Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability

Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense SNPheritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report the uncertainty in REML estimation uses standard errors (SE), which rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals. In addition, for larger datasets (e.g., tens of thousands of individuals), the construction of SEs itself may require considerable time, as it requires expensive matrix inversions and multiplications. Here, we present FIESTA (Fast confidence IntErvals using STochastic Approximation), a method for constructing accurate confidence intervals (CIs). FIESTA is based on parametric bootstrap sampling, and therefore avoids unjustified assumptions on the distribution of the heritability estimator. FIESTA uses stochastic approximation techniques, which accelerate the construction of CIs by several orders of magnitude, compared to previous approaches as well as to the analytical approximation used by SEs. FIESTA builds accurate CIs rapidly, e.g., requiring only several seconds for datasets of tens of thousands of individuals, making FIESTA a very fast solution to the problem of building accurate CIs for heritability for all dataset sizes.