We could obtain 450 known associations between 292 microbes and 38 diseases from Human Microbe-Disease Association Database (HMDAD) (Ma et al., 2017). For the reason that there were several grades of microbe classification, and when using 16s RNA sequences to study microbes, only the information in the level of genus would be acquired, we revealed the microbes which were likely to be related with human diseases in genus level. Besides, we defined the adjacency matrix A, if there was known association between disease d(i) and microbes m(j), the value of the element A(d(i), m(j)) matrix A was 1. We applied the variable nd, nm to denote the number of diseases and microbes studied, respectively.

Inspired by this article (Laarhoven et al., 2011), Considering the assumption that if two similar diseases were associated with two microbes, respectively, the two microbes were likely to be similar, and there were similar interaction and non-interaction pattern between diseases and microbes, Gaussian interaction profile kernel similarity for disease KD was constructed to indicated the similarities between diseases based on the known associations of disease-microbe pairs. Firstly, binary vector IP(d(i)) was defined to represented the interaction profiles of diseases d(i) by observing whether there was a known association between disease d(i) and each microbe (i.e., the ith row of the adjacency matrix A). Then, the Gaussian interaction profile kernel similarity between disease d(i) and d(i) could be calculated as follow:

Here, parameter γ_d was introduced to regulated the kernel bandwidth and got by normalizing another parameter γ′_d by the average number of related microbes of all the diseases. γ_d was calculated as follow:

where the value of γ′_d was 1.

The definition of Gaussian interaction profile kernel similarity for microbe KM was similar to KD

From the above we could see that Gaussian interaction profile kernel similarity was only based on the adjacency matrix A. If we wanted to effectively and scientifically predict potential disease-associated microbes, it was necessary to introduce other datasets in combination with the Gaussian interaction profile kernel similarity. Based on the disease and corresponding symptom recorded in PubMed bibliography. Zhou et al. (2014) calculated similarity between diseases and constructed the symptom-based human disease network (HSDN). Here, we integrated the Gaussian interaction profile kernel similarity for disease KD and the symptom-based disease similarity SDM to obtained the Integrating symptom-based disease similarity SD, and the calculation of SD was defined as follow:

Motivated by this paper (Rayhan et al., 2017), we constructed a novel calculation model of ABHMDA to predict disease-related microbes and the flow chart of the algorithm was shown in Figure 1. The core idea of ABHMDA was to train different classifiers (weak classifiers) for the same training samples, and then grouped these weak classifiers with different ratios to form a stronger classifier to score and sort samples. Here, we chose the decision tree as our weak classifier. The specific steps were mainly divided into three steps: integrating the data, training the model, and scoring the samples. In the first step, we integrated the Gaussian interaction profile kernel similarity for microbe KM and the Integrating symptom-based disease similarity SD. In the second step, we firstly referred to the sample with confirmed association as a positive sample, otherwise it was an unknown sample. On account of the unknown sample accounting for about 97% in all the samples, that was to say, there were far more unknown samples than positive ones, and it was unreasonable to directly train such unbalanced datasets. Here, we introduced a novel method to balance the datasets. In this method, we applied the k-mean clustering to divide the unknown sample into k parts, and then randomly extract some samples from each part as negative samples, while positive samples kept unchanged. There were researchers studying the effect to random extraction when k took different values, and the results shown that the optimal value of parameter k was 23. In order to make the dataset used for training more balanced, the number of the unknown samples randomly selected ought to be approximately equal to the positive sample. In the end, the negative and positive samples together formed the training samples. Each training sample was weighted with an initial weight of 1n, where n was the total number of training samples. The main purpose of the training process was to calculate the proportion of each weak classifier in the final strong classifier and update the weight of each training sample according to whether it was classified correctly by the last classifier and the overall classification accuracy of the last classifier. After updating, the new training sample set with modified weight values was sent to the next weak classifier for training. Here, we built lists D_I,h(i) and Y , all of which had n elements. The value of each element in D_i was the weight of the corresponding sample when the ith weak classifier trained the sample. The value of i was 0, 1, 2,,,,29. In other words, D₀ was a list with all elements being 1n. The value of the element in label lists h(i) and Y was only 0 or 1, and the difference between them was that the value of h(i)_j depended on the prediction of the ith weak classifier, while the value of Y_j depended on whether the corresponding sample was a positive sample, if the corresponding sample was a positive sample, the value of Y_j was equal to 1, otherwise 0. The error function ∈_i was calculated as follow:

It could be seen from the formula that the error function ∈_i was equal to the sum of the weights of the samples, whose label predicted by the weak classifier h(i)_j was different from the known label Y_j. That was to say ∈_i was equal to the sum of the weights of all the samples that were predicted wrong. Then the proportion of the ith weak classifier in the strong classifier could be defined as follow:

It could be seen from equation (5) that the smaller the error function was, the larger the proportion of the weak classifier in the strong classifier would be. And the variate Z_i could be calculated as follow:

The weight of the sample could be updated according to the following formula:

Here j = 0, 1, 2...n - 1. After the weights of samples being updated, the samples with the new weights were sent to the next weak classifier to start the next training until all the weak classifiers completed the training (Theoretically, the more weak classifiers, the higher the prediction accuracy of strong classifier. But when the weak classifier reached a certain number, the prediction accuracy tended to be stable. And then as the number of weak classifiers increased, accuracy was not significantly improved, but the prediction process took longer. We compared the prediction results with 20, 30, and 40 weak classifiers, the accuracy of using 30 and 40 weak classifiers was basically the same, which was better than 20 weak classifiers. However, the prediction time of 40 weak classifiers was longer than using 30 classifiers. Comprehensive consideration of prediction time and accuracy, here, we chose to use 30 weak classifiers to form the final strong classifier.), then the training process was end. The next step was to score the sample, and the score of the jth sample was defined as follows:

Here, HH(i)_j was the score scored by the ith weak classifier for the jth sample. That was to say, the score of the sample was equal to the sum of the product of the sample’s goal scored by weak classifier and the corresponding weight (The corresponding data and code had been submitted to the website²).

In order to verify the prediction performance of ABHMDA, we implemented global and local LOOCV for our model based on the database HMDAD (Ma et al., 2017) which recorded 450 known associations between 39 diseases and 292 miRNAs. Specifically, each of the 450 samples (positive samples) with known association was left out in turn as a test sample while the remaining 449 were used for model training, while all of the samples without known associations were considered as candidate samples (unknown samples). In global LOOCV, we sorted the test sample with all candidate samples based on the score marked by calculation model, while the test sample was ranked with the candidate samples that contained the same disease as the test sample in local LOOCV. We evaluated the prediction performance of models based on the AUC value of the LOOCV. To be specific, only the test sample ranked above a certain threshold, could it be considered as a correct prediction, and then we set the true positive rate (TPR, sensitivity) as the horizontal axis and the false positive rate (FPR, 1-specificity) as the vertical axis. Therefore, we could plot the Receiver operating characteristics (ROC) curve, which was composed of points corresponding to different thresholds, then we could obtain the Area under the ROC curve (AUC). A model with an AUC value equal to 0.5 was equivalent to a random prediction. When the AUC took the maximum value of 1, the model had excellent prediction performance. In other words, when the value of AUC was greater than 0.5 and less than 1, the larger the value was, the better the prediction performance of the model would be.

As shown in Figure 2, the global LOOCV value of ABHMDA was 0.8869, which was significantly larger than that of KATZHMDA (0.8644) and LRLSHMDA (0.8843). What was more, the local LOOCV value of our model reached 0.7910, which was also obviously better than KATZHMDA (0.6998) and LRLSHMDA (0.7508). These results confirmed the superior prediction performance of ABHMDA

In order to further assess the prediction ability of ABHMDA, we implemented two case studies on some important diseases of human. In the first kind, there were 10938 unknown samples about 39 diseases and 292 miRNAs in HMDAD. We sorted and ranked all unknown samples corresponding to the same disease and verified whether the association between the top 10 microbes and the disease studied was verified by the relevant literature. In the second kind, we converted all 1 in the adjacency matrix A to 0 and sorted all the samples (positive and unknown samples) corresponding to the same disease and then verified the association between disease and the 10 microbes most likely associated with it predicted by the model in the database HMDAD. In other words, the purpose of the second case study was to verify our model’s power to predict microbes associated with new diseases without any known related microbes. Here, we implemented the first case study on asthma, Colorectal carcinoma, and the second case on Type 1 diabetes.

As an inflammatory disease on the airway, it was very difficult to completely cure asthma under current medical conditions (Preston et al., 2007). According to statistics, there were about 300 million asthma patients worldwide, and in recent years its morbidity and mortality had also increased rapidly, especially in developing countries (Sagar et al., 2014). Therefore, a deeper study of asthma was imperative, and studies had shown that there was a close relationship between the microbes in the respiratory tract and the development and progression of asthma (Marri et al., 2013). For example, studies had shown that Firmicutes was reduced in asthmatic patients compared with normal humans (Wu et al., 2018). In contrast, Proteobacteria accounted for a larger proportion of microorganisms in asthma patients than normal people (Marri et al., 2013). What’s more, there was evidence that when the hypopharyngeal area of Neonates was infected with Streptococcus pneumoniae, the risk of developing asthma was increased compared to uninfected (Bisgaard et al., 2007). We implemented the first case study of asthma and the 10 microbes predicted to be most relevant to asthma were all verified by literatures. For instance, the experimental results showed that the abundance of Lachnospiraceae (First in the prediction list) in asthma patients was 1.9 times that of normal people (Jung et al., 2016). The researchers found that the relative abundance of Veillonella (Second in prediction list) in infants at risk of asthma was significantly lower than in normal people, and inoculation of sterile mice with Veillonella could improve its airway inflammation, which provided new ideas for the treatment of asthma (Arrieta et al., 2015). Moreover, there was evidence that if there was Clostridium coccoides (Third in prediction list) in a 3 week old baby’s stool, he was at risk of developing asthma, so Clostridium coccoides may become an early diagnostic target for asthma (Vael et al., 2011; See Table 1).

To facilitate further research and validation, we provided a ranking of the relevant probabilities for all pairs of disease-microbe pairs without confirmed association (See Supplementary Table S1).

Colorectal carcinoma (CRC) was a common gastrointestinal malignant tumor in China (Xue et al., 2014). As one of the top cancers with the highest morbidity and mortality worldwide, it was estimated that there were approximately one million new cases of CRC and 500000 deaths per year (Sun et al., 2013). What was more serious was that its incidence would continue to increase in the next few decades, and the survival rate in 5 years was less than 60% (Sun et al., 2011). Therefore, it was necessary to study the pathogenesis of CRC to explored new treatment methods, and studies had shown that microbes played an important role in the development and progression of cancer that were closely related to inflammation like CRC (Liang et al., 2014). For example, there were studies showing that the number of Lactobacillus hamster increased significantly during the formation of CRC (Liang et al., 2014). The researchers compared CRC cases with the normal control group and found that the relative abundance of phylum Bacteroidetes in the case group reached 16.2%, which was much higher than 9.9% of the normal group (Ahn et al., 2013). We applied ABHMDA to implement the first case study on CRC, and the 10 predicted microorganisms most likely to be associated with CRC were all verified by related literature in PubMed. There was evidence that the relative abundance of Veillonella (First in the prediction list) in CRC cancer tissues was 2.87% and only 0.68% in the intestinal lumen (Chen et al., 2012). Pyogenic liver abscess was identified as an early manifestation of adult CRC, and an 11-year follow-up study showed that pyogenic liver abscess patients with Klebsiella (Second in the prediction list) pneumoniae had a higher probability of having CRC than those without (Huang et al., 2012). What was more, there were studies showing that Enterobacteriaceae (Third in the prediction list) was very rich in CRC patients (Arthur et al., 2014). From the above results, it could be seen that the predicted performance of ABHMDA was very reliable (See Table 2).

Type 1 diabetes was an autoimmune disease which resulted from the immune-mediated destruction of insulin-producing pancreatic β cells (Li et al., 2014). The incidence of Type 1 diabetes was increasing globally, but the proportion of patients suffering from genetic factors was decreasing, which suggested that the virus, nutrition, and overweight were very likely to have become the main cause of Type 1 diabetes (Islam et al., 2014). Studies had shown that the abnormality in the gut microbiota was closely related to the development of Type 1 diabetes (De Goffau et al., 2014). The number of Firmicutes and Actinomycetes were significantly reduced in children with Type 1 diabetes compared with normal people (Murri et al., 2013). We conducted the second case study on Type 1 diabetes to test the prediction power of ABHMDA to predict the potential microbe-related of new diseases, and the results showed that 7 of the top 10 potential disease-related microbes predicted were validated by the database HMDAD. The associations between Type 1 diabetes and microbe Veillonella (First in the prediction list) with Bacteroidaceae (Second in the prediction list) were confirmed by HANDAD. Some researchers had found that patients with Type 1 diabetes had increased colonization of Enterobacteriaceae (Third in the prediction list) in addition to Escherichia coli compared with normal people (Soyucen et al., 2014). The above results indicated that ABHMDA’s ability to predict microbes associated with new diseases was also reliable (See Table 3).