Reformas en sanidad y educación

Several machine learning algorithms exist that have been applied to microbiome data. Regression methods are commonly used to assess correlations between variables and can be useful in selecting subsets of predictors related to the response, shrinking coefficients to reduce variance, and reducing dimensionality of the data [257]. Elastic net regression, which includes the lasso and ridge methods, is particularly useful for high- dimensional data. Both of these models constrain coefficient estimates, which shrinks them towards zero and reduces their variance, resulting in improved prediction accuracy. They also contain a penalty factor that creates bias within the model but decreases variance, resulting in overall increased accuracy [261]. Both ridge and lasso contain a λ tuning parameter that must be determined by cross-validation using a subset of the data. An increasing value of λ in ridge regression reduces the coefficients but keeps all predictors in the model. In lasso, increasing values of λ result in some coefficients becoming zero, which effectively removes the predictors they correspond to from the model. Lasso regression therefore performs variable selection, which decreases the complexity and dimensionality of the data. The elastic net method, which combines both lasso and ridge regression, is useful in that it provides a less flexible approach and prevents overfitting of the model, which can lead to inaccurate predictions.

Both lasso and ridge regression are types of linear classification models that may not adequately model microbiome data, which is usually non-linear in nature [261]. As a

result, non-linear regression models are more frequently used, such as support vector machines (SVM), random forests (RF), and neural networks. SVM is a generalization of the maximal margin classifier, and is depicted in Figure 5.1 [257]. It consists of a

hyperplane (labeled the maximal margin hyperplane in Figure 5.1) that optimally separates the data points. The maximal margin establishes the best choice of separating hyperplane, since infinite hyperplanes could separate the data. Here, the distance between possible hyperplanes and the observations is measured. The maximal margin hyperplane is the hyperplane with the largest distance between it and the nearest observations. These nearest observations (white points in Figure 5.1) are termed support vectors because they establish and support the maximal margin. The dependence of the margin on a subset of

Figure 5.1: The Maximal Margin Classifier. A hyperplane (maximal margin hyperplane; solid line) separates the data. Observations closest to the hyperplane act as support vectors (white data points) that establish the maximal margin (dotted lines).

the data allows for more accurate and consistent classification of incoming data. In many cases, it is not possible to neatly separate data by a linear hyperplane. Further, data may need to be classified into more than two categories. The SVM was developed to address both of these issues. The SVM enlarges feature space using kernels in order to encompass non-linear data. A kernel is a mathematical function that describes the similarity of two data points, allowing use of equations specific to non-linear data. An appropriate kernel function will establish non-linear boundaries for the maximal margin classifier that best fits the data. Incorporation of more than one class is a more difficult challenge and relies on one-versus-one or one-versus-all approaches. In one-versus-one, pairs of classes are compared in order to determine classification. In one-versus-all, each class is compared to all the others to classify observations. Though SVM is useful in categorizing linear data into binary classes, neural networks and RF may be more appropriate choices for most microbiome data.

The development of artificial neural networks was influenced by biological neural networks, in which a single neuron communicates with several other neurons through axons [254]. Though several types of neural networks exist, all function on a similar structural basis, as shown in Figure 5.2. The most used neural network is the multilayer perceptron, which consists of between one and three hidden layers of neurons and an output neuron [254]. Each neuron is connected to every neuron in the layer preceding it but neurons within the same layer are not connected to each other. This is essential to

accurate classification within the model. Each neuron-to-neuron link is associated with a weight. The input values are multiplied by this weight before being subjected to the transfer function in the next layer of neurons. Each of these next neurons also has an associated weight that the resulting values from the previous layer are multiplied by before being subjected to the transfer function again. This process is referred to as feed- forward propagation and results in varying weights of evidence that allow the network to choose the best classification of the input data. The universality theorem states that, with the right number of neurons and the right choice of weights, a neural network model can be used to solve any classification problem accurately [254]. Unfortunately, knowing what these correct choices are is more difficult. The choice of correct weights for a neural network is done through a training process known as backpropagation of error. This is an

Figure 5.2: Neural Networks. Input neurons receive a weighted sum of data, which is transformed by a mathematical function by interconnected sets of hidden layer

neurons. Multiplication by the weights is used to determine classification of the output data.

iterative method in which a range of weights is assigned to the model and input is propagated through the network. Both the error and each neuron’s degree of

responsibility for it can be calculated backwards through the network and used to adjust the weights appropriately. Though highly accurate and applicable to nearly any

classification problem, neural networks are prone to overfitting and can be

computationally expensive, both of which are partly due to the problem of choosing the optimal number of neurons for the network.

The RF algorithm is an extension of decision tree methods that divides the predictor variables in a dataset into homogenous groups that predict the response variable [261]. The predictors are divided by the process of recursive binary splitting, which is a top-down, greedy approach [257]. It is top-down in that splitting begins with all the predictors present, and it is greedy because the best choice for each specific split is made rather than the split that will generate a better tree for the entire data

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Figure 5.3: Decision Tree. PCA was used to cluster species abundance data for airway microbiota from burn patients and a decision tree was applied to determine which patient variables explain the clustering. The data was split by days spent on the ventilator and percent human DNA in the sample.

set. Figure 5.3 gives an example of a decision tree applied to airway microbiome data. Here, principle components analysis (PCA) was used to cluster species abundance data by similarity. Clusters were assigned numbers and a decision tree was used to predict which patient clinical variables explain the clustering. The labels at each split indicate the variables that best predict the data, the numbers at each leaf represent the mean of the cluster assignments for each group, and the number of samples at each split is indicated by n=x. At the top of the tree, all the data was split based on the number of days the patient spent on the ventilator. Patients with less than eight days (right side of the top branch) were predicted to be in cluster five (mean of cluster assignments = 4.9). Patients with greater than or equal to eight days (left side of the top branch) were further split by the percent of human DNA present in the sample. If the sample had less than 52.81% human DNA (left side of the branch) the sample was predicted to be in cluster two (mean cluster assignment = 1.789). If the same sample had more DNA than that (right side of the branch) it was predicted to be in cluster three (mean cluster assignment = 3.211). To put it another way, if a patient spent less than eight days on the ventilator, their airway microbiota was predicted to be in cluster five. If they spent eight or more days on the ventilator and had less than 52.81% human DNA in their airway sample, their microbiota would be in cluster two. If they spent eight or more days on the ventilator and had

52.81% or more human DNA, their microbiota would be in cluster three. Decision trees are easy to interpret but their simplicity means that they lack the predictive accuracy and power of other classification methods. Further, because they simultaneously consider all the predictors, they can be biased towards variables that dominate the data. Aggregation of trees can greatly improve prediction accuracy and several methods exist to do this, of

which RF is the most powerful. In the RF model, a number of decision trees are built

using bootstrapping, which consists of randomly resampling the data and is a powerful way of estimating variance. Unlike the decision tree method, however, RF only selects a subset of the predictors to make each tree. This randomization process eliminates bias that may be present due to dominance of certain predictors among the others. It also decorrelates the trees, which produces less variability and more reliability in the resulting average of the trees. Figure 5.4 illustrates how the RF model works. The other strength of the RF algorithm is its ability to deal with compositional, sparse data. Decorrelation of

Figure 5.4: Random Forests. The random forest algorithm builds many decision trees based on a subset of the predictors in a dataset. The resulting tree is an average of these decorrelated trees and has improved accuracy and reliability over a single decision tree.

the trees accommodates the spurious correlations that arise due to the nature of compositional data, and zeros in the data can be handled due to the method being non- parametric [262]. The RF algorithm is an improvement over decision tree methods and is a powerful predictive tool that can appropriately manage microbiome data.

Several studies have used these algorithms to predict outcomes or groupings based on microbiome data, such as subsistence groups in rural Africa from gut microbial community composition [26] and presence of pneumonia in patients based on upper respiratory tract microbiota [233]. However, the field is lacking validation of machine learning algorithms that accurately predict outcomes from microbiome data. Several studies have addressed this issue by comparing performance of several algorithms on microbiome data. Pasolli et. al. used support vector machines (SVM), random forests (RF), and lasso and elastic net regression algorithms to predict disease state among 2,424 publicly available metagenomic datasets [247]. RF produced the best classification accuracy as evaluated by area under the curve (AUC), a metric that summarizes true positive and false positive rates. The study also explored whether a reduced set of features (e.g. bacterial species) selected by each of the algorithms could be used to accurately predict disease state. Though feature selection produced good AUC, the best results were obtained with more than 60 bacterial species, indicating the importance of microbiota complexity in predicting outcomes. Statnikov et. al. applied 18 machine learning algorithms from seven families, including the four discussed above, to 1,802 human microbiome samples [249]. This work emphasizes the variation present in human microbiome datasets and the challenges they bring to classifying this data, particularly in the case of disease prediction. However, of the methods described here, Statnikov et. al.

found that SVM, RF, and ridge regression outperformed neural network classification. Pasolli et. al. found RF to be most accurate but used a different dataset, which will vary from Statnikov et. al.’s dataset, and did not include neural networks in the models they evaluated. Regardless of the difference in results, these studies confirm the utility of machine learning algorithms in predicting patient outcomes from microbiome data and establish RF, SVM, and ridge regression as appropriate models to use.

5.1.3 Application of Supervised and Unsupervised Methods to Burn Patient Airway