The Efficacy of Shape Radiomics and Deep Features for Glioblastoma Survival Prediction by Deep Learning ^†

Abstract

Glioblastoma (known as glioblastoma multiforme) is one of the most aggressive brain malignancies, accounting for 48% of all primary brain tumors. For that reason, overall survival prediction plays a vital role in diagnosis and treatment planning for glioblastoma patients. The main target of our research is to demonstrate the effectiveness of features extracted from the combination of the whole tumor and enhancing tumor to the overall survival prediction. By the proposed method, there are two kinds of features, including shape radiomics and deep features, which is utilized for this task. Firstly, optimal shape radiomics features, consisting of sphericity, maximum 3D diameter, and surface area, are selected using the Cox proportional hazard model. Secondly, deep features are extracted by ResNet18 directly from magnetic resonance images. Finally, the combination of selected shape features, deep features, and clinical information fits the regression model for overall survival prediction. The proposed method achieves promising results, which obtained 57.1% and 97,531.8 for accuracy and mean squared error metrics, respectively. Furthermore, using selected features, the result on the mean squared error metric is slightly better than the competing methods. The experiments are conducted on the Brain Tumor Segmentation Challenge (BraTS) 2018 validation dataset.

1. Introduction

Gliomas are a primary brain tumor type forming when the glial cells grow out of control. Gliomas grow in the brain and develop in the spinal cord part. The most common aggressive brain tumor accounts for around 80% of primary tumors in the brain [1]. Gliomas are categorized into four grades (I, II, III, and IV), and the treatment planning depends on the level of Grade. While Grade I and II are considered low-grade gliomas (LGG), Grade III and IV are known as high-grade gliomas (HGG). The LGG group (known as the benign tumor) has long-term survival compared to the HGG group. The IV grade type is the most aggressive primary brain tumor known as glioblastoma (GBM). Glioblastoma could occur in all ages, especially in older people. Nowadays, the treatment for GBM only extends the survival time of patients less than two years and the treatment are required immediately [2]. GBM has four intra-tumoral structures, including enhancing tumor (ET), non-enhancing tumor (nET), necrotic and edema, as shown in Figure 1. The intra-tumoral structure is categorized into three GBM tumor regions: the whole tumor containing all sub-tumoral structures, the tumor core structures except for edema, and the separate ET part.

Magnetic resonance imaging (MRI) is one of the most widespread invasive techniques in neuro-oncology for diagnosis and treatment planning. Depending on the mode setting on the MRI machine, there are four modalities, including T1-weighted (T1), T1-weighted contrast enhance (T1Ce), T2-weighted (T2), and fluid attenuation inversion recovery (FLAIR), shown in Figure 2 below. Different MRI modalities are used to evaluate the level of the tumor, its evolution, and the response for treatment [2]. While the T1Ce modality has a contrast-enhancing agent, Gadolinium, injected into the body and enhances the tumor core’s brightness, the FLAIR modality suppresses the fluid (mainly cerebrospinal fluid) CSF) and enhances an edema part.

Recently, radiomics features extracted from the MRI modalities and segmented maps of tumors have been utilized to predict prognosis and therapeutic response for various cancer types. The radiomics features include many valuable features, which describe the statistics, the shape, and the texture of the brain tumor. Research shows the relationship between the radiomics features of the tumor and the survival day of GBM patient. Inspired by the importance of shape feature to OS days of the patient [2], this study aims to evaluate the most significant shape features to estimate the survival time of patients. Moreover, the deep learning model is applied to predict the OS time of patients.

In this paper, we propose a method to predict the survival time of patients, including two stages. First, because of the small-sized-enhancing tumors in the GBM, DK-Net [4] is used to segment the tumor region. After that, the univariate and multivariate Cox proportional hazard model (CoxPH) is applied to find the most significant shape features related to the survival time of GBM patients. Next, deep features are extracted using 3D ResNet18 to utilize the information of tumors from segmented maps. Finally, selected radiomics features, deep features, and clinical information are concatenated and fit into the multi-layers perceptron to predict the survival time of patients (in days). Our contribution in this work is shown below:

• Sphericity, 3D maximum diameter, and surface area are three significant shape features relevant to the survival analysis of glioblastoma patients. Furthermore, these features from the enhancing tumor have more effect on patients’ survival time than those from the whole tumor based on hazard ratio.
• Aside from shape features, the extracted features (known as deep features) from enhancing tumor and whole tumor are essential for survival prediction compared to those from the whole tumor only; therefore, enhancing tumor’s characteristics affects the survival prediction for GBM patients.

2. Related Work

In recent years, much research has been conducted to predict the OS days of GBM patients. Most trending method contains two stages: segmentation and uses radiomics features from the segmented map to predict the survival time. Shboul et al. use the ensemble of random forest (RF) and convolutional neural network (CNN) to obtain the segmented map, and after that, RF predictive model is used to predict the survival days using 240 most essential features out of 1366 features in total based on Kaplan–Meier curve [5]. In [6], Baid et al. use the 3D Unet model with three stages of encoder–decoder architecture to obtain the segmented maps. After that, radiomics features are extracted and fit a multi-layer perceptron (MLP) network for OS prediction. Feng et al. use the ensemble of 3D UNets with the variation of input size, the number of encoder/decoder blocks, and the number of layers to robust the results of the segmentation task. Based on the segmentation result, the volume, shape, and surface area are manually identified and combined with clinical information to obtain OS days via linear regression [7]. In [8], and boosting ensemble of three different networks, including Unet [9], DFKZnet [10], and CA-CNN [11], was applied to obtain the final segmentation result via majority voting. Fourteen selected radiomics features are fit to RF for OS prediction. Madjid [12] et al. found that location-based features efficiently enhance the prediction result. They identify the location-based features by the distance from the tumor to the brain’s center, the largest diameter of the tumor, and the vertical slide number having the most oversized tumor diameter. Combined with the selected radiomics features, the OS prediction result slightly improves. According to [13], deep features are extracted from MRI modalities via a CNN network that describes the tumor’s size, shape, and texture. Further, the NLSE model is proposed with the integration of the non-local module and the squeeze-and-excitation module to robust the segmentation results. Finally, The factor analysis is applied to reduce radiomics features and deep features, and all the remaining features fit the RF regression to obtain OS days.

Moreover, due to the time-consumption of tumor segmentation for ground-truth labeling, some researchers proposed that using the extracted features from MRI modalities directly. In [14], Renato et al. proposed an OS prediction method without segmentation by using a saliency map that identifies the tumor’s location. Combined with clinical information, the OS prediction results are promising compared to other methods. According to [15], Linmin Pei et al. extract high-dimensional features directly from the CNN network to obtain OS prediction results—ages are the additional features used to improve the results. Relevant features are selected by the LASSO method, and all the features are fit to linear regression to obtain results.

3. Materials and Methods

3.1. Overview

Inspired by the effectiveness of shape radiomics features from the ET and WT [2], our method contains two stages, including segmentation and survival prediction based on selected shape features. First, due to the importance of enhancing the tumor [1], DK-Net [4] is utilized to enhance the result of the ET segmented map. After that, all the shape radiomics features are extracted from ET and WT parts, and hazard ratio evaluated by Cox proportional hazard model is applied to demonstrate the importance of each feature to the survival time of patients. Next, using a 3D ResNet18, deep features are extracted from the whole tumor and the enhancing tumor. Then, a random forest algorithm is applied to select the most nine important deep features from ET and WT. Finally, selected shape features, deep features, and clinical features are fit into a multi-layer perceptron for survival prediction of GBM patients. The architecture of our model is shown in Figure 3.

3.2. Dataset

The experiments were performed on the Brain Tumor Segmentation (BraTS) 2018 Dataset [3,16,17]. The BraTS 2018 dataset contains 285 and 66 training and valid dataset samples; however, only 163 and 53 samples were used for the survival prediction task. Each patient sample consists of 4 MRI modalities, including T1-weighted, post-contrast T1-weighted (T1Ce), T2-weighted (T2), and T2 fluid attenuated inversion recovery (FLAIR). In addition, the ground truth for segmentation is provided for training data, containing label 1 for nET/necrotic, label 2 for edema, label 4 for ET, and label 0 for background. Further, survival days are given for each patient in training data. For data analysis, due to the accuracy of labeling, we utilize the training data for the effectiveness of shape radiomics feature to survival time of patients. In addition, clinical information such as age, tumor grade, and resection status is also provided in this dataset. The resection status contains gross total resection (GTR), subtotal resection (STR), and NA (not available) for HGG patients.

3.3. Segmentation

DKNet [4] is used for the brain tumor segmentation task to segment into tumor sub-regions, including edema, necrotic, and enhancing tumor. DKNet is based on a variant of 3D U-Net called the dilated multi-fiber network (DMFNet) [18] with encoder–decoder architecture. One of the advantages of this model is that it could detect the small-sized tumor in the brain, significantly enhancing tumors in gliomas. Moreover, reducing computation cost and memory while keeping good overall performance is also the advantage of this model. In 3D UNet and any variant of this network, the purpose of down-sampling layers is that extract features and extend the receptive field, but the resolution of features could be reduced dramatically; therefore, the feature of small objects can be lost. DKNet is multitask learning with two tasks. The first task is brain tumor segmentation from four MRI modalities with three-segmented masks of regions, including whole tumor (WT), tumor core (TC), and enhancing tumor (ET). The second task is additional feature reconstruction by adding an up-sampling layer and an multi-fiber unit after each encoder layer. The second task remains the crucial features in the following layers and minimizing the information loss on small objects, especially on ET.

3.4. Tumor Shape Radiomics Features Analysis

After segmentation, shape radiomics features are extracted from the enhancing tumor and the whole tumor of total patients in training data. Tumor shape feature plays a vital role in the OS prognosis of patients. Furthermore, these features describe the tumor’s shape, geometry, and specific surface. All the features are derived from T1Ce and the ground truth to analyze their relationship and survival time.

There are 14 shape features extracted from the open-source Pyradiomics library [19], which are mesh volume, minor axis length, sphericity, surface area, surface volume ratio, voxel volume, elongation, flatness, least axis length, major axis length, maximum 2D diameter column, maximum 2D diameter row, maximum 2D diameter slice, and maximum 3D diameter. Each feature describes specific properties of tumor shape. Cox proportional hazard model (CoxPH) and Kaplan–Meier (KM) estimator are applied to evaluate the relationship between the shape features and the survival time of patients.

Kaplan–Meier (KM) estimator is a statistics method measuring the fraction of the living patients in a certain amount of time after treatment. The KM survival curve is the probability of surviving in the given time while considering the time in many small intervals [20]. The KM estimator is calculated by Equation (1). Based on the KM estimator method, KM curves is a plot over time to compare the survival function of different groups.

$$S\left(t\right)=\prod _{i:t_i<t}(1-\frac{d_i}{n_i})$$

(1)

where:

• $t_i$ is the time point at least one patient dead.
• $d_i$ is number of patients dead at $t_i$.
• $n_i$ is number of patients surviving until time $t_i$.

Cox proportional hazard model (CoxPH) is a regression model using statistics method for investigating the association between one or several predictors and the survival time in medical field. The purpose of CoxPH is to evaluate the effect of one or several factors on survival time of patients. Cox model is denoted by hazard function h(t) [21]. Hazard function h(t) is considered as the risk of dying of each patient at time t. For given vector of predictors z, CoxPH model is expressed as follows:

$$h\left(t\right|\mathbf{z})=h_0\left(t\right)\ast \exp \left({\beta }^{\prime }\mathbf{z}\right)$$

(2)

where:

• h(t|z): hazard function determined by given vector of several predictors z.
• $h_0\left(t\right)$: is an unspecific function of time.
• $\exp \left({\beta }^{\prime }\mathbf{z}\right)$: hazard ratio (HR). HR = 1: predictors does not have effect on survival time, HR < 1: associated with improved survival time, HR > 1: associated with increased risk or decreased survival time [21].

Alternatively, CoxPH is also expressed in term of cumulative hazard function as below:

$$H\left(t\right|\mathbf{z})=H_0\left(t\right)\ast \exp \left({\beta }^{\prime }\mathbf{z}\right)$$

(3)

where $H_0\left(t\right)$ is the baseline cumulative hazard function, which is calculated by the Nelson–Aalen estimator by Equation (4).

$$H(t_{\left(i\right)})=\sum _{j=1}^i\frac{d_j}{n_j}$$

(4)

where $d_j\left(t\right)$ is number of deaths at time $t_{\left(i\right)}$ and $n_j$ is the number of alive patients before time $t_{\left(i\right)}$.

Based on the Breslow estimator, the relationship between the cumulative hazard function and survival function is established by following Formula (5); therefore, cumulative hazard function and survival function have an opposite relationship and are based on the CoxPH model, and we can evaluate, which shape features are significantly related to survival time. Furthermore, because HR = 1 means no effect of features on survival time, 95% confident interval (CI) of HR also does not include 1 (null value). Further, p-value is considered statistics significant if its value equals or is smaller than 0.05 in CoxPH regression model.

$$S\left(t\right)=\exp \left(-H\left(t\right|\mathbf{z})\right)$$

(5)

The relationship between shape radiomics features and patients’ survival days are evaluated by the Cox proportional hazard regression model and the KM curve. Firstly, each shape feature fits into the univariate Cox regression model and is judged by the hazard ratio (HR), 95% confidence interval (CI), and p-value. Then, by dividing each feature into two groups based on the median value of each significant shape feature, we could evaluate the effect of each feature on patients’ survival time following the KM survival curve.

3.5. Deep Feature Extraction

While FLAIR is the best modality for radiologists to see the WT, ET boundaries are best visualized in T1ce [22]. Because of that reason, CNN architecture is utilized to extract the high-level features from FLAIR and T1ce modalities for WT and ET, respectively. First, the MRI modalities are cropped into 128 × 128 × 128 to remove the background voxel. After that, ResNet18 architecture, pre-trained in ImageNet, is applied to extract meaningful information from MRI modalities. ResNet18 has four layers, containing two basic blocks in each layer, followed by two modified fully connected (FC) layers with 512, 101 nodes, respectively. The skip connection is also applied in each convolution layer. The output of ResNet18 is the survival days of patients. The deep features are chosen from the last FC layer of this network, containing the most meaningful features to predict the OS days of patients related to each kind of tumor. The detailed architecture of the network is shown in Figure 4. The feature selection technique is essential for the over-fitting problem reduction in the survival prediction task and keep the most meaningful features related to survival time of patients; therefore, a random forest algorithm is applied to find most of the nine essential features from ET and WT, respectively.

3.6. Overall Survival Prediction

There are six shape radiomics features and 18 extracted deep features combined with age, which is trained to predict the survival time of GBM patients. Linear regression (LR), light gradient boosting (LightGBM), and multi-layer perceptron (MLP) are applied to build the predictive model to evaluate the effectiveness of each model for this survival task separately. The training dataset is split into training and validation datasets by 80:20 ratio to avoid the over-fitting problem. For the MLP model, the output is the survival days of patients, which are evaluated on the classification of three survival groups as described in the previous section. MLP has two fully connected (FC) layers, followed by ReLU activation action after FC layer.

4. Results

4.1. Segmentation

All 285 training data are used in the training process. Sixty-six patients are provided for validation. The dice index, 95 Hausdorff (HD) distances of enhancing tumor (ET), whole tumor (WT), and tumor core (TC) will be calculated by submitting to CBICA’s Image Processing Portal. The result is obtained by this method in

Table 1. Results of segmentation for BraTS 2018 validation dataset.

Method	Dice ET	Dice TC	Dice WT	HD 95 ET	HD 95 TC	HD 95 WT
DKNet	0.8182	0.8181	0.8876	2.6835	5.6112	4.6000

.

4.2. Evaluation Metrics for Survival Prediction

The survival prediction results are evaluated in three different metrics including accuracy, mean squared error (MSE), and SpearmanR metrics. All the results are submitted to online link for result evaluation. The main task is classification, which divided into three groups: short survivors (<10 months), medium survivors (≥10 months and ≤15 months), and long survivors (>15 months). The accuracy metrics are calculated by following equation:

$$Accuracy=\frac{NumberofCorrectedpredictions}{Totalnumberofpatients}$$

(6)

Moreover, the MSE metric shows the difference between the prediction days and the actual survival days of patients (ground truth) provided in the dataset because this is supervised learning method. The lower the MSE values are, the better prediction values are. SpearmanR metric describes the strength and the direction of monotonic association between predicted results and ground truth (GT). The value of SpearmanR is in the range of −1 to +1. If the SpearmanR value is close to 1, the ranking of the patients’ survival time is closer to the order of GT’s. The MSE and SpearmanR metrics are calculated by following equations:

$$MSE=\frac{{\sum }_k^n{(d_k-d_k^{\prime })}^2}{n}$$

(7)

where $d_k$ and $d_k^{\prime }$ are predicted days and actual survival days of patients (GT), respectively.

$$SpearmanR=1-\frac{6\sum d_i^2}{n(n^2-1)}$$

(8)

where n is total number of patients, $d_i$ is difference in paired ranks between predicted days and GT days [23].

4.3. Shape Radiomics Features Analysis

The univariate CoxPH regression model demonstrates the importance of each shape radiomics feature, as shown in Table 2. As shown in the table, sphericity, surface area, and 3D maximum diameter of tumor for both the whole tumor and the enhancing tumor are significant predictors for OS prognosis with a p-value < 0.05. Moreover, the HR and its 95% CI are smaller than 1, which means that the patients with larger sphericity values have a longer survival time. On the contrary, patients with smaller maximum 3D diameter and surface area values have longer survival time based on HR and its 95% CI. Some other features also have a p-value < 0.05; however, the HR ratio and its CI contain one so that the effectiveness for OS prediction is poor and no means; therefore, other features are not considered significant predictors for this task. Furthermore, age is the significant predictor for survival prediction based on the result in Table 2. The meaning of the most three significant shape predictors are described below:

• Surface area measures the total area of the tumor’s surface on a 3D dimension.
• Maximum 3D diameter is the most significant Euclidean distance between tumor surface mesh vertices [19].
• Sphericity measures the roundness of the shape of the tumor region relative to a sphere [19].

Table 2. Shape radiomics features and clinical information analysis based on univariate CoxPH model.

	HR	95% CI	p-Value
Enhancing Tumor
Elongation	0.779	0.284–2.138	0.6
Flatness	0.837	0.319–2.195	0.7
Least Axis Length	1.018	1.002–1.035	0.06
Major Axis Length	1.013	1.004–1.021	0.07
Maximum 2D Diameter Column	1.011	0.960–1.022	0.06
Maximum 2D Diameter Row	1.014	1.000–1.024	0.004
Maximum 2D Diameter Slice	1.012	0.990–1.021	0.005
Maximum 3D Diameter	1.112	1.023–1.223	0.005
Mesh Volume	1	1–1	0.05
Minor Axis Length	1.019	1.004–1.033	0.06
Sphericity	0.184	0.049–0.698	0.01
Surface Area	1.231	1.139–1.342	0.0001
Surface Volume Ratio	1.054	0.642–1.729	0.8
Voxel Volume	1	1–1	0.04
Whole Tumor
Elongation	0.514	0.122–2.160	0.4
Flatness	0.315	0.068–1.456	0.1
Least Axis Length	1.012	0.995–1.028	0.2
Major Axis Length	1.012	1.003–1.012	0.07
Maximum 2D Diameter Column	1.008	1.000–1.016	0.06
Maximum 2D Diameter Row	1.009	0.992–1.017	0.04
Maximum 2D Diameter Slice	1.010	1.000–1.017	0.03
Maximum 3D Diameter	1.017	1.011–1.028	0.03
Mesh Volume	1	1–1	0.1
Minor Axis Length	1.016	0.984–1.031	0.02
Sphericity	0.2669	0.069–0.762	0.02
Surface Area	1.023	1.003–1.127	0.02
Surface Volume Ratio	0.796	0.201–3.151	0.7
Voxel Volume	1	1–1	0.1
Clinical Information
Age	1.036	1.021–1.051	0.000001

Table 2. Shape radiomics features and clinical information analysis based on univariate CoxPH model.

	HR	95% CI	p-Value
Enhancing Tumor
Elongation	0.779	0.284–2.138	0.6
Flatness	0.837	0.319–2.195	0.7
Least Axis Length	1.018	1.002–1.035	0.06
Major Axis Length	1.013	1.004–1.021	0.07
Maximum 2D Diameter Column	1.011	0.960–1.022	0.06
Maximum 2D Diameter Row	1.014	1.000–1.024	0.004
Maximum 2D Diameter Slice	1.012	0.990–1.021	0.005
Maximum 3D Diameter	1.112	1.023–1.223	0.005
Mesh Volume	1	1–1	0.05
Minor Axis Length	1.019	1.004–1.033	0.06
Sphericity	0.184	0.049–0.698	0.01
Surface Area	1.231	1.139–1.342	0.0001
Surface Volume Ratio	1.054	0.642–1.729	0.8
Voxel Volume	1	1–1	0.04
Whole Tumor
Elongation	0.514	0.122–2.160	0.4
Flatness	0.315	0.068–1.456	0.1
Least Axis Length	1.012	0.995–1.028	0.2
Major Axis Length	1.012	1.003–1.012	0.07
Maximum 2D Diameter Column	1.008	1.000–1.016	0.06
Maximum 2D Diameter Row	1.009	0.992–1.017	0.04
Maximum 2D Diameter Slice	1.010	1.000–1.017	0.03
Maximum 3D Diameter	1.017	1.011–1.028	0.03
Mesh Volume	1	1–1	0.1
Minor Axis Length	1.016	0.984–1.031	0.02
Sphericity	0.2669	0.069–0.762	0.02
Surface Area	1.023	1.003–1.127	0.02
Surface Volume Ratio	0.796	0.201–3.151	0.7
Voxel Volume	1	1–1	0.1
Clinical Information
Age	1.036	1.021–1.051	0.000001

From Table 2, three shape radiomics features, including sphericity, 3D maximum diameter, and surface area consider as significant predictors for survival tasks. In detail, selected shape features extracted from the enhancing tumor have more effect on survival time based on HR. Consequently, enhancing tumor plays an essential role in survival prediction.

For detail analysis, Kaplan–Meier (KM) estimators are utilized to evaluate the relationship between each feature to survival time of GBM patients. The Kaplan–Meier estimator is a non-parametric method used to measure the ratio of patients living for a specific time after treatment [20]. For experiments, two patient groups are generated based on the median value of each selected feature. Then, KM curves are plotted for both selected shape features for two group patients. Further, the log-rank test is applied to compare the survival function between two groups for each shape feature based on the p-value. If the p-value of the log-rank test is smaller than 0.05, two groups are statistically significant, mentioning different distribution between two groups. According to the KM curve and log-rank test, patients with a smaller surface area, longer 3D maximum diameter, and smaller sphericity ratios have a longer survival time than others for ET and WT tumors. The detail information about KM curves and log-rank test (p-value) for each feature is shown in Figure 5, Figure 6 and Figure 7.

4.4. Overall Survival Prediction

Aside from the three significant shape features, deep features are utilized to have a high-level meaning related to the survival time of patients from ET and WT tumors. The effectiveness of deep features from ET and WT is demonstrated by using ResNet18. From

Table 3. The results of OS prediction based on deep features (DFs) extracted from ET, WT using 3D ResNet18.

DFs	Accuracy	MSE
WT DFs	0.393	244,139.9
ET DFs	0.321	185,454.8
Selected DFs (18 features)	0.464	123,320.8

, using selected deep features from ET and WT, the accuracy and the MSE results are slightly improved compared to using deep features from ET and WT separately.

After that, combined with selected shape features and age, the predicted result is evaluated in the online portal https://ipp.cbica.upenn.edu/ (accessed on 1 February 2022). There are 28 validation patients with unknown survival times. There result of three predictive models are shown in

Table 4. The results of OS prediction from different combination features of three predictive models (SFs: 6 selected shape features, DFs: 18 selected deep features) based on accuracy (Acc) and mean squared error (MSE) metrics.

Features	Linear Regression		LightGBM		MLP
	Acc	MSE	Acc	MSE	Acc	MSE
SFs + Age	0.536	128,839.4	0.500	108,577.9	0.536	99,482.7
SFs + DFs + Age	0.500	116,463.9	0.464	99,577.4	0.571	97,531.8

.

From Table 4, MLP obtains better results compared to other machine learning models, which achieves 57.1% and 97,531.8 on accuracy and MSE evaluation metrics, respectively. Compared to Linh et al. [2] result, when we use only selected shape features, the result on MSE metrics improves slightly, which decreases from 152,250.8 to 99,482.7 while the accuracy result is the same; therefore, sphericity, 3D maximum diameter, and surface area are three significant predictors for survival prediction of patients. Adding the deep feature and MLP predictive model could improve classification and regressive tasks.

Further, compared to other methods on the BraTS18 validation dataset in

Table 5. Comparison between our method and others in BraTS18 validation dataset.

Methods	Accuracy	MSE	SpearmanR
[7]	0.321	103,839.4	0.247
[24]	0.500	97,759.5	0.267
[22]	0.571	5,955,021.1	0.427
[2]	0.536	152,250.8	0.216
Ours	0.571	97,531.8	0.294

, our method achieves promising results with 57.1% and 97,531.8 on accuracy and MSE metrics, respectively,

5. Discussion

In this paper, there are three significant predictors, including sphericity, surface area, and maximum 3D diameter related to survival time of glioblastoma patients based on CoxPH and KM survival curve. GBM patients with lower surface tumor area, lower maximum 3D diameter, and higher sphericity ratio have longer survival times. Furthermore, compared with WT, shape features extracted from ET have more effect on the survival time of patients based on hazard ratio, which means ET is important for GBM survival prediction. Combined with deep features from the enhancing tumor and the whole tumor, survival time prediction is promising and could be applied for clinical prognosis in the future; however, compared to Baid et al. [22], the SpearmanR coefficient in our result is not good, which means the order of predicted survival time is unstable for time series analysis. Moreover, the medical meaning of deep features from ET and WT is ambiguous. For future work, we will try to predict the survival time of patients in the same order compared to the actual survival days. Furthermore, we need to clarify and prove the practical significance of the deep features in the medical field for further applications.

6. Conclusions

This paper proposes a framework for predicting the overall survival time for glioblastoma patients in two stages. The first stage is the segmentation of brain tumors based on DKNet, which improves the segmented enhancing tumor in brain tumors. The second stage is shape radiomics, and deep features are extracted from the combination of enhancing tumor and the whole tumor fit into a multi-layer perceptron model to predict the overall survival time. It has been seen from experimental results on BraTS18 compared to other existing methods [22,24] that our proposed method achieves 57.1% and 97,531.8, which are competitive results for the accuracy metric and slightly higher values on mean squared error metric, respectively. For another BraTS dataset, the accuracy of existing studies [14] is around 55%, and machine learning or multi-layer perceptron predictive models are preferable choices for survival tasks. Optimal features finding and feature selection are trending approaches to ensure robust performance of the survival prediction tasks. Compared to the current approach, our method highlights the effect of each shape radiomics feature on the survival time of glioblastoma patients. Sphericity, surface area, and the maximum 3D diameter are the three most significant predictors affecting the survival time of glioblastoma patients via the Cox proportional model. Combined with the deep features extracted from enhancing tumor and whole tumor, we obtain promising survival results on the BraTS18 dataset. Although our approach obtains a competitive result, the performance of the proposed model is validated on the small-sized dataset, which can be improved by expanding the number of patients on a larger dataset in the future.