusion.⁸ Since feature selection methods determine which features to be used for classification analysis, the quality of these methods directly affects classification result. Further research is needed to optimize and standardize feature selection to improve tumor classification.

Fourth, classification: A variety of multivariate classifiers such as LDA, SVM, ANN, cluster analysis and random forest have been applied to tumor classification. The classification performances of 6 classifiers (naïve Bayes, k-nearest neighbor (kNN), classification tree, SVM, ANN, logistic regression) have been examined in a recent study which reported the tumor classification results, i.e., the overall classification accuracy of these classifiers (using 3D texture features): 92% for SVM and ANN; 90% for logistic regression; 88% for naïve Bayes; 83% for classification tree and kNN.¹⁴ The large differences in classification performances (e.g., 83% vs. 92%) indicates the importance of selecting the best classifier for the data (for patients with specific tumor types and grades), standardizing classifier for each tumor type and grade, and optimizing the classifier for the best classification performance.

Taken together, variations in each step along the imaging processing chain of tumor classification could accumulate and cause the large variations in final classification results among the studies. Therefore, optimizing and standardizing the imaging processing chain of tumor classification may reduce the large variations of classification results among the studies, improve classification performance, and enhance the diagnostic values of MRI imaging modalities.

Survival/outcome assessment with multivariate analysis in pediatric brain tumors

Compared with tumor classification studies, the survival assessment studies have larger sample sizes (2 studies have sample sizes >300) and there are less variations in the survival results among the studies. However, as indicated in the AUC (0.68) of the final multivariate survival model,²⁴ the error rate in the multivariate survival analysis is un-neglectable. The process of survival assessment in pediatric brain tumors can also be viewed as a data processing chain, and several factors along the chain have impacts on the final results.

First, data selection for analysis: A wide range of data can be used for patients’ survival assessment (patient’s age, gender, symptoms, tumor characteristics, diagnostic latency, treatments, etc.). Some data needs to be extracted or computed from raw data. For example, imaging features such as ACTC (Apparent transient coefficient in tumor, a measure of the gradient change of ADC from the peri-tumoral edema into the tumor core) extracted from DWI are associated with survival.¹⁹ Since each data contributes to the final survival results differently (i.e., each has different weight) and some data are of low quality, data needs to be screened and selected (e.g., according to their weights) for survival analysis. Different data selection affects survival estimate. Thus, optimizing and standardizing data selection may reduce errors and improve survival analysis.

Second, statistical analysis: Survival assessment is a standard approach:

1. Use Kaplan-Meier method to estimate progression-free survival (PFS) and overall survival (OS), and compute differences in OS between different groups (tumor groups or grades) with univariate analysis through Kaplan-Meier survival plots;
2. Use multivariate Cox proportional hazards model to evaluate the significance of associated data variables (prognostic factors that are associated with survival) indicated by the univariate analysis.

However, the methods that select data variables or prognostic factors may vary among studies (either from univariate analysis to multivariate analysis, or in refining the multivariate analysis model). Bootstrapping is needed to validate the final multivariate model so that the results of survival analysis may be more accurate and the final model may be generalizable.²⁴ Taken together, optimizing and standardizing the data processing chain in survival assessment may reduce errors, improve survival estimation, and enhance the identification of prognostic factors in survival analysis.

A method comparison between multivariate analyses in tumor classification and survival assessment is presented in Table 3. Compared with relatively complex imaging data and their processing in tumor classification, the relatively simple data and their processing in survival assessment make it possible to perform multivariate survival analysis on large samples (e.g., n>300), which makes the results of survival analysis (based on large samples) more stable and reliable.

In summary, this paper reviewed the studies that applied multivariate analysis to tumor classification (segmentation) and survival (outcome) assessment in pediatric brain tumors. The large variations in the classification results among the tumor classification studies (even in similar patient populations) may be reduced by optimizing and standardizing image processing chains of tumor classification. Similarly, optimizing and standardizing data processing chains of survival assessment may improve survival analysis and reduce errors in survival estimates and identification of prognostic factors.

As multivariate analytic approaches, data processing technologies and imaging techniques advance in the Big Data era of the 21^st century, it is anticipated that the obstacles in the complex imaging data processing in tumor classification will be overcome and complex data processing will be revolutionized. This will make accurate automatic tumor classification/segmentation (for each tumor type and grade) possible to early detect and treat tumors, guide treatment planning, monitor tumor progression and treatment effects, together with advanced survival assessment to guide life-saving rescue and recovery planning, revolutionize patient care, and truly benefit children with brain tumors.

None.

Author declares that there is no conflict of interest.

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