Computational intelligence identifies alkaline phosphatase (ALP),alpha-fetoprotein (AFP),and hemoglobin levels as most predictive survival factors for hepatocellular carcinoma

Data pre-processing and imputation

Before employing a machine learning algorithm, data needs to be pre-processed. ³⁶ In particular, X i , with i ∈ { 1 , ⋯ , n f } , can be a categorical feature space (the values of the features belong to a finite unsorted set) or a numerical-valued feature space (the values of the features belong to a possibly infinite sorted set).

In the case of categorical feature space with more than two categories, if the algorithm is not able to handle multi-categorical features (for example, Support Vector Machines and Neural Networks), we will opt for the one hot encoding and we map it in a numerical feature space. ³² Note also that some values of X may be missing. ³⁷

In this case, if the missing value is in a categorical feature, we introduce an additional category for missing values for that feature. If, instead, the missing value is associated with a numerical feature, we replace the missing value with the mean value of that feature and we introduce an additional logical feature to indicate whether the value of that feature is missing or not for a particular sample.

Algorithms

In this section we briefly recall the four algorithms that we have exploited in this study by pointing out the idea behind them, how to use them, and their hyper-parameters. The selected algorithms represent the most effective algorithms in four families of methods ³¹ : rule based methods, ensemble methods, kernel methods, and neural networks.

Handling unbalanced classes

Data available in bioinformatics for binary classification are often strongly unbalanced.^49–51 However, most learning algorithms work badly with imbalanced datasets and tend to perform poorly on the minority class and for these reasons several techniques have been developed to address this issue. ³³

The first step toward the solution of this problem is to avoid applying the inappropriate evaluation metrics for model generated using imbalanced data. ⁵² For example, overall accuracy is a very dangerous metric in this context since the more unbalanced is the dataset the more this metric tends to promote models which poorly perform on the minority class. For this reason, in this study we also included other metrics like Matthews correlation coefficient (MCC), ⁵³ F 1 score, precision-recall area under the curve (PR AUC), ⁵⁴ and receiver operating characteristic area under the curve (ROC AUC), ⁵⁵ which are more suited for the case of imbalanced data (Supplemental Material Information). Since the MCC produces a high score only if the classifier is able to correctly predict the majority of positives and negatives, we focused on this statistical indicator and ranked our method performances according to it.^36,56 A high MCC, in fact, means high sensitivity, specificity, precision, and negative predictive value. A high value of other common rates such as F 1 score and accuracy, instead, do not guarantee them.

The second step toward the mitigation of the effects of having an unbalanced dataset is to modify the algorithm or the data, but currently the most practical and effective method involves the re-sampling of the data to synthesize a balanced dataset. ³³ For this purpose we can under- or over-sample the dataset. Under-sampling balances the dataset by reducing the size of the abundant class. By keeping all samples in the rare class and randomly selecting an equal number of samples in the abundant class, a new balanced dataset can be retrieved for further modeling. Note that this method wastes a great deal of information (many samples may not be used). For this reason the oversampling strategy is more often exploited. It tries to balance the dataset by increasing the size of rare samples. Rather than removing abundant samples, artificial synthetized samples are generated (for example by repetition, by bootstrapping, or by synthetic minority). The latter method is the one that we exploited in this paper.

Model selection and error estimation

MS and EE deal with the problem of tuning and assessing the performance of a learning algorithm. ³⁴ Resampling techniques like k-fold cross validation and non-parametric bootstrap are often used by practitioners because they work well in many situations. ⁵⁷ Other alternatives exist, which represent foundations in the Statistical Learning Theory and give more insight into the learning process. Examples of methods in this last category include the seminal work of the Vapnik-Chervonenkis Dimension, its improvement with the Rademacher Complexity, the theory of compression, the Algorithmic Stability breakthrough, the PAC-Bayes theory, and more recently the Differential Privacy theory. ³⁴

In this work we will exploit the resampling techniques which rely on a simple idea: the original dataset D n is resampled once or many ( n r ) times, with or without replacement, to build three independent datasets called learning, validation and test sets, respectively ℒ l r , V v r , and T t r , with r ∈ { 1 , ⋯ , n r } . Note that ℒ l r ∩ V v r = ⊘ , ℒ l r ∩ T t r = ⊘ , V v r ∩ T t r = ⊘ , and ℒ l r ∪ V v r ∪ T t r = D n for all r ∈ { 1 , ⋯ , n r } .

Then, to select the best combination of the hyper-parameters ℋ in a set of possible ones ℌ = { ℋ 1 , ℋ 2 , ⋯ } for the algorithm A ℋ or, in other words, to perform the MS phase, we needed to apply the following procedure:

ℋ * : arg min ℋ ∈ ℌ ∑ r = 1 n r M ( A ℋ ( ℒ l r ) , V v r ) ,

(1)

where A ℋ ( ℒ l r ) is a model built with the algorithm A with its set of hyper-parameters ℋ and with the data ℒ l r and where M ( f , V v r ) is a desired metric. Since the data in ℒ l r are independent from the ones in V v r , the idea is that ℋ * should be the set of hyper-parameters which allows to achieve a small error on a data set, that is, independent from the training set.

Then, to evaluate the performance of the optimal model which is f A * = A ℋ * ( D n ) or, in other words, to perform the EE phase, the following procedure has to be applied:

M ( f A * ) = 1 n r ∑ r = 1 n r M ( A ℋ * ( ℒ l r ∪ V v r ) , T t r ) .

(2)

Since the data in ℒ l r ∪ V v r are independent from the ones in T t r , M ( f A * ) is an unbiased estimator of the true performance, measured with the metric M , of the final model. ³⁴

If n r = 1 , if l , v , and t are aprioristically set such that n = l + v + t , and if the resample procedure is performed without replacement, the hold out method is obtained. ³⁴ For implementing the complete nested k -fold cross validation, instead, it is needed to set n r ≤ ( n k ) ( n − n k k ) , l = ( k − 2 ) n k , v = n k , and t = n k and the resampling must be done without replacement. ⁵⁷ Finally, for implementing the nested non-parametric bootstrap, l = n and ℒ l r must be sampled with replacement from D n , while V v r and T t r are sampled without replacement from the sample of D n that have not been sampled in ℒ l r . ⁵⁷ Note that for the bootstrap procedure n r ≤ ( 2 n − 1 n ) . In this study, we exploited the complete nested k -fold cross validation because it represents the state-of-the-art approach. ³⁴

Feature ranking

Once we built the models and they showed their effectiveness in predicting the desired quantities, we decided to investigate how these models are affected by the different features used in the model identification phase. We performed this operation to understand if the models also have a foundation which relies on the underlying phenomena or if the model just captures spurious correlations. ³⁵

This procedure is called feature ranking (FR) and allows one to detect if the learned models appropriately take into account the relevant features. We consider relevant features the ones that are known to be important based on the literature or on the knowledge of the experts on the scientific problem.

The failure of the computational model to properly account for the relevant features might indicate poor quality in the measurements or spurious correlations. FR therefore represents an important step of model verification, since it should generate consistent results with the available knowledge of the phenomena under examination.

Since Random Forests was the method which obtained the best results in binary classification (Table 4), we took advantage of this ensemble learning technique to perform the feature ranking.

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Table 4.

Results of the survival prediction made with machine learning classifiers.

Method	MCC	F1 score	Accuracy	PR AUC	ROC AUC
RF	*+0.526 ± 0.011	*0.811 ± 0.005	*0.772 ± 0.005	0.149 ± 0.005	*0.766 ± 0.006
Linear SVM	+0.522 ± 0.011	*0.811 ± 0.005	0.771 ± 0.005	0.143 ± 0.005	0.763 ± 0.006
MLP	+0.456 ± 0.173	0.801 ± 0.090	0.727 ± 0.112	0.036 ± 0.044	0.695 ± 0.087
Radial SVM	+0.318 ± 0.130	0.744 ± 0.062	0.680 ± 0.065	0.191 ± 0.061	0.663 ± 0.068
DT	+0.295 ± 0.013	0.714 ± 0.006	0.659 ± 0.006	*0.211 ± 0.005	0.650 ± 0.006
Method	TP rate	TN rate	PPV	NPV
RF	0.794 ± 0.007	*0.738 ± 0.009	*0.829 ± 0.006	0.692 ± 0.009
Linear SVM	0.801 ± 0.007	0.724 ± 0.009	0.821 ± 0.006	0.697 ± 0.009
MLP	*0.950 ± 0.054	0.439 ± 0.174	0.705 ± 0.145	*0.836 ± 0.181
Radial SVM	0.729 ± 0.087	0.597 ± 0.087	0.765 ± 0.071	0.547 ± 0.127
DT	0.690 ± 0.008	0.610 ± 0.010	0.741 ± 0.007	0.549 ± 0.010

AUC: area under the curve; DT: decision tree; MCC: Matthews correlation coefficient (worst value = −1 and best value = +1); MLP: multi-layer perceptron neural network; NPV: negative predictive value; PPV: positive predictive value, precision; PR: precision-recall curve; RF: Random Forests; ROC: receiver operating characteristic curve; SVM: support vector machine; TN rate: true negative rate, specificity; TP rate: true positive rate, sensitivity, recall.

Each result is the average value of n F R executions ± standard deviation. Positive data instances: survived patients (class 1). Negative data instances: deceased patients (class 0). F₁ score, accuracy, TP rate, TN rate, PPV, NPV, PR AUC, ROC AUC: worst value = 0 and best value = +1. Confusion matrix threshold for TP rate, TN rate, PPV, and NPV: 0.5. We highlighted with an asterisk * the top results for each score. We report the formulas of these rates in the Supplemental Material Information.

Computational pipeline for binary classification and feature ranking

We can recap here the computation pipeline of the analysis with the following steps:

Biostatistics univariate tests

After using machine learning for feature ranking, we decided to rank the features by using the results of univariate traditional statistical tests which statistically express the relationship between each clinical factor and survival.

As done by Patrício et al. ²⁰ when analyzing health records of patients with breast cancer, we first applied the Shapiro–Wilk test ⁶⁸ to each feature to check their distribution. Since the normality assumptions were unmet, we then applied the Mann–Whitney U test to the real-valued features, the Kruskal–Wallis test to the category features, the chi-squared ( χ 2 ) test to the binary features, and ranked their p -values.

The Mann–Whitney U test (or Wilcoxon rank–sum test), ⁶⁹ applied to each feature in relation to the survival target, states whether we can reject the null hypothesis that the distributions of the each feature for the two groups of samples defined by survival are the same. The Kruskal–Wallis test ⁷⁰ is a variant of the Mann–Whitney U test to use for ordinal category features.

The chi-squared test ⁷¹ between two variables checks how likely an observed distribution is due to chance. The Mann–Whitney U test should be employed for features with real values, while the chi-squared test should be employed for non-ordinal category features.

A low p -value generated by these tests (close to 0) means that the analyzed feature strongly relates to survival, while a high p -value (close to 1) means the there is no significant relationship. Once we obtained a p -value for each feature, we ranked them from the lowest (highest correlation with survival) to the highest (lowest correlation with survival), generating a feature ranking for the real features and a feature ranking for the binary features.

Survival prediction

We listed the survival prediction results in Table 4, by ranking them on the Matthews correlation coefficients. ⁵³ We chose the MCC because it is the only confusion matrix score that generates a high score only if the classifier obtained a high score on the sensitivity, specificity, precision, and negative predictive value.^36,56

Our results show that all the methods were able to correctly predict most of the survived patients (positive data instances) and all the methods except MLP were capable of correctly precicting the majority of deceased patients (negative data instances), by obtaining MCC from +0.295 to +0.526 on average (Table 4). Random Forests outperformed all the other methods, by achieving the top MCC, F 1 score, accuracy, ROC AUC, specificity, and positive predictive value. Decision Tree performed better than the other algorithms regarding the precision-recall area under the curve (PR AUC); while the multi-layer perceptron neural network achieved the top sensitivity and negative predictive value.

All methods performed better on recall than on specificity, by obtaining an almost perfect true positive rate of 0.950 (MLP) as top recall and by attaining a top 0.738 true negative rate (RF). We believe this difference is caused by the dataset imbalance, since there are 38.18% negative data instances (deceased patients) and 61.82 positive data instances (survived patients). The high scores of precision and negative predictive value confirm the confidence of our survival prediction. ⁷²

Our results show that the classifiers perform more efficiently when used to predict patients with high chance to decease (TP rate) than patients with high chance to survive (TN rate). This condition results being more advisable to us because, as we mentioned earlier, predicting patients more at risk of death is more urgent.

Machine learning clinical feature ranking

Since Random Forests obtained the best results classifying the survival target (Survival prediction), we decided to employ this method to detect the most predictive features, able to discriminate survived patients from deceased patients. We applied an ensemble learning feature ranking n FR times, each generating a ranking for the mean Gini purity decrease and a ranking for the mean accuracy decrease. We merged together the n FR Gini rankings and the n FR accuracy rankings through Borda’s method, and finally merged the two final rankings through the same technique.

The results showed ALP, AFP, Hemoglobin, Albumin, and Ferritin as top five clinical factors to distinguish survived patients from deceased patients in both the final Gini ranking and the final accuracy ranking. Regarding the features ranked in the last positions, instead, the two final rankings were discordant. Alcohol, Cirrhosis, Sex, Hallmark, and Obesity resulted being the less relevant factors in the merged ranking (Table 5).

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Table 5.

Clinical feature ranking results.

Merged ranking position	Borda score	Clinical feature	Gini decrease final position	Gini decrease average position	Accuracy decrease final position	Accuracy decrease average position
1	2	ALP	1	1.3	1	1.5
2	4	AFP	2	1.7	2	1.9
3	6	Hemoglobin	3	3	3	3
4	8	Albumin	4	4.3	4	4.1
5	10	Ferritin	5	5.1	5	5
6	13	PS	7	7.6	6	6.4
7	14	AST	6	6	8	7.8
8	18	Symptoms	11	12	7	6.5
9	21	Platelets	10	10	11	11.2
10	22	Age	8	7.7	14	14.5
11	27	Total bil	14	14.8	13	14.1
12	28	Dir bil	19	17.6	9	9.3
13	29	GGT	9	9.3	20	20.5
14	33	Creatinine	15	15.5	18	20.3
15	34	INR	12	12.2	22	22.1
16	36	Ascites	26	25.3	10	10.9
17	37	Major dim	18	17.2	19	20.3
18	38	Iron	21	21.2	17	17.5
19	39	Hemochro	27	27.1	12	13.8
20	40	Leucocytes	13	13.1	27	26.4
21	41	Varices	25	24.9	16	15.4
22	43	MCV	17	16.4	26	25.9
23	43	Metastasis	28	28.1	15	14.6
24	44	Sat	23	22.7	21	20.7
25	44	Total proteins	16	15.6	28	26.9
26	46	Packs year	22	22.6	24	24.6
27	53	HBsAg	30	30.1	23	23.8
28	60	ALT	20	19.8	40	41
29	61	HCVAb	31	30.6	30	30.4
30	61	PVT	36	35.8	25	25.8
31	63	Nodules	29	29.5	34	34.3
32	64	Endemic	32	32.8	32	30.6
33	64	PHT	35	35.4	29	29.9
34	66	HBcAb	33	32.9	33	32.8
35	68	Grams day	24	24.5	44	42.3
36	70	Encephalopathy	39	39	31	30.4
37	73	Diabetes	38	37.8	35	37.5
38	77	AHT	40	40.5	37	38.7
39	77	HIV	41	41.1	36	37.5
40	81	Smoking	34	33.5	47	43.2
41	82	CRI	43	43.3	39	39.5
42	83	Spleno	37	36.5	46	42.5
43	84	HBeAg	46	45.5	38	39.5
44	85	NASH	42	42	43	42.2
45	89	Alcohol	47	46.5	42	42.1
46	90	Cirrhosis	49	49	41	41.7
47	93	Sex	48	48	45	42.4
48	93	Hallmark	44	43.5	49	46.6
49	93	Obesity	45	45.3	48	45.1

We merged the ranking obtained by Random Forests with the Gini purity decrease and the ranking obtained by Random Forests with the accuracy decrease, through Borda’s method. ⁷³ Accuracy decrease average position: rank obtained by applying Borda’s method to the accuracy decrease n F R rankings. Accuracy decrease final position: ranking obtained from the accuracy decrease average position ranking. Gini decrease average position: rank obtained by applying Borda’s method to the Gini decrease n F R rankings. Gini decrease final position: ranking obtained from the Gini decrease average position ranking. Borda score: score obtained by applying Borda’s method to the Gini decrease final position ranking and the accuracy decrease final position ranking. Merged ranking position: final ranking obtained through the Borda score ranking.

As an example, we report a Gini ranking and an accuracy ranking generated by one of the applications of Random Forests out of n FR executions (Figure 1).

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Figure 1.

Random Forests feature selection. Indicative example of Random Forests feature selection through accuracy reduction (left) and Random Forests feature selection through Gini impurity (right), obtained in one of the n F R executions.

Biostatistics feature ranking

The Shapiro–Wilk test (Supplemental Table S1) produced a p -values close to 0 for each feature, meaning that the null hypothesis of normality is rejected, and each variable distribution is non-normal.

We applied the Mann–Whitney U test to the real-valued features, the chi-squared test to the binary features, and the Kruskall-Wallis test to the ordinal category features, all paired with survival, and then ranked the features according to their p -values (Table 6). The tests’ results showed ALP, AFP, Hemoglobin, Direct Bilirubin (Dir Bil), AST, Ferritin, Symptoms, Metastasis, PS, Ascites as most significant features, having a p -value lower than 0.005 (Table 6).

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Table 6.

Results of the Mann–Whitney U test applied to the real features (left), chi-squared test applied to the binary features (center), and Kruskal-Wallis test applied to the ordinal category features (right).

Position	Feature	Mann–Whitney U test	Feature	Chi-squared test	Feature	Kruskal–Wallis test
		p-value		p-value		p-value
1	*ALP	1 . 000 × 10 − 06	*Symptoms	5 . 000 × 10 − 04	*PS	2 . 000 × 10 − 06
2	*AFP	4 . 000 × 10 − 06	*Metastasis	4 . 498 × 10 − 03	*Ascites	1 . 050 × 10 − 03
3	*Hemoglobin	6 . 800 × 10 − 05	PVT	1 . 050 × 10 − 02	Encephalopathy	1 . 865 × 10 − 01
4	*Albumin	2 . 100 × 10 − 04	HCVAb	1 . 749 × 10 − 01	Nodules	2 . 269 × 10 − 01
5	*Dir bil	1 . 354 × 10 − 03	Diabetes	1 . 769 × 10 − 01
6	*AST	1 . 769 × 10 − 03	Endemic	3 . 258 × 10 − 01
7	*Ferritin	1 . 999 × 10 − 03	CRI	3 . 283 × 10 − 01
8	Iron	9 . 132 × 10 − 03	HBeAg	3 . 818 × 10 − 01
9	GGT	1 . 912 × 10 − 02	AHT	4 . 138 × 10 − 01
10	Major dim	2 . 816 × 10 − 02	Smoking	4 . 543 × 10 − 01
11	INR	3 . 298 × 10 − 02	Varices	6 . 842 × 10 − 01
12	Total bil	3 . 330 × 10 − 02	HBcAb	6 . 867 × 10 − 01
13	Age	3 . 568 × 10 − 02	Sex	6 . 972 × 10 − 01
14	Creatinine	9 . 698 × 10 − 02	Hemochro	6 . 972 × 10 − 01
15	Platelets	1 . 213 × 10 − 01	PHT	6 . 992 × 10 − 01
16	Leucocytes	1 . 405 × 10 − 01	NASH	7 . 176 × 10 − 01
17	Total proteins	1 . 514 × 10 − 01	Alcohol	7 . 201 × 10 − 01
18	Sat	3 . 319 × 10 − 01	Spleno	7 . 421 × 10 − 01
19	Packs year	3 . 940 × 10 − 01	Cirrhosis	7 . 871 × 10 − 01
20	Grams day	4 . 404 × 10 − 01	HBsAg	7 . 906 × 10 − 01
21	MCV	4 . 415 × 10 − 01	Obesity	8 . 156 × 10 − 01
22	ALT	6 . 641 × 10 − 01	Hallmark	8 . 666 × 10 − 01
23			HIV	1

We highlight with an asterisk * the features having p-value lower than the significance threshold p = 0 . 005 = 5 × 10 − 3 .

Exection times

We executed our scripts on a Dell Latitude 3540 personal computer running a Linux CentOS 7.10 operating system and R version 3.6. The execution of the binary classification methods took around 45 minutes, the exection of the feature ranking techniques took around 45 min and 30 s, while the execution of the biostatistics tests took around 5 seconds.

Survival prediction

Our survival prediction results show that computational intelligence can effectively predict survival of patients from their clinical records, in few minutes and with small computational resources.

Our methods achieved good prediction results on all the confusion matrix rates (Survival prediction), and even outperformed the results obtained by the original dataset curators Santos et al. ²⁷ which obtained a top performance score of ROC AUC = 0.700 through a neural network augmented sets approach. Our Random Forests classifier, in fact, obtained an average ROC AUC = 0.766 (Table 5). We believe that our improvement on the results, compared to the original study ²⁷ is due mainly to the predictive power of Random Forests, ³⁹ that often outperforms artificial neural networks and all the other machine learning techniques in health informatics binary classification tasks.^19,74–77

Other studies have applied machine learning methods to predict survival and rank the clinical features on this HCC dataset (Dataset), but they included methodological mistakes that led to inflated and overoptimistic results. Ksikazek et al. ⁷⁸ obtained inflated prediction scores due to several wrong machine learning practices: they split the dataset into a training set and a test set, used the test set for the hyper-parameter optimization of their Genetic Algorithm, and then applied their trained model on the same test set, generating high predictive results. The correct practice necessitates to splitting the dataset into three separate subsets: training set, validation set, and test set.^34,36,43 The validation set should be employed for the hyper-parameter optimization, and the test set should be left untouched as a “held-out set” until the end, and used for the final classification made with trained optimized model. ⁷⁹

In a parallel work, Sawhney et al. ⁸⁰ committed a similar mistake: they decided to reduce the number of features of the dataset to predict survival, but they did it on the same subset they employed for testing their classification method. Again, the correct practice would have necessitated to splitting the dataset into three independent subsets: training set, feature reduction set, and test set. The “held-out” test set should have been used only at the end, after the training phase and the feature reduction phase. Additionally, the authors did not provide enough details on their feature reduction procedure.

Because of these malpractices, from a data analytics point of view, we did not compare our predictions performance with the results achieved by Ksikazek et al. ⁷⁸ and Sawhney et al. ⁸⁰ because the latter are biased and optimistic due to several data snooping issues (for example, some of the training data instances were employed also in the test set). ⁸¹

Clinical feature ranking obtained by our Random Forests approach

Regarding feature ranking, our machine learning approach identified clinical factors already known to be HCC predictive or prognostic factors in the gastroenterology community (Table 6).

Yu et al. ⁸² and Parikh and Sawant ⁸³ for example, confirmed the predictive power of alkaline phosphatase (ALP) level for survival of patients having hepatocellular carcinoma. ALP is the top most predictive clinical factor found by our approach (Table 6). On the second position of our ranking we found alpha-fetoprotein (AFP), which was found to be strongly correlated to survival of patients having HCC by Tangkijvanich et al., ⁸⁴ Johnson, ⁸⁵ Johnson and Williams, ⁸⁶ and Tyson et al., ⁸⁷ in studies independent from each other. Finkelmeier et al. ⁸⁸ confirmed the predictive importance of Hemoglobin level, which is on the third position of our ranking. The fourth position of our ranking lists the Albumin level, which has been confirmed to be related conditions of patients having hepatocellular carcinoma by Carr and Guerra ⁸⁹ and Tanriverdi. ⁹⁰

Regarding the Ferritin level found in the blood of patients, listed on fifth position of our ranking, the scientific literature contains several studies confirming this association.^91–93 However, since the Ferritin feature has almost half of its values missing in the the original dataset (Dataset), we have to warn that the data imputation technique we used might have influenced this outcome.

The fact that our approach ranked factors already known to the gastroenterology community as most predictive of survival for patients having HCC confirms the effectiveness of our feature ranking approach. Interestingly, our approach listed ALP level, AFP level, Hemoglobin level, and Ferritin level in positions higher than other known HCC clinical factors.

The last five positions of our ranking, in fact, list Alcohol consumption, Cirrhosis, Sex, Radiological Hallmark, and Obesity as least predictive features for HCC patient survival. Even if the daily consumption of alcohol is known to be related to to hepatocellular carcinoma, ⁹⁴ our analysis suggests it is unrelated to survival. Regarding Cirrhosis, even if often present in patients with hepatocellular carcinoma, ⁹⁵ our ranking recommends it as non-predictive of survival. A study by Sangiovanni et al. ⁹⁶ confirms the increased chances of survival for patients with HCC and cirrhosis. Our analysis suggests that the patient’s sex is not prognostic of survival, even if HCC is more common among men. Even if the hepatocellular carcinoma diagnosis is confirmed by the Radiological Hallmark, our study states that this aspect cannot say anything about possible survival or decease of the patient. Obesity is a known risk factor for HCC, ⁹⁷ but our study suggests, that is, independent from the survival of the patient.

Clinical feature ranking obtained by our univariate statistical tests

Regarding biostastistics univariate tests, we noticed these techniques identified as most relevant clinical factors the same top eight features found by Random Forests (ALP, AFP, Hemoglobin, Albumin, Ferritin, PS, AST, Symptoms), plus other ones that were on lowest Random Forests ranks. Our ensemble learning technique, in fact, put Direct Bilirubin on 12th position, Ascites on 16th position, and Metastasis on 23rd position out of 49.

Platelet count, Age, and Total Bilirubin result being more relevant than Direct Bilirubin in our machine learning ranking, confirming the effectiveness of Random Forests in this task. Platelet count, in fact, is a known prognostic factor in hepatocellular carcinoma, ⁹⁸ but it was undetected as relevant feature by the univariate statistical tests (Table 6). Age is another important factor: older patients have less chance to survive HCC, ⁹⁹ but Age was unseen as a key factor by the univariate statistical tests (Table 6).

Ascites is a prognostic factor employed by the Okuda HCC staging definition ⁸ that was introduced in 1985 and by the Chinese University Prognostic Index ¹³ in 2002, but was excluded from more common staging systems such as the TNM Classification of Malignant Tumors.^16,17

Metastasis was detected as a significant factor by the univariate statistical tests, but not by our Random Forests ranking.

HCC most predictive clinical features according to other studies

In the scientific literature, other papers claim alternative survival or mortality factors for HCC patients, which we compare with our top ranked features.

Cai et al. ¹⁰⁰ listed tumor size and vascular invasion as the most relevant clinical features for survival of patients with hepatocellular carcinoma. The study of El-Fattah et al. ¹⁰¹ instead, stated that age, race, tumor size, AFP level, the American Joint Committee on Cancer (AJCC) stage, and the year of diagnosis were the most relevant factors for survival in the medical records of HCC-diagnosed patients. Falkson et al. ¹⁰² identified impaired performance status, male sex, older age, and disease symptoms (jaundice and reduced appetite) as factors most mortality-related. The research study of Vauthey et al. ¹⁰³ identified cirrhosis and vascular invasion as clinical aspects more correlated to mortality.

Treatment for HCC, albumin level, and TNM stage were the most predictive survival features found by Kawaguchi et al. ¹⁰⁴ in a recent article. Singal et al. ¹⁰⁵ listed AFP and being a male as two relevant signs of potential survival from HCC. The article of Chaudhari et al. ¹⁰⁶ instead, listed age, stage of disease, multiplicity, tumor thrombosis, lymphovascular invasion, nodal and distant metastases and completeness of resection as relevant factors for patients survival from HCC.

Two of these studies confirmed the relevance of AFP level,^101,105 which we ranked 2 n d in our analysis (Table 5), endorsing the predictive power of the α -fetoprotein level in blood, that now can be considered a strong biomarker of survival from HCC.

Two studies listed male sex as a top predictive factor,^101,106 which we listed in the last positions of our ranking (Table 5): this discordance leaves room for further analysis about this aspect.