The Use of the Random Number Generator and Artificial Intelligence Analysis for Dimensionality Reduction of Follicular Lymphoma Transcriptomic Data

Abstract

Follicular lymphoma (FL) is one of the most frequent subtypes of non-Hodgkin lymphomas. This research predicted the prognosis of 184 untreated follicular lymphoma patients (LLMPP GSE16131 series), using gene expression data and artificial intelligence (AI) neural networks. A new strategy based on the random number generation was used to create 120 different and independent multilayer perceptron (MLP) solutions, and 22,215 gene probes were ranked according to their averaged normalized importance for predicting the overall survival. After dimensionality reduction, the final neural network architecture included (1) newly identified predictor genes related to cell adhesion and migration, cell signaling, and metabolism (EPB41L4B, MOCOS, SPIN2A, BTD, SRGAP3, CTNS, PRB1, L1CAM, and CEP57); (2) the international prognostic index (IPI); and (3) other relevant immuno-oncology, immune microenvironment, and checkpoint markers (CD163, CSF1R, FOXP3, PDCD1, TNFRSF14 (HVEM), and IL10). The performance of this neural network was good, with an area under the curve (AUC) of 0.89. A comparison with other machine learning techniques (C5 tree, logistic regression, Bayesian network, discriminant analysis, KNN algorithms, LSVM, random trees, SVM, tree-AS, XGBoost linear, XGBoost tree, CHAID, Quest, C&R tree, random forest, and neural network) was also made. In conclusion, the overall survival of follicular lymphoma was predicted with a neural network with high accuracy.

1. Introduction

Follicular lymphoma (FL) is a tumor of the immune system that is derived from germinal center B lymphocytes, which include both centrocytes (small cleaved follicular center cells), and centroblasts (large noncleaved cells). Histologically, it is also characterized by a follicular (nodular) growth pattern in most of the cases [1,2]. Centrocytes and centroblasts form the neoplastic follicles, which also include a tumoral immune microenvironment characterized by a variable infiltration of T lymphocytes (CD4+ helper, PD-1 (PDCD1)+follicular T helper cells (TFH cells), FOXP3+regulatory T (Tregs), and CD8+ cytotoxic), follicular dendritic cells, and tumor-associated macrophages (M2-like TAMs) that express CD163, CSF1R, and HVEM (TNFRSF14) [2,3,4,5].

The pathogenesis of FL is still not understood [3,4,5]. The overexpression of the BCL2 oncogene due to translocation t(14;18) is identified in around 85% of the cases, but other factors are involved in the neoplastic transformation, including acquired mutations such as chromatin-modifying enzymes [6,7].

FL is the second most frequent indolent non-Hodgkin lymphoma (NHLs), which is characterized by a survival without treatment of several years. FL accounts for 35% of NHLs, with an estimated frequency of 3.18 cases per 100,000 people, and it affects middle-aged individuals [5,8,9]. The clinical course of FL is variable. While some patients can be left without treatment for five years or more, others who have a more disseminated disease and rapid tumor growth require treatment sooner [2,5,10,11]. At the time of diagnosis, the FL international prognostic index (FLIPI) [12] and the PRIMA prognostic index (PRIMA-PI) [13] are two of the most frequently used measures [5]. Nevertheless, identifying which patients are at higher risk of disease progression and exitus still requires further investigation.

Artificial neural networks (ANNs) are a subset of machine learning that are inspired by the human brain, simulating the neuronal network. The structure of ANNs comprises an input layer, one or more hidden layers, and an output layer. Each node (the artificial neuron) is connected to another and has an associated weight and threshold. There are several types of ANNs. The perceptron is the oldest. This research used feedforward neural networks, or multilayer perceptrons (MLPs) [14].

Because neural networks use random numbers, they create a different model by each execution. If you wanted to replicate a result of a neural network accurately, four conditions should be fulfilled: (1) the same data order, (2) the same variable order, (3) the same procedure setting, and (4) the same initialization value for the random number generator.

The MLP procedure uses random number generation during the random assignment of partitions, random subsampling for initialization of synaptic weights, random subsampling for automatic architecture selection, and the simulated annealing algorithm used in weight initialization and automatic architecture selection [15].

The main aim of the work was to take advantage of the random number generator to obtain multiple (n = 120) different and independent neural network solutions. The MLP procedures correlated the gene expression of follicular lymphoma with the clinicopathological features of the patients. The gene expression included all the genes of the array. Using this approach, after averaging the normalized importance for predicting the overall survival, the most relevant markers were identified.

2. Materials and Methods

Multilayer perceptron analyses were performed as described previously [16,17,18,19,20,21,22,23]. In summary, the multilayer perceptron architecture was composed of an input layer, a hidden layer, and an output layer. The input layer included the whole set of genes of the array (method 1, 22,215 nodes), and used the standardized rescaling method for covariates (i.e., predictors, genes). The hidden layer had 1 layer of nodes and used the hyperbolic tangent activation function. The number of nodes of the hidden layer ranged from 1 to 50, and it was automatically computed to find the best architecture. The output layer had two nodes, one for the overall survival output of the dead and another for the alive, and used the softmax activation function.

The cases were randomly assigned to a training set (70%) and test set (30%). A holdout set was not used. In the final model, the type of training was batch, with a scaled conjugate gradient optimization algorithm. The training options were the following: initial lambda (0.0000005), initial sigma (0.00005), interval center (0), interval offset (±0.5)

The gene expression data of follicular lymphoma corresponded to the publicly available GSE16131 dataset (Affymetrix GPL96/97, HG-U133A/B; Affymetrix Inc., Santa Clara, CA, 95051-0704 USA). This series comprised 184 untreated patients, with diagnostic biopsies from fresh-frozen tumor lymph nodes. This series was last updated on 10 August 2018. The data were analyzed using the microarray suite version 5.0 (MAS 5.0) using the Affymetrix (ThermoFisher, Waltham, WA, USA), default settings and global scaling as the normalization method. The trimmed mean target intensity of each array was arbitrarily set to 500. The data were normalized and log2 transformed. Each node of the input layer corresponded to one gene probe (22,215 probes). For the final integrative analysis, each node corresponded to one gene; the gene probes were collapsed using the maximum expression to obtain one gene expression value of each gene.

The MLP procedure was repeated 120 times (because of the random number generator, 120 different and independent solutions were calculated), and the results were averaged to obtain the final neural network solution. The genes were ranked according to their averaged normalized importance for predicting the overall survival outcome.

Additional statistics included overall survival analysis using Cox regression with the method enter and backward conditional (IBM SPSS Statistics for Windows, Version 26.0. Armonk, NY: IBM Corp).

The clinicopathological characteristics of the series were as follows: age > 60 years (61/182, 33.5%), stage > 2 (129/180, 71.7%), extranodal sites > 1 (24/184, 13%), LDH level ratio > 1 (46/160, 28.7%), IPI score 2–3 (74/160, 46.3%), immune response ratio 2:1 high (≥0.97) (48/184, 26.1%). The cases were mainly BCL2/IGH translocation (14;18) positive (147/164, 89.6%).

The analysis was performed in a desktop workstation equipped with an AMD Ryzen 9 5900X 12-Core Processor (3.70 GHz, 16.0 GB of RAM), and an Nvidia GeForce RTX 3060 Ti GPU.

3. Results

The summary of the procedure and results is shown in Figure 1.

The analysis took advantage of the random number generator to create 120 different and independent MLP neural network solutions. The MLP was characterized by 22,215 input nodes (gene probes) and 2 output nodes (overall survival outcome, dead vs. alive). Each solution ranked the 22,215 gene probes according to their normalized importance for predicting the overall survival. Once the normalized importances for each gene probe were averaged, 1 solution/model remained. Further dimensionality reduction led to 17 gene probes. The explainability of the model relied on Cox regression analyses, Hazar Risks, and correlation with the International Prognostic Index as well as the Immune Response signatures (Explainable Artificial Intelligence (XAI)).

3.1. Generation of 120 Different Predictive Models for Overall Survival Using MLP Neural Networks

Based on the gene expression of 22,215 gene probes, an MLP analysis was repeated 120 times to predict the overall survival outcome (dead vs. alive). The results of each 120 MLPs included the network structure (diagram and synaptic weights), the network performance (model summary, classification results, ROC curve, cumulative gains chart, lift chart, predicted by observed chart, and residual by predicted chart), and the independent variable (i.e., gene probes, predictors) independent variable importance analysis. As a result, the 22,215 probes were ranked according to their normalized importance for predicting the overall survival outcome. In total, 120 ranks were obtained.

Figure 2 shows the variability of the normalized importance for the top 10 most important probes and the bottom 10 less relevant probes based on the normalized importance values.

Normalized importance of the top 10 most important gene probes against the bottom 10 least relevant ones. The MLP analysis was repeated 120 times, and all the gene probes were ranked according to their normalized importance for predicting the overall survival outcome (dead vs. alive). Each MLP analysis created a different valid prognostic model because of the random number generation process. This figure shows how the normalized importance for the top 10 gene probes had higher variability than the top least relevant probes. For instance, for the most relevant probe (211748_x_at, num 1), the normalized importance ranged from 0.25 to 1, with a range of 0.75, median of 0.64, and average of 0.63 ±0.24 STD. For the least relevant probe (204409_s_at, num. 22,215), the normalized importance ranged from 0.045 to 0.27, with a range of 0.22, median of 0.12, and average of 0.12 ±0.05 STD. For each gen probe, the 120 values of the normalized importance were averaged and ranked to create a final prognostic model.

For each probe, the 120 normalized importance values were averaged. Finally, all the 22,215 probes were ranked according to their averaged normalized importance for predicting the overall survival. The top 5 probes more relevant for prediction were 211748_x_at (averaged normalized importance 0.63), 212187_x_at (0.61), 219971_at (0.59), 203788_s_at (0.59), and 203892_at (0.57).

The correlations between the top 10 gene probes were tested using a covariance matrix. The results showed that some gene probes had positive values (e.g., 211748_x_at and 212187_x_at had a covariance of 0.28). Therefore, both variables tend to increase or decrease in tandem. The covariance matrix is shown in

Table A1. Covariate matrix between the top 10 gene probes.

	211748_x_at	212187_x_at	219971_at	203788_s_at	203892_at	214461_at	202540_s_at	205272_s_at	207436_x_at	208791_at
211748_x_at	0.3106
212187_x_at	0.2817	0.2752
219971_at	0.1735	0.1674	0.4121
203788_s_at	−0.0123	−0.0129	−0.0106	0.2564
203892_at	0.0289	0.0205	0.0366	0.0398	0.2449
214461_at	0.0358	0.0197	−0.0193	0.0213	0.0014	0.3596
202540_s_at	−0.0227	−0.0267	−0.0402	−0.0227	−0.0487	0.0061	0.2111
205272_s_at	0.0171	0.0166	0.0245	−0.0139	0.3841	−0.0534	−0.1129	2.0909
207436_x_at	−0.0199	−0.0204	−0.0959	0.0190	−0.0261	0.0134	0.1088	−0.0626	0.1878
208791_at	0.3040	0.2744	0.1746	−0.0392	0.0364	0.0512	−0.0148	0.0290	−0.0163	0.6622

.

Of note, the differential gene expression was also analyzed using the GEO2R software of the NCBI under the standard setup (GPL96). The groups were defined according to the follow-up status: (overall survival) dead vs alive. The significance level cut-off was 0.05, the volcano and MA plot contrasts were alive vs dead, and the adjustment to the p-values used the Benjamini and Hochberg false discovery rate. The results showed significant p values, but the adjusted p values were not significant. The 5th most significant gene probes were 216965_x_at, 220650_s_at, 216542_x_at, 211130_x_at, and 221600_s_at that in the MLP neural network had a rank based on the normalized importance (NI) of 16,193 of 22,215 (0.23 NI), 2,709 (0.32 NI), 7,252 (0.27 NI), 3,641 (0.3 NI), and 11,666 (0.25 NI), respectively. Generally, this method failed to provide useful results for our situation. Therefore, our MLP neural network strategy is a more promising analysis strategy.

3.2. Dimensionality Reduction for Predicting the Overall Survival

The 100 topmost important gene probes were selected from the previous step, and a survival analysis was undertaken for overall survival using Cox regression, with the method backward stepwise (conditional LR). In the last step, num. 53, only 48 gene probes remained in the model. Next, an MLP analysis for overall survival was performed using the 48 gene probes, and the gene probes were ranked according to their normalized importance for predicting the overall survival (the performance of this MLP neural network was good, with an area under the curve of 0.832) (

Table A2. Correlation between the gene expression and the overall survival using Cox regression analysis and MLP neural network.

Num.	Gene Probe	Gene Symbol	B	p Value	Hazard Risk (HR)	95.0% CI for HR		MLP
						Lower	Upper	NI
1	216846_at	IGLJ3	2.0	2.35 × 10−7	7.5	3.5	16.1	1.000
2	211704_s_at	SPIN2A/B	0.6	0.083002	1.9	0.9	3.8	0.881
3	214116_at	BTD	−1.6	7.6 × 10−8	0.2	0.1	0.4	0.876
4	209794_at	SRGAP3	−1.1	0.033109	0.3	0.1	0.9	0.839
5	204925_at	CTNS	1.7	0.000263	5.3	2.2	13.1	0.838
6	220161_s_at	EPB41L4B	1.6	4.7 × 10−9	5.0	2.9	8.5	0.767
7	210546_x_at	CTAG1A	1.0	3.23 × 10−6	2.7	1.8	4.0	0.757
8	210597_x_at	PRB1	1.0	1.46 × 10−5	2.7	1.7	4.3	0.701
9	219959_at	MOCOS	0.7	0.001377	2.0	1.3	3.0	0.689
10	204584_at	L1CAM	−0.9	0.000622	0.4	0.2	0.7	0.661
11	213050_at	COBL	−1.1	0.001523	0.3	0.2	0.7	0.646
12	215507_x_at	-	−0.5	0.082379	0.6	0.4	1.1	0.645
13	203491_s_at	CEP57	−0.5	0.016744	0.6	0.4	0.9	0.629
14	221765_at	UGCG	−0.4	0.069669	0.7	0.5	1.0	0.599
15	201729_s_at	KIAA0100	3.1	6.79 × 10−6	22.4	5.8	86.5	0.547
16	213272_s_at	TMEM159	1.3	0.003146	3.8	1.6	9.4	0.525
17	212187_x_at	PTGDS	1.9	0.000211	6.7	2.4	18.2	0.521
18	220600_at	ELP6	0.9	0.002653	2.4	1.4	4.3	0.519
19	205839_s_at	BZRAP1	−0.9	0.015594	0.4	0.2	0.8	0.503
20	204738_s_at	KRIT1	−1.3	0.000619	0.3	0.1	0.6	0.493
21	221196_x_at	BRCC3	1.2	0.001986	3.3	1.6	7.2	0.470
22	215788_at	CFAP74	−0.7	0.02512	0.5	0.3	0.9	0.465
23	203892_at	WFDC2	1.3	0.001288	3.6	1.6	7.7	0.459
24	219349_s_at	EXOC2	−0.8	0.045831	0.4	0.2	1.0	0.452
25	208791_at	CLU	1.2	0.000159	3.4	1.8	6.5	0.450
26	215287_at	STRN	0.9	0.002545	2.4	1.4	4.2	0.443
27	219361_s_at	AEN	1.6	0.000405	4.8	2.0	11.4	0.439
28	207436_x_at	SORBS1	−0.8	0.07232	0.4	0.2	1.1	0.436
29	219815_at	GAL3ST4	−1.9	2.15 × 10−5	0.1	0.1	0.4	0.418
30	215183_at	-	−1.3	0.001	0.3	0.1	0.6	0.416
31	207356_at	DEFB4A	−1.4	0.000927	0.2	0.1	0.6	0.405
32	218268_at	TBC1D15	2.2	0.000131	8.9	2.9	27.5	0.388
33	215867_x_at	CA12	−1.8	4.6 × 10−5	0.2	0.1	0.4	0.342
34	214876_s_at	TUBGCP5	−0.9	0.000816	0.4	0.2	0.7	0.332
35	213539_at	CD3D	−2.8	5.16 × 10−8	0.1	0.0	0.2	0.332
36	207752_x_at	PRB1	−0.7	0.002323	0.5	0.3	0.8	0.292
37	210312_s_at	IFT20	−1.8	0.002342	0.2	0.1	0.5	0.273
38	41397_at	ZNF821	−1.2	0.000852	0.3	0.1	0.6	0.260
39	204547_at	RAB40B	0.8	0.019527	2.2	1.1	4.4	0.252
40	214465_at	ORM1	1.3	1.14 × 10−5	3.7	2.1	6.6	0.242
41	201131_s_at	CDH1	−0.7	0.008031	0.5	0.3	0.8	0.231
42	210039_s_at	PRKCQ	1.0	0.089034	2.7	0.9	8.2	0.224
43	207377_at	PPP1R2P9	−0.8	0.037392	0.4	0.2	1.0	0.210
44	206994_at	CST4	0.7	0.006194	1.9	1.2	3.1	0.200
45	214408_s_at	RFPL1S	0.7	0.014436	2.0	1.1	3.5	0.200
46	216699_s_at	KLK1	−0.7	0.045702	0.5	0.3	1.0	0.119
47	221004_s_at	ITM2C	−0.5	0.077654	0.6	0.4	1.1	0.080
48	211262_at	PCSK6	−1.0	0.02704	0.4	0.1	0.9	0.028

Cox regression analysis for predicting the overall survival. The analysis included as predictors the gene expression of the top 100 gene probes, previously identified as prognostic value in the multiple 120 MLP neural network analyses. A Cox regression, backward stepwise (conditional LR), correlated the gene expression of the 100 gene probes with the overall survival of the patients. As a result, 48 gene probes were identified. Additionally, the 48 gene probes were ranked according to their normalized importance (NI) for predicting the overall survival outcome using a MLP neural network. B, beta; SE, standard error; HR, hazard risk; MLP, multilayer perceptron; NI, normalized importance.

).

Further dimensionality reduction consisted of searching for the minimal number of gene probes necessary to obtain the highest area under the curve (AUC) using an MLP analysis: the optimal minimum number of genes were using the first 17th gene probes that provided an AUC of 0.842. The 17 genes were the following: IGLJ3, SPIN2A/B, BTD, SRGAP3, CTNS, EPB41L4B, CTAG1A, PRB1, MOCOS, L1CAM, COBL, 215507_x_at, CEP57, UGCG, KIAA0100, TMEM159, and PTGDS (Figure 3).

Based on 48 gene probes previously identified using the MLP neural network and Cox regression analysis, the minimal reasonable (defined as AUC > 0.8) number of gene probes to predict the overall survival was identified with multiple MLPs. With 17 genes (A) an MLP neural network (B) predicted the overall survival outcome (dead vs. alive) with an area under the curve (AUC) of 0.842 (C). The most relevant genes according to the normalized importance for predicting the overall survival were IGLJ3, SPIN2A/B, BTD, SRGAP3, and CTNS (D).

3.3. Correlation with the International Prognostic Index (IPI) and the Immune Response (IR)

The prognostic value for predicting the overall survival of the set of 17 genes was correlated with other known follicular lymphoma prognostic markers, including the International Prognostic Index (IPI) score and the Immune Response (IR). The analysis was performed using Cox regression for overall survival, with the gene expression of the 17 gene probes, IPI, and the IR (method, backward conditional). In the final model (step 14), only IPI, IR, and four gene probes kept the significance: high IPI (Hazard Risk (HR) = 3.3, p < 0.001), IR type 2 (HR = 3.0, p < 0.001), SRGAP3 (HR = 0.47, p = 0.006), PRB1 (HR = 1.47, p < 0.001), L1CAM (HR = 0.7, p = 0.016), and CEP57 (HR = 0.654, p < 0.001).

3.4. Gene Set Enrichment Analysis (GSEA)

The prognostic values of the highlighted 48 and 17 gene sets were evaluated using the Gene Set Enrichment Analysis (GSEA) technique, in the same database. In case of genes with multiple probes, the probes were collapsed to the maximum expression values. The GSEA technique showed enrichment toward the dead phenotype of the overall survival (Figure 4).

The GSEA technique was used to confirm the results of the MLP neural network and the Cox regression analysis. The GSEA plots showed enrichment of the part of the genes toward the overall survival outcome of the dead. When using the set of 17 genes, in the core enrichment the EPB41L4B, MOCOS, and SPIN2A genes were found. Of note, the Hazard Risks of these genes were 2.9, 2.0, and 1.9 in the Cox regression analysis (Table A1).

3.5. Final Integrative Analysis

A final integrative analysis was performed using an MLP neural network. The input layer included the previously highlighted predictor genes (EPB41L4B, MOCOS, SPIN2A, BTD, SRGAP3, CTNS, PRB1, L1CAM, and CEP57), the international prognostic index (IPI), and other relevant genes of the immune microenvironment and immune response (CD163, CSF1R, FOXP3, PDCD1, TNFRSF14, and IL10). In this analysis, each gene had a gene expression value which corresponded to the collapsed maximum gene expression in the case of multiple probes for one gene symbol. The performance of this neural network was good, with an area under the curve (AUC) of 0.89. The genes and IPI were ranked according to their normalized importance for predicting the overall survival of the patients (Figure 5). The most relevant were SRGAP3, CEP57, EPB41L4B, the international prognostic index (IPI), and SPIN2A, IL10, MOCOS and CD163 (normalized importance >60%).

A final overall survival model was created using the previously highlighted genes, the international prognostic index (IPI), and relevant genes of the immune response and microenvironment. The performance of this network was good, with an area under the curve (AUC) of 0.89. In the model, the most relevant gene was SRGAP3, which had an importance of 0.103 and a normalized importance of 100%. It was followed by CEP57, with importance of 0.094 and normalized importance of 90.7%.

This final integrative analysis was based on the MLP neural network. Nevertheless, there are other machine learning methods that can also contribute to the modeling of the pathogenesis of follicular lymphoma. Therefore, the overall survival outcome (dead vs alive, target) was predicted using the same 16 variables (inputs) of the analysis of Figure 5. Among all available models, the overall survival prediction was tested using 16 methods including C5 Tree, logistic regression, Bayesian network, discriminant analysis, KNN algorithms, LSVM, random trees, SVM, Tree-AS, XGBoost linear, XGBoost tree, CHAID, Quest, C&R Tree, Random forest, and neural net. Among these, 10 models were successfully used. The models were ranked according to their overall accuracy for predicting the overall survival. The results are shown in

Table 1. Modeling the overall survival outcome using other machine learning models.

Num.	Model	Overall Accuracy (%)	No. Fields Used	Variables Used in the Final Model
1	XGBoost tree	100	16	16
2	Random trees	97.2	16	13 (predictor importance: PRB1, CSF1R, IL10, L1CAM, BTD, MOCOS, FOXP3, PDCD1, EPB41L4B, and IPI score; top 10 inputs)
3	Random forest	86.9	16	Predictor importance: IPI score 1, CEP57, L1CAM, EPB41L4B, TNFRSF14, BTD, SPIN2A, PDCD1, CTNS, SRGAP3, IL10, MOCOS, PRB1, FOXP3, CD163, CSF1R, and IPI score 2
4	LSVM	74.4	16	Predictor importance: SRGAP3, IPI score, L1CAM, CD163, EPB41L4B, PDCD1, CSF1R, IL10, MOCOS, BTD; top 10 inputs
5	Neural network	69.4 (79.9% of overall percent correct)	16	Predictor importance: SRGAP3, IL10, TNFRSF14, EPB41L4B, CD163, SPIN2A, IPI score, CEP57, MOCOS, PDCD1, PRB1, L1CAM, CTNS, FOXP3, CSF1R, BTD
6	SVM	68.9	16	16
7	C&R tree	68.9	6	IPI score
8	C5 tree	67.8	1	IPI score
9	XGBoost linear	67.8	16	16
10	Quest	67.8	6	IPI score
11	Tree-AS	67.2	1	IPI score
12	CHAID	67.2	1	IPI score
13	Logistic regression	66.7	16	Equation for dead outcome: −1.8*SRGAP3 + −0.9*CEP57 + 1.0*EPB41L4B + 0.8*SPIN2A + 0.7*IL10 + 0.15*MOCOS + 0.3*CD163 + 0.9*CTNS + 0.1*BTD + −0.01*PDCD1 + −0.4*L1CAM + −0.1*PRB1 + 0.5*TNFRSF14 + −0.4*CSF1R + 0.03*FOXP3 + −1.1*IPI score = 1 + 0.7*IPI score = 2 + −3.8.
14	Discriminant analysis	66.7	15	16, except IPI score
15	KNN algorithm	63.4	16	16
16	Bayesian network	57.4	16	16

.

The final integrative model of MLP neural network (Figure 5) was compared to other machine learning techniques.

4. Discussion

Follicular lymphoma is one of the most frequent non-Hodgkin lymphomas in Western countries. The pathogenesis of follicular lymphoma is still not fully understood. Currently, it is considered that the malignant transformation of follicular B lymphocytes is a complex, multistep process during which genetic and epigenetic modifications occur [24].

In adults, the development of follicular lymphoma starts with the overexpression of BCL2 due to the translocation with the immunoglobulin promoter/enhancer elements, the t(14;18)(q32;q21) [25]. In follicular lymphoma, other gene translocations are found such as BCL6 and MYC translocations that have prognostic relevance. For instance, the presence of BCL6 translocation and/or copy number gains of BCL6 is associated with a favorable prognosis [25]. Many other genetic lesions are identified in follicular lymphoma: 1p, 6q, 10q, and 17p copy number losses, and 1, 6p, 7, 8, 12q, X copy number gains, and 18q/dup [1,5,24]. Somatic mutations have also been identified, including mutations of KMT2D, CREBBP, EZH2, EP300, HIST1H1E, KMT2C, ARID1A, and SMARCA4 [6,24,25,26,27,28,29,30,31,32,33].

The tumor immune microenvironment, host immune response, and immune checkpoint are also relevant in the pathogenesis of follicular lymphoma. For example, we previously reported that high percentages of FOXP3+regulative T lymphocytes (Tregs) and high Programmed cell death protein 1 (PD-1)+follicular T lymphocytes (TFH cells) were associated with a good overall survival of the follicular lymphoma patients and higher risk of transformation to diffuse large B-cell lymphoma (DLBCL) [3,4]. Conversely, high frequencies of HVEM (TNFRSF14)+cells, mainly including macrophages and follicular lymphoma B centroblasts, but low B- and T-lymphocyte attenuator (BTLA) were associated with a poor overall survival [34]. Another marker related to macrophages [21], the Macrophage colony-stimulating factor 1 receptor (CSF1R) and interleukin-10 (IL10) were also associated with the prognosis of follicular lymphoma [35] and diffuse large B-cell lymphoma [36]. In the final model, the input nodes of the input layer of the MLP neural network included (1) immune microenvironment markers (i.e., CD163, CSF1R, FOXP3, PDCD1, TNFRSF14, and IL10); (2) the most relevant genes identified in the MLP neural network that had used the random number generator for the artificial intelligence analysis and dimensionality reduction (i.e., EPB41L4B, MOCOS, SPIN2A, BTD, SRGAP3, CTNS, PRB1, L1CAM, and CEP57); and (3) the international prognostic index (IPI) as the most relevant clinical variable. As a result, the neural network managed to predict the overall survival of the follicular lymphoma patients with high performance, with an area under the curve of 0.89. Therefore, this research managed to combine previously identified clinical and tumor immune microenvironment markers with newly highlighted genes. The biological functions of these genes are shown in

Table 2. The biological function of the highlighted genes using the MLP neural network.

Gene	Protein	Function
EPB41L4B	Band 4.1-like protein 4B	Promotes cellular adhesion, migration, and motility
MOCOS	Molybdenum cofactor sulfurase	Molybdopterin cofactor metabolic process
SPIN2A	Spindlin-2A	Regulation of cell cycle progression
BTD	Biotinidase	Biotin metabolic process
SRGAP3	SLIT-ROBO Rho GTPase-activating protein 3	Negative regulation of cell migration
CTNS	Cystinosin	Positive regulation of TORC1 signaling
PRB1	Basic salivary proline-rich protein 1	Glycoprotein
L1CAM	Neural cell adhesion molecule L1	Cell adhesion and in the generation of transmembrane signals at tyrosine kinase receptors
CEP57	Centrosomal protein CEP57L1	Centrosomal protein, which may be required for microtubule attachment to centrosomes.

Information obtained from UniProt.

. Generally, these genes had a function in cell adhesion and migration, cell signaling, and metabolism.

In our analysis setup, each time a neural network was performed produced a different result. To replicate the results exactly, the same procedure set up, the same order of the data, the same variable order, in addition to using the same initialization value for the random number generator, is necessary. In this study, all the parameters were the same except for the random number generator. The MLP procedure uses random number generation during the random assignment of partitions, random subsampling for the initialization of synaptic weights, random subsampling for automatic architecture selection, and the simulated annealing algorithm used in weight initialization and automatic architecture selection [14,15,16,19,22,37,38]. This methodology design is very similar to ensemble learning, such as random forest. As a result, 120 different and independent solutions were calculated to predict the overall survival outcome (dead vs alive). Therefore, 120 neural networks predicted the survival of the patients with different combinations of 22,215 gene probes. Since the dataset was the same for each calculation, the averaged solution may be the “most adequate” to explain the pathogenesis of follicular lymphoma. From an initial number of 22,215 gene probes, the dimensionality reduction strategy highlighted 48 genes. These genes represent the averaged solution of all MLP analyses. Therefore, these genes are expected to play an important role in the pathogenesis of follicular lymphoma. This fact was confirmed in the GSEA analysis and in the final MLP network, as shown in Figure 5. In summary, we took advantage of the random number generator to highlight new pathogenic markers of follicular lymphoma.

5. Conclusions

This research took advantage of the random number generator to create multiple different and independent artificial neural networks that after dimensionality reduction highlighted a small set of prognostic genes. A final model integrated these genes with known immune tumor microenvironment markers and the international prognostic index to create a neural network that predicted the overall survival of follicular lymphoma with high performance.