Motivation Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect non-linear effects of both categorical and continuous covariates, as well as their interactions. Detecting disease effects is hindered by the fact that they often occur rapidly near the disease initiation time, and this time point cannot be exactly observed. An additional challenge is that the effect magnitude can be heterogeneous over the subjects. Results We present lgpr, a widely applicable and interpretable method for non-parametric analysis of longitudinal data using additive Gaussian processes. We demonstrate that it outperforms previous approaches in identifying the relevant categorical and continuous covariates in various settings. Furthermore, it implements important novel features, including the ability to account for the heterogeneity of covariate effects, their temporal uncertainty, and appropriate observation models for different types of biomedical data. The lgpr tool is implemented as a comprehensive and user-friendly R-package. Availability and implementation lgpr is available at jtimonen.github.io/lgpr-usage with documentation, tutorials, test data and code for reproducing the experiments of this article. Supplementary information Supplementary data are available at Bioinformatics online.

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data, and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers, and propose robust and effective alternatives which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences.

Ordinary differential equations (ODEs) provide a powerful formalism to model molecular networks mechanistically. However, inferring the model structure, given a set of time course measurements and a large number of alternative molecular mechanisms, is a challenging and open research question. Existing search heuristics are designed only for finding a single best model configuration and cannot account for the uncertainty in selecting the network components. In this study, we present a novel Markov chain Monte Carlo approach for performing Bayesian model structure inference over ODE models. We formulate a Metropolis algorithm that explores the model space efficiently and is suitable for obtaining probabilistic inferences about the network structure. The method and its special parallelization possibilities are demonstrated using simulated data. Furthermore, we apply the method to a time course RNA sequencing data set to infer the structure of the transiently evolving core regulatory network that steers the T helper 17 (Th17) cell differentiation. Our results are in agreement with the earlier finding that the Th17 lineage-specific differentiation program evolves in three sequential phases. Further, the analysis provides us with probabilistic predictions on the molecular interactions that are active in different phases of Th17 cell differentiation.

Gaussian process (GP) models that combine both categorical and continuous input variables have found use e.g. in longitudinal data analysis and computer experiments. However, standard inference for these models has the typical cubic scaling, and common scalable approximation schemes for GPs cannot be applied since the covariance function is non-continuous. In this work, we derive a basis function approximation scheme for mixed-domain covariance functions, which scales linearly with respect to the number of observations and total number of basis functions. The proposed approach is naturally applicable to Bayesian GP regression with arbitrary observation models. We demonstrate the approach in a longitudinal data modelling context and show that it approximates the exact GP model accurately, requiring only a fraction of the runtime compared to fitting the corresponding exact model.

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