The ensemble method random forests has become a popular classification tool in bioinformatics and related fields. The out-of-bag error is an error estimation technique often used to evaluate the accuracy of a random forest and to select appropriate values for tuning parameters, such as the number of candidate predictors that are randomly drawn for a split, referred to as mtry. However, for binary classification problems with metric predictors it has been shown that the out-of-bag error can overestimate the true prediction error depending on the choices of random forests parameters. Based on simulated and real data this paper aims to identify settings for which this overestimation is likely. It is, moreover, questionable whether the out-of-bag error can be used in classification tasks for selecting tuning parameters like mtry, because the overestimation is seen to depend on the parameter mtry. The simulation-based and real-data based studies with metric predictor variables performed in this paper show that the overestimation is largest in balanced settings and in settings with few observations, a large number of predictor variables, small correlations between predictors and weak effects. There was hardly any impact of the overestimation on tuning parameter selection. However, although the prediction performance of random forests was not substantially affected when using the out-of-bag error for tuning parameter selection in the present studies, one cannot be sure that this applies to all future data. For settings with metric predictor variables it is therefore strongly recommended to use stratified subsampling with sampling fractions that are proportional to the class sizes for both tuning parameter selection and error estimation in random forests. This yielded less biased estimates of the true prediction error. In unbalanced settings, in which there is a strong interest in predicting observations from the smaller classes well, sampling the same number of observations from each class is a promising alternative.

Background: In the last few years, multi-omics data, that is, datasets containing different types of high-dimensional molecular variables for the same samples, have become increasingly available. To date, several comparison studies focused on feature selection methods for omics data, but to our knowledge, none compared these methods for the special case of multi-omics data. Given that these data have specific structures that differentiate them from single-omics data, it is unclear whether different feature selection strategies may be optimal for such data. In this paper, using 15 cancer multi-omics datasets we compared four filter methods, two embedded methods, and two wrapper methods with respect to their performance in the prediction of a binary outcome in several situations that may affect the prediction results. As classifiers, we used support vector machines and random forests. The methods were compared using repeated fivefold cross-validation. The accuracy, the AUC, and the Brier score served as performance metrics. Results: The results suggested that, first, the chosen number of selected features affects the predictive performance for many feature selection methods but not all. Second, whether the features were selected by data type or from all data types concurrently did not considerably affect the predictive performance, but for some methods, concurrent selection took more time. Third, regardless of which performance measure was considered, the feature selection methods mRMR, the permutation importance of random forests, and the Lasso tended to outperform the other considered methods. Here, mRMR and the permutation importance of random forests already delivered strong predictive performance when considering only a few selected features. Finally, the wrapper methods were computationally much more expensive than the filter and embedded methods. Conclusions: We recommend the permutation importance of random forests and the filter method mRMR for feature selection using multi-omics data, where, however, mRMR is considerably more computationally costly.

The diversity forest algorithm is an alternative candidate node split sampling scheme that makes innovative complex split procedures in random forests possible. While conventional univariable, binary splitting suffices for obtaining strong predictive performance, new complex split procedures can help tackling practically important issues. For example, interactions between features can be exploited effectively by bivariable splitting. With diversity forests, each split is selected from a candidate split set that is sampled in the following way: for $$l = 1, \dots , {nsplits}$$l = 1 , ⋯ , nsplits : (1) sample one split problem; (2) sample a single or few splits from the split problem sampled in (1) and add this or these splits to the candidate split set. The split problems are specifically structured collections of splits that depend on the respective split procedure considered. This sampling scheme makes innovative complex split procedures computationally tangible while avoiding overfitting. Important general properties of the diversity forest algorithm are evaluated empirically using univariable, binary splitting. Based on 220 data sets with binary outcomes, diversity forests are compared with conventional random forests and random forests using extremely randomized trees. It is seen that the split sampling scheme of diversity forests does not impair the predictive performance of random forests and that the performance is quite robust with regard to the specified nsplits value. The recently developed interaction forests are the first diversity forest method that uses a complex split procedure. Interaction forests allow modeling and detecting interactions between features effectively. Further potential complex split procedures are discussed as an outlook.

The inclusion of high-dimensional omics data in prediction models has become a well-studied topic in the last decades. Although most of these methods do not account for possibly different types of variables in the set of covariates available in the same dataset, there are many such scenarios where the variables can be structured in blocks of different types, e.g., clinical, transcriptomic, and methylation data. To date, there exist a few computationally intensive approaches that make use of block structures of this kind. In this paper we present priority-Lasso, an intuitive and practical analysis strategy for building prediction models based on Lasso that takes such block structures into account. It requires the definition of a priority order of blocks of data. Lasso models are calculated successively for every block and the fitted values of every step are included as an offset in the fit of the next step. We apply priority-Lasso in different settings on an acute myeloid leukemia (AML) dataset consisting of clinical variables, cytogenetics, gene mutations and expression variables, and compare its performance on an independent validation dataset to the performance of standard Lasso models. The results show that priority-Lasso is able to keep pace with Lasso in terms of prediction accuracy. Variables of blocks with higher priorities are favored over variables of blocks with lower priority, which results in easily usable and transportable models for clinical practice.

In the last years more and more multi-omics data are becoming available, that is, data featuring measurements of several types of omics data for each patient. Using multi-omics data as covariate data in outcome prediction is both promising and challenging due to the complex structure of such data. Random forest is a prediction method known for its ability to render complex dependency patterns between the outcome and the covariates. Against this background we developed five candidate random forest variants tailored to multi-omics covariate data. These variants modify the split point selection of random forest to incorporate the block structure of multi-omics data and can be applied to any outcome type for which a random forest variant exists, such as categorical, continuous and survival outcomes. Using 20 publicly available multi-omics data sets with survival outcome we compared the prediction performances of the block forest variants with alternatives. We also considered the common special case of having clinical covariates and measurements of a single omics data type available. We identify one variant termed “block forest” that outperformed all other approaches in the comparison study. In particular, it performed significantly better than standard random survival forest (adjusted p-value: 0.027). The two best performing variants have in common that the block choice is randomized in the split point selection procedure. In the case of having clinical covariates and a single omics data type available, the improvements of the variants over random survival forest were larger than in the case of the multi-omics data. The degrees of improvements over random survival forest varied strongly across data sets. Moreover, considering all clinical covariates mandatorily improved the performance. This result should however be interpreted with caution, because the level of predictive information contained in clinical covariates depends on the specific application. The new prediction method block forest for multi-omics data can significantly improve the prediction performance of random forest and outperformed alternatives in the comparison. Block forest is particularly effective for the special case of using clinical covariates in combination with measurements of a single omics data type.