Definition of the problem and selection of study design

The problem we aim to solve needs to be precisely defined and well understood. As with all research the starting point is critical review of the previous knowledge in the area, formulation of a research question and choice of appropriate study design (Katz, Reference Katz2006). For example, a longitudinal collection of patients’ data may allow investigation of the risk of an occurrence or relapse concerning a disease over time. Designs such as the case-control that collect data of disease and healthy individuals at just one point in time, will be appropriate to test the ability of a set of factors in predicting a diagnosis.

Data collection and pre-processing

Ideally, quality data will include a well-defined selection of patients, and a rigorous collection of relevant predictors and outcomes. Before analysis, the main steps of data pre-processing include data cleaning, data reduction and data transformation.

Cleaning refers to the treatment of missing data, a common problem in psychiatric research, and this is important as inadequate missing data treatment may lead to an overestimation of prediction accuracy (Batista & Monard, Reference Batista and Monard2002). Discarding individuals or variables with missing values (‘the complete-case analysis’) may bias analysis if the units with missing values differ systematically from the completely observed cases, especially if percentage of missingness is high. A preferable approach may be to estimate or ‘impute’ missing values using either classical statistics or SL. SL methods (e.g. tree-based methods; Ding et al. Reference Ding, Simonoff and Eklan2010) (Table 1) are free of assumptions and have been found to outperform classical statistical methods of imputation. For example, the methods based on SL techniques were the most suited for the imputation of missing values in a study aiming to predict cancer recurrence, and led to a significant enhancement of prognosis accuracy compared to imputation methods based on statistical procedures (Jerez et al. Reference Jerez, Molina, Garcia-Laencina, Alba, Ribelles, Martin and Franco2010).

Table 1. Main properties of a set of selected statistical learning algorithms

All methods listed above can be used for classification (categorical outcome) and for regression (quantitative outcomes) problems. All of them can handle multiple continuous and categorical predictors.

Data reduction involves obtaining a reduced representation of the data volume that can achieve the same (or almost the same) analytical results. By creating new features as a result of the aggregation or eliminating features that are not meaningful for prediction (‘feature selection’) tasks can be made more computationally tractable. Reducing the number of features also makes models more easily interpretable. This point is critical for the success of a predictive algorithm, especially if there are thousands of features at the outset (Guyon, Reference Guyon2003; Witten & Tibshirani, Reference Witten and Tibshirani2010). Feature reduction can be performed as a part of pre-processing or during the modelling step using algorithms that perform an internal feature selection (elastic net regression; Zou & Hastie, Reference Zou and Hastie2005) or Classification and Regression Tree (CART) algorithms (Rokach & Maimon, Reference Rokach and Maimon2008) (Table 1). The latter will usually improve reliability and increase confidence in selected features (Caruana & Niculescu-Mizil, Reference Caruana and Niculescu-Mizil2006; Krstajic et al. Reference Krstajic, Buturovic, Leahy and Thomas2014).

Fig. 2. (a) Data simulated from a follow-up study of major depression patients. Age of depression onset (years) and the MADRS score at baseline ranging from 0 to 60 (0–6, normal; 7–19, mild depression; 20–34, moderate depression; >34, severe depression) are the predictor variables. The outcome is remission status at the end of the follow-up (YES or NO). (b) The Naive Bayes classifier is often represented as this type of graph. The direction of the arrows states that each class causes certain features, with a certain probability. (c) A hyper plane (a line, in dimension 2) is built at a maximal distance to every dashed line (called margin). A new case (point) will be classified as remission or non-remission depending on his relative position to the line (aka decision boundary). (d) A simple decision tree suggesting that patients with age of onset lower than 29 are more likely to reach a remission. (e) Each node represents an artificial neuron and each arrow a connection from the output of one neuron to the input of another.

Data transformation methods depend on the specific SL algorithm to be used (Kotsiantis et al. Reference Kotsiantis, Kanellopoulos and Pintelas2006). Three common data transformations are scaling, decompositions and aggregations. Many SL methods (e.g. the elastic net regression; Zou & Hastie, Reference Zou and Hastie2005) require all predictors to have the same scale such as between 0 and 1. Decomposition may be applied to features that represent a complex concept, as they may be more useful to a ML method when split into their constituent parts (e.g. a date can be split into day, month and year). Aggregation is appropriate when there are features that are more meaningful to the problem when combined into a single feature.

Training and validation of the model

The data used to run a learning algorithm are called training data. In supervised ML the program is told what the output should look like, for example what subjects belong to what category label. A second set of data is called the test dataset. Here the labels are again known to the researcher but in this run the program is only given the input data and the task is to correctly assign the outputs or labels. Ideally the test data and the training set should be completely independent but in practice researchers very often randomly split datasets of labelled data in two parts and arbitrarily define one part as the learning data and the other as the test set. If the algorithm is able to estimate correct labels in this new set of cases, i.e. the called prediction error is small (e.g. the number of falsely classified cases is much smaller than chance classification), the classifier may be considered to be ‘valid’ to be used in estimating outcomes for cases with unknown outcomes. As elsewhere in classification problems a variety of measures are used to assess prediction accuracy (Steyerberg et al. Reference Steyerberg, Vickers, Cook, Gerds, Gonen, Obuchowski, Pencina and Kattan2010), for example sensitivity (the proportion of correctly classified recovered cases) and specificity (the proportion of correctly not recovered cases) for binary classifications.

Wolpert & Macready (Reference Wolpert and Macready1997) consider that there is unlikely to be a single technique that will always do best for all learning problems. Hand (Reference Hand2006) advocated that we should base our selection on a compromise between the accuracy of the model in predicting outcomes for new cases and the interpretability of the result.

Specific ML terminologies that have been adopted by the SL community are introduced in Table 2. A more detailed set of definitions can be found in (Kohavi, Reference Kohavi1998).

Table 2. Glossary of statistical/machine learning terms used in this paper

Table 1 summarizes seven popular SL algorithms. More detailed information about specific learning algorithms can be found elsewhere (Mitchell, Reference Mitchell1997, Reference Mitchell2006; Vapnik, Reference Vapnik1998; Scholkopf et al. Reference Scholkopf, Guyon and Weston2003; Malley et al. Reference Malley, Malley and Pajevic2011).

A common scheme to train different classifiers and select one based on ability to predict outcomes is the K-fold cross-validation (CV). This is a procedure where the original training sample is randomly divided in K subsamples, K-1 samples are used as a new training set and one is left out as an occasional ‘test’ set in K iterations (Fig. 3). The prediction error is then computed across test samples. Minimizing the prediction error from the CV loop is used to select the best algorithm and the best predictive model produced by the same algorithm. CV provides a nearly unbiased prediction error on new observations from the same population (Kohavi, Reference Kohavi1995).

Fig. 3. Example of a 5-fold cross-validation. Data are randomly split in 5-fold of equal size. At every step, one fold is selected as test dataset and the remaining four are used as training data. This procedure is repeated five times, selecting in every step a different fold as test data.

Introducing a generated predictive knowledge to a practical setting

A nice example is provided by the work of Perlis and colleagues (Perlis, Reference Perlis2013) who ran a prospective investigation to identify clinical predictors of antidepressant treatment resistance. The authors selected 15 easy-to-obtain features for patients with known response and adopted a SL approach. Based on the best model obtained, the team developed a web-based clinical decision support system that given the values for the 15 variables for a particular patient suffering from major depression could aid in predicting the risk of being resistant to an antidepressant treatment.

Dealing with heterogeneous sources of information

Data from different sources (e.g. large longitudinal clinical trials or cohort studies, electronic health records, national health registries) has a greater potential for establishing novel useful ways of categorizing patients’ groups (patient stratification) and for revealing unknown disease correlations compared to learning from each source independently (Shi et al. Reference Shi, Paiement, Grangier and Yu2012). Specific SL algorithms have demonstrated impressive empirical performance on a wide variety of classification tasks involving heterogeneous Big Datasets (e.g. decision-tree approaches; Breiman, Reference Breiman1984), regularized regression models (Zou & Hastie, Reference Zou and Hastie2005), as well as support vector machines (Lewis et al. Reference Lewis, Jebara and Noble2006) (Table 1). Integrating such data is a challenge that may include the problem that data are stored in many different formats. However, the handling of Big Data from a variety of sources is becoming ever more feasible and affordable, with many institutions employing their own local clusters of computers (banks of many micro-computers hooked up in parallel and providing huge computational power). ‘Cloud’ computing is another increasingly available option. This refers to using the Internet to access the vast computational resources that are offered commercially by companies such as Amazon, Google and Microsoft.

The IMAGEN study (Whelan et al. Reference Whelan, Watts, Orr, Althoff, Artiges, Banaschewski, Barker, Bokde, Buchel, Carvalho, Conrod, Flor, Fauth-Buhler, Frouin, Gallinat, Gan, Gowland, Heinz, Ittermann, Lawrence, Mann, Martinot, Nees, Ortiz, Paillere-Martinot, Paus, Pausova, Rietschel, Robbins, Smolka, Strohle, Schumann and Garavan2014) is a good example where researchers integrated data from very heterogeneous domains and applied a SL approach of analysis. Domains included brain structure and function, individual personality and cognitive differences, environmental factors, life experiences, and candidate genes. They applied elastic net regularized regression (Zou & Hastie, Reference Zou and Hastie2005) to generate models to predict current and future adolescent alcohol misuse based on such holistic characterization. This ‘regularized’ approach automatically dropped out features that were not contributing to the class predictions. Thus the final model incorporated a subset of the most relevant variables for prediction selected from all of the explored families of predictors. The favoured models pointed to life experiences, neurobiological differences and personality as important antecedents of binge drinking, suggesting possible targets for prevention. The authors reported specific predictors in their models along with their regression coefficient as a standard and interpretable measure of strength between each predictor and the outcome. The approach correctly predicted alcohol misuse for individuals not in the original dataset, emphasizing the model's capability to generalize to novel data.

The search for meaningful predictors of a psychiatric outcome in high-dimensional datasets

Big Datasets in psychiatry research can be ‘Big’ regarding volume and number of features but involving a relative smaller sample size. For example, even though GWAS typically now contain tens of thousands of subjects, there may be many millions of data points. Increasingly large-scale case-control studies also include gene expression, genome sequencing and epigenetics, proteomics or metabolomics inflating the data to research subject ratio even more. This is often called the high-dimensional data problem, or the ‘p > N’ problem (where p is the number of features and N the number of observations). Such data are commonly represented in a matrix, with more columns than rows. The classical approach of comparing thousands of single association tests and then ranking features by their statistical significance is not an optimal solution. The first concern is that multiple testing increases the risk of spurious findings due to chance. The application of stringent methods to correct this can lead to the detection of strong contributors to outcome at the expense of overlooking smaller contributors. This poses a problem in complex traits and disorders that, by their nature are multifactorial. Another related weakness is that independent analysis variable by variable does not permit inferences about combinations of variables. Generalized linear regression models (Hosmer et al. Reference Hosmer, Lemeshow and Sturdivant2013) are problematic in estimating the effect of such combinations. This kind of model is in danger of explaining mainly noise instead of the relationships between variables (and so models are poor in generalizing to new datasets). This problem is known as overfitting (Table 2). A second problem for generalized linear regression is correlation between features, i.e. the situation where if one feature changes, so do one or more other features, an effect known as multicollinearity (Table 2). An example is genetic variation. Due to the fact that most of our genetic information is inherited in ‘blocks’ from our parents, the information at different positions of our genome is expected to be highly correlated within families. Blocks, albeit smaller ones, also occur within genetically homogenous populations. Multicollinearity can seriously distort the interpretation of a model, making it less accurate by introducing bias within the coefficients of the model (Maddala & Lahiri, Reference Maddala and Lahiri2009) and increasing uncertainty, as reflected in inflated standard errors (Glantz & Slinker, Reference Glantz and Slinker2000; Miles & Shevlin, Reference Miles and Shevlin2001).

Supervised SL models offer a means to overcome these problems and to maximize the predictive power, hence providing exciting opportunities for individualized risk prediction based on personal profiles (Ashley et al. Reference Ashley, Butte, Wheeler, Chen, Klein, Dewey, Dudley, Ormond, Pavlovic, Morgan, Pushkarev, Neff, Hudgins, Gong, Hodges, Berlin, Thorn, Sangkuhl, Hebert, Woon, Sagreiya, Whaley, Knowles, Chou, Thakuria, Rosenbaum, Zaranek, Church, Greely, Quake and Altman2010; Manolio, Reference Manolio2013). SL models such as the multivariate adaptive regression splines (MARS) procedure (Friedman, Reference Friedman1991), the CART (Breiman, Reference Breiman1984), elastic net regularized regression (Tibshirani, Reference Tibshirani1994; Zou & Hastie, Reference Zou and Hastie2005; Friedman et al. Reference Friedman, Hastie and Tibshirani2010) and support vector machines (Cortes & Vapnik, Reference Cortes, Vapnik and Saitta1995) (Table 1) perform especially well in the high-dimensional scenario and in the presence of correlation between predictors (Libbrecht & Noble, Reference Libbrecht and Noble2015). They also allow to efficient identification of informative patterns of interactions between clinical and biomarker variables, which are known to play an important role in the development and treatment of many complex diseases (Lehner, Reference Lehner2007; Ashworth et al. Reference Ashworth, Lord and Reis-Filho2011), but are often missed by single association tests (Cordell, Reference Cordell2009).

Models in practice: the case of stratified and personalized medicine

In recent years stratified and personalized medicine became of interest in mental health research which utilizes molecular biomarkers (Kapur et al. Reference Kapur, Phillips and Insel2012), demographic and clinical information, including patients’ health records, to identify subgroups of patients who are likely to respond similarly to treatment using SL methods. Major depressive disorder is a prime example of a common disorder where there are many available drugs but where there is no straightforward way of deciding which treatment is likely to work for a given individual (Simon & Perlis, Reference Simon and Perlis2010). The Genome-based Therapeutic Drugs for Depression (GENDEP Investigators et al. 2013) project is a study aiming to test clinical and genetic data as predictors of treatment response to two antidepressant drugs (Uher et al. Reference Uher, Maier, Hauser, Marusic, Schmael, Mors, Henigsberg, Souery, Placentino, Rietschel, Zobel, Dmitrzak-Weglarz, Petrovic, Jorgensen, Kalember, Giovannini, Barreto, Elkin, Landau, Farmer, Aitchison and McGuffin2009, Reference Uher, Perroud, Ng, Hauser, Henigsberg, Maier, Mors, Placentino, Rietschel, Souery, Zagar, Czerski, Jerman, Larsen, Schulze, Zobel, Cohen-Woods, Pirlo, Butler, Muglia, Barnes, Lathrop, Farmer, Breen, Aitchison, Craig, Lewis and McGuffin2010). The need for prediction at individual level involving hundreds of thousands of variables prompted the use of SL methods (Iniesta et al. Reference Iniesta, Malki, Maier, Rietschel, Mors, Hauser, Henigsberg, Dernovsek, Souery, Stahl, Dobson, Aitchison, Farmer, Lewis, McGuffin and Uher2016). The challenge was the integration of clinical with biological markers and deriving optimal models with minimal risk of overfitting. Demographic, clinical and genetic predictors were combined in a model to predict the change in severity symptoms after a 12-week period in a sample of patients randomly treated with one of the two drugs. A linear regularized elastic net model (Zou & Hastie, Reference Zou and Hastie2005) looked for the best combination of variables in predicting symptoms course. Interestingly, the feature selection approach of elastic net allowed building drug-specific models that were able to predict treatment outcome with accuracy above a clinical significance threshold. The results suggested a potential for individualized indications for antidepressant drugs. The benefits of using the elastic net were several: first, the elastic net provided an efficient internal method of search and selection of predictors from a large set of variables available. Second, the iterative CV procedure used allowed the selection of predictors based on their ability in predicting outcome for unseen cases, which was the aim of this research. Third, this flexible approach reported distinct and specific models to each outcome and drug sample. Fourth, the elastic net allowed estimation of the combined predictive ability of a high number of variables while preventing the models from overfitting.

The hoped for impact of this type of research is the introduction of a predictive model (last box in Fig. 1) as a clinical decision support system. For a model to be useful in the practical scenario there is a list of challenges we need to overcome. First, the model should have been externally validated in a test dataset. Very often the validation of models built in sample of patients with very specific characteristics (e.g. those coming from randomized clinical trials) is difficult because it is hard to find another similar sample that can work as a ‘test’ dataset. Second, as a consequence, such models tend to poorly generalize to other populations. For example, if a model was built for a homogeneous ethnical population of white Caucasian patients and ethnicity has an effect on outcome, there is no guarantee that such model will predict well for an individual of different ethnicity. Thus some authors argue matching treatments to individuals is a too ambitious aim, as given any model, there can always be a relevant-to-outcome patient characteristic that was not included nor validated. However, it is not all bad news; several studies in cancer were able to find almost perfect biomarkers for treatment selection, specifically for chemotherapy treatment and some progress towards stratified medicine is appearing feasible in psychiatry (Perlis, Reference Perlis2013; Iniesta et al. Reference Iniesta, Malki, Maier, Rietschel, Mors, Hauser, Henigsberg, Dernovsek, Souery, Stahl, Dobson, Aitchison, Farmer, Lewis, McGuffin and Uher2016). A third challenge is the generation of easy-to-use tools in the clinical setting. Ideally models should involve a reasonable number of easy-to-obtain variables and be implemented through tools that allow a quick introduction of patients’ data and a simple and clear display of model outputs.

We can conclude that Big Data are becoming a major challenge for statistical analysts in mental health research and a paradigm shift in methods is needed. Statistical learning provides a set of tools that can successfully help in the understanding of such complex datasets. Such methods can be useful as an alternative or in addition to ‘classical’ statistical inference methods based solely on hypothesis testing which has been criticized by many statisticians for many years (Breiman, Reference Breiman2001a ; Nuzzo, Reference Nuzzo2014). Big Data analysis and the derivation of predictive SL models for stratified medicine in psychiatry is an emerging and hot area, and such tools have the potential to facilitate a better targeting of interventions and diagnosis of patients.