FEMA-Long: Modeling unstructured covariances for discovery of time-dependent effects in large-scale longitudinal datasets

While linear mixed-effects (LME) models are common for analyzing longitudinal data, most users rely on random intercepts or simple stationary covariance, due to unavailability of computationally tractable solutions. Here, we extend the Fast and Efficient Mixed-Effects Algorithm (FEMA) and present FEMA-Long, a computationally tractable approach to flexibly modeling longitudinal covariance suitable for high-dimensional data. FEMA-Long can: i) model unstructured covariance, ii) model covariates as smooth functions using splines, iii) discover time-dependent effects of covariates with spline interactions, and iv) use these flexible longitudinal modeling strategies to perform longitudinal genome-wide association studies and discover time-dependent genetic effects, in a computationally scalable manner, suitable for high-dimensional data. Through extensive simulations, we show that estimates from FEMA-Long are accurate, while being up to several thousand times faster and with minimal carbon footprint. To show the utility of FEMA-Long for discovering novel biological signal, using data from the Norwegian Mother, Father and Child Cohort Study (MoBa), we performed a longitudinal genome-wide association study with non-linear SNP-by-time interaction on length, weight, and BMI of 68,273 infants with up to six measurements in the first year of life. We found dynamic patterns of random effects including time-varying heritability and genetic correlations, as well as several genetic variants showing time-dependent effects, highlighting the applicability of FEMA-Long to enable novel discoveries.Author summary: Most large-scale datasets have complexities such as repeated measures, related individuals, or other dependencies across samples, preventing the use of standard regression approaches for analysis. In such circumstances, linear mixed-effects modeling is often employed. However, for high-dimensional datasets, fitting these models is quite challenging. Further, most standard uses of linear mixed-effects modeling focus on simpler covariance models, which may not hold. Here, we introduce FEMA-Long, a novel computationally efficient analytical framework for fitting linear mixed-effects models with time-varying random effects, as well as allowing the effect of the covariates to change smoothly over time by using splines. This is particularly relevant when, for example, studying the effect of genetic variants on phenotypes, where the effects could be non-linear over time. The FEMA-Long framework allows time-varying heritability as well as discovery of genetic variants that show time-dependent effects. By performing a genome-wide association study on data from the Norwegian Mother, Father and Child Cohort Study (MoBa) using FEMA-Long, we show the discovery of genetic variants with time-dependent effects on infant length, weight, and BMI during the first year of life. Our results highlight the potential of using FEMA-Long to make novel discoveries that can lead to biological insights on the genetics of complex traits as well as improve the potential of using genetics for personalized prediction.