Survival Prediction After Transarterial Chemoembolization for Hepatocellular Carcinoma: a Deep Multitask Survival Analysis Approach

Abstract

The accurate prediction of postoperative survival time of patients with Barcelona Clinic Liver Cancer (BCLC) stage B hepatocellular carcinoma (HCC) is important for postoperative health care. Survival analysis is a common method used to predict the occurrence time of events of interest in the medical field. At present, the mainstream survival analysis models, such as the Cox proportional risk model, should make strict assumptions about the potential random process to solve the censored data, thus potentially limiting their application in clinical practice. In this paper, we propose a novel deep multitask survival model (DMSM) to analyze HCC survival data. Specifically, DMSM transforms the traditional survival time prediction problem of patients with HCC into a survival probability prediction problem at multiple time points and applies entropy regularization and ranking loss to optimize a multitask neural network. Compared with the traditional methods of deleting censored data and strong hypothesis, DMSM makes full use of all the information in the censored data but does not need to make any assumption. In addition, we identify the risk factors affecting the prognosis of patients with HCC and visualize the importance of ranking these factors. On the basis of the analysis of a real dataset of patients with BCLC stage B HCC, experimental results on three different validation datasets show that the DMSM achieves competitive performance with concordance index of 0.779, 0.727, and 0.780 and integrated Brier score (IBS) of 0.172, 0.138, and 0.135, respectively. Our DMSM has a comparatively small standard deviation (0.002, 0.002, and 0.003) for IBS of bootstrapping 100 times. The DMSM we proposed can be utilized as an effective survival analysis model and provide an important means for the accurate prediction of postoperative survival time of patients with BCLC stage B HCC.

Appendix

• A. Data Preprocessing

Three cohorts (i.e., derivation, internal, and multicenter testing cohorts) have missing values. The number and percentage of HCC patients with missing values in each variable of datasets are provided in Table 4.

Missing values are a common problem in clinical medical data. Therefore, to ensure data quality, we must take appropriate measures to reduce data problems as much as possible. Specifically, our HCC data include continuous variables and categorical variables. For continuous features, we impute the median value of each feature and fill in the missing value, and for categorical features, we completed missing values by replacing values by the most common occurrence. On the basis of the recommendations of HCC clinical medical experts, we used the inclusion and exclusion criteria mentioned above, excluded some abnormal feature values, and removed nine features (lymph node metastasis, distant metastasis, invasion of vena cava or atrium, invasion of hepatic veins, branch of invaded portal vein, portal vein invasion, PS score, hepatic encephalopathy, and treatment response in last time slice). Therefore, the last 21 features (include Child-Pugh) related to demographic, clinical, and biological features of patients were filtered into the model.

Then, we use the standard score method for continuous features and one-hot encoding for categorical variables to perform data normalization. For feature X, the standard score method’s output is

$${X}^{\hbox{'}}=\frac{X-\mu (X)}{\delta (X)}$$

(1)

μ is the mean, and δ is the standard deviation.

Table 4 Statistics of the missing values in each feature of three datasets

• 2 Hyperparameter Tuning for the Baselines

For each experiment, we use fivefold cross-validation to maximize the concordance index (C-index) on the validation dataset and obtain the optimal hyperparameters of the model. In our DMSM, hyperparameters include batch size, learning rate, nodes, λ, β, and activation. The hyperparameters tuned for DMSM and other comparative models are presented below, and the optimal selection of hyperparameters is based on grid search.

DMSM: The number of nodes in hidden layer is selected from [5, 10, 15, 20, 25, 30]; the activation function is selected from [RELU, Sigmoid, Tanh]; the batch size is selected from [32, 64, 128, 256, 512]; the size of the learning rate is selected from [0.0001, 0.001, 0.01, 0.1]; the size of λ is selected from [0.01, 0.05, 0.1, 0.5, 1.0]; the size of β is selected from [0.001, 0.005, 0.01, 0.05, 0.1, 0.5]. We perform fivefold cross-validation, randomly select parameters from a given grid, and finally select the set of hyperparameters with the highest C-index. The hyperparameters for DMSM method and two-baseline models are shown in Tables 5 and 6.

RSF: We followed the experimental settings provided in the RSF GitHub repository.¹

The size of Max_depth is selected from 5, 10, 15, and 20; the max_features is selected from [“sqrt,” “int,” “float,” “log2”]; the sample_size_pct is selected from [0.55, 0.60, 0.65, 0.70]; the min_node_size is selected from [10, 20, 30, 40, 50]; the number of num_trees is selected from [100, 200, 300, 400, 500]. The hyperparameters are shown in Table 7.

DeepHit: We followed the experimental settings provided in the DeepHit GitHub repository.² The size of alpha is selected from [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]; the size of sigma is selected from [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]; the num_nodes is selected from [[4, 8], [4, 16], [8, 16], [8, 32], [16, 32], [32, 32].The selection interval of the learning rate and batch size is the same as above. The hyperparameters are shown in Table 8.

Table 5 DMSM experimental hyperparameters

Table 6 Hyperparameters of two-baseline models

Table 7 Hyperparameters of RSF model

Table 8 Hyperparameters of DeepHit model