  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 nonlinear 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. We present lgpr, a widely
applicable and interpretable method for nonparametric 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. lgpr is available at
jtimonen.github.io/lgpr-usage with documentation, tutorials, test data, and
code for reproducing the experiments of this paper.
