Tracking Cross-Validated Estimates of Prediction Error as Studies Accumulate

Optimal ensemble construction for multistudy prediction with applications to mortality estimation

It is increasingly common to encounter prediction tasks in the biomedical sciences for which multiple datasets are available for model training. Common approaches such as pooling datasets before model fitting can produce poor out-of-study prediction performance when datasets are heterogeneous. Theoretical and applied work has shown multistudy ensembling to be a viable alternative that leverages the variability across datasets in a manner that promotes model generalizability. Multistudy ensembling uses a two-stage stacking strategy which fits study-specific models and estimates ensemble weights separately. This approach ignores, however, the ensemble properties at the model-fitting stage, potentially resulting in performance losses. Motivated by challenges in the estimation of COVID-attributable mortality, we propose optimal ensemble construction, an approach to multistudy stacking whereby we jointly estimate ensemble weights and parameters associated with study-specific models. We prove that limiting cases of our approach yield existing methods such as multistudy stacking and pooling datasets before model fitting. We propose an efficient block coordinate descent algorithm to optimize the loss function. We use our method to perform multicountry COVID-19 baseline mortality prediction. We show that when little data is available for a country before the onset of the pandemic, leveraging data from other countries can substantially improve prediction accuracy. We further compare and characterize the method's performance in data-driven simulations and other numerical experiments. Our method remains competitive with or outperforms multistudy stacking and other earlier methods in the COVID-19 data application and in a range of simulation settings.

Batch normalization followed by merging is powerful for phenotype prediction integrating multiple heterogeneous studies

Heterogeneity in different genomic studies compromises the performance of machine learning models in cross-study phenotype predictions. Overcoming heterogeneity when incorporating different studies in terms of phenotype prediction is a challenging and critical step for developing machine learning algorithms with reproducible prediction performance on independent datasets. We investigated the best approaches to integrate different studies of the same type of omics data under a variety of different heterogeneities. We developed a comprehensive workflow to simulate a variety of different types of heterogeneity and evaluate the performances of different integration methods together with batch normalization by using ComBat. We also demonstrated the results through realistic applications on six colorectal cancer (CRC) metagenomic studies and six tuberculosis (TB) gene expression studies, respectively. We showed that heterogeneity in different genomic studies can markedly negatively impact the machine learning classifier's reproducibility. ComBat normalization improved the prediction performance of machine learning classifier when heterogeneous populations are present, and could successfully remove batch effects within the same population. We also showed that the machine learning classifier's prediction accuracy can be markedly decreased as the underlying disease model became more different in training and test populations. Comparing different merging and integration methods, we found that merging and integration methods can outperform each other in different scenarios. In the realistic applications, we observed that the prediction accuracy improved when applying ComBat normalization with merging or integration methods in both CRC and TB studies. We illustrated that batch normalization is essential for mitigating both population differences of different studies and batch effects. We also showed that both merging strategy and integration methods can achieve good performances when combined with batch normalization. In addition, we explored the potential of boosting phenotype prediction performance by rank aggregation methods and showed that rank aggregation methods had similar performance as other ensemble learning approaches.

Robustifying genomic classifiers to batch effects via ensemble learning

MOTIVATION

Genomic data are often produced in batches due to practical restrictions, which may lead to unwanted variation in data caused by discrepancies across batches. Such 'batch effects' often have negative impact on downstream biological analysis and need careful consideration. In practice, batch effects are usually addressed by specifically designed software, which merge the data from different batches, then estimate batch effects and remove them from the data. Here, we focus on classification and prediction problems, and propose a different strategy based on ensemble learning. We first develop prediction models within each batch, then integrate them through ensemble weighting methods.

RESULTS

We provide a systematic comparison between these two strategies using studies targeting diverse populations infected with tuberculosis. In one study, we simulated increasing levels of heterogeneity across random subsets of the study, which we treat as simulated batches. We then use the two methods to develop a genomic classifier for the binary indicator of disease status. We evaluate the accuracy of prediction in another independent study targeting a different population cohort. We observed that in independent validation, while merging followed by batch adjustment provides better discrimination at low level of heterogeneity, our ensemble learning strategy achieves more robust performance, especially at high severity of batch effects. These observations provide practical guidelines for handling batch effects in the development and evaluation of genomic classifiers.

AVAILABILITY AND IMPLEMENTATION

The data underlying this article are available in the article and in its online supplementary material. Processed data is available in the Github repository with implementation code, at https://github.com/zhangyuqing/bea_ensemble.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The impact of different sources of heterogeneity on loss of accuracy from genomic prediction models

Cross-study validation (CSV) of prediction models is an alternative to traditional cross-validation (CV) in domains where multiple comparable datasets are available. Although many studies have noted potential sources of heterogeneity in genomic studies, to our knowledge none have systematically investigated their intertwined impacts on prediction accuracy across studies. We employ a hybrid parametric/non-parametric bootstrap method to realistically simulate publicly available compendia of microarray, RNA-seq, and whole metagenome shotgun microbiome studies of health outcomes. Three types of heterogeneity between studies are manipulated and studied: (i) imbalances in the prevalence of clinical and pathological covariates, (ii) differences in gene covariance that could be caused by batch, platform, or tumor purity effects, and (iii) differences in the "true" model that associates gene expression and clinical factors to outcome. We assess model accuracy, while altering these factors. Lower accuracy is seen in CSV than in CV. Surprisingly, heterogeneity in known clinical covariates and differences in gene covariance structure have very limited contributions in the loss of accuracy when validating in new studies. However, forcing identical generative models greatly reduces the within/across study difference. These results, observed consistently for multiple disease outcomes and omics platforms, suggest that the most easily identifiable sources of study heterogeneity are not necessarily the primary ones that undermine the ability to accurately replicate the accuracy of omics prediction models in new studies. Unidentified heterogeneity, such as could arise from unmeasured confounding, may be more important.

Training replicable predictors in multiple studies

This article considers replicability of the performance of predictors across studies. We suggest a general approach to investigating this issue, based on ensembles of prediction models trained on different studies. We quantify how the common practice of training on a single study accounts in part for the observed challenges in replicability of prediction performance. We also investigate whether ensembles of predictors trained on multiple studies can be combined, using unique criteria, to design robust ensemble learners trained upfront to incorporate replicability into different contexts and populations.