Dataset Information

Survival Mixture Density Networks.

ABSTRACT: Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

SUBMITTER: Han X

PROVIDER: S-EPMC10498417 | biostudies-literature | 2022 Aug

REPOSITORIES: biostudies-literature

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Publications

Survival Mixture Density Networks.

Han Xintian X Goldstein Mark M Ranganath Rajesh R

Proceedings of machine learning research 20220801

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive f ...[more]

PMID: 37706207

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Project description:BackgroundReference intervals represent the expected range of physiological test results in a healthy population and are essential to support medical decision making. Particularly in the context of pediatric reference intervals, where recruitment regulations make prospective studies challenging to conduct, indirect estimation strategies are becoming increasingly important. Established indirect methods enable robust identification of the distribution of "healthy" samples from laboratory databases, which include unlabeled pathologic cases, but are currently severely limited when adjusting for essential patient characteristics such as age. Here, we propose the use of mixture density networks (MDN) to overcome this problem and model all parameters of the mixture distribution in a single step.ResultsEstimated reference intervals from varying settings with simulated data demonstrate the ability to accurately estimate latent distributions from unlabeled data using different implementations of MDNs. Comparing the performance with alternative estimation approaches further highlights the importance of modeling the mixture component weights as a function of the input in order to avoid biased estimates for all other parameters and the resulting reference intervals. We also provide a strategy to generate partially customized starting weights to improve proper identification of the latent components. Finally, the application on real-world hemoglobin samples provides results in line with current gold standard approaches, but also suggests further investigations with respect to adequate regularization strategies in order to prevent overfitting the data.ConclusionsMixture density networks provide a promising approach capable of extracting the distribution of healthy samples from unlabeled laboratory databases while simultaneously and explicitly estimating all parameters and component weights as non-linear functions of the covariate(s), thereby allowing the estimation of age-dependent reference intervals in a single step. Further studies on model regularization and asymmetric component distributions are warranted to consolidate our findings and expand the scope of applications.

Project description:BackgroundInference of gene networks typically relies on measurements across a wide range of conditions or treatments. Although one network structure is predicted, the relationship between genes could vary across conditions. A comprehensive approach to infer general and condition-dependent gene networks was evaluated. This approach integrated Bayesian network and Gaussian mixture models to describe continuous microarray gene expression measurements, and three gene networks were predicted.ResultsThe first reconstructions of a circadian rhythm pathway in honey bees and an adherens junction pathway in mouse embryos were obtained. In addition, general and condition-specific gene relationships, some unexpected, were detected in these two pathways and in a yeast cell-cycle pathway. The mixture Bayesian network approach identified all (honey bee circadian rhythm and mouse adherens junction pathways) or the vast majority (yeast cell-cycle pathway) of the gene relationships reported in empirical studies. Findings across the three pathways and data sets indicate that the mixture Bayesian network approach is well-suited to infer gene pathways based on microarray data. Furthermore, the interpretation of model estimates provided a broader understanding of the relationships between genes. The mixture models offered a comprehensive description of the relationships among genes in complex biological processes or across a wide range of conditions. The mixture parameter estimates and corresponding odds that the gene network inferred for a sample pertained to each mixture component allowed the uncovering of both general and condition-dependent gene relationships and patterns of expression.ConclusionThis study demonstrated the two main benefits of learning gene pathways using mixture Bayesian networks. First, the identification of the optimal number of mixture components supported by the data offered a robust approach to infer gene relationships and estimate gene expression profiles. Second, the classification of conditions and observations into groups that support particular mixture components helped to uncover both gene relationships that are unique or common across conditions. Results from the application of mixture Bayesian networks substantially augmented the understanding of gene networks and demonstrated the added-value of this methodology to infer gene networks.

Dataset Information

Survival Mixture Density Networks.

Publications

Survival Mixture Density Networks.

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