Fast and Accurate Detection of Multiple QTL

TL;DR

This paper introduces PruneDIRECT, a novel optimization algorithm that significantly accelerates the detection of multiple QTLs in genetic studies while maintaining accuracy comparable to exhaustive searches.

Contribution

PruneDIRECT provides a guaranteed, fast, and reliable method for multi-locus QTL scans by incorporating Lipschitz bounds to prune search regions, avoiding heuristic termination.

Findings

PruneDIRECT is over 50 times faster than exhaustive search for three QTL mapping.

The algorithm guarantees accuracy comparable to exhaustive search due to its error bounds.

Speedup increases with the strength of the QTL signals.

Abstract

We present a new computational scheme that enables efficient and reliable Quantitative Trait Loci (QTL) scans for experimental populations. Using a standard brute-force exhaustive search effectively prohibits accurate QTL scans involving more than two loci to be performed in practice, at least if permutation testing is used to determine significance. Some more elaborate global optimization approaches, e.g. DIRECT, have earlier been adopted to QTL search problems. Dramatic speedups have been reported for high-dimensional scans. However, since a heuristic termination criterion must be used in these types of algorithms the accuracy of the optimization process cannot be guaranteed. Indeed, earlier results show that a small bias in the significance thresholds is sometimes introduced. Our new optimization scheme, PruneDIRECT, is based on an analysis leading to a computable (Lipschitz) bound on the slope of a transformed objective function. The bound is derived for both infinite size and finite size populations. Introducing a Lipschitz bound in DIRECT leads to an algorithm related to classical Lipschitz optimization. Regions in the search space can be permanently excluded (pruned) during the optimization process. Heuristic termination criteria can thus be avoided. Hence, PruneDIRECT has a well-defined error bound and can in practice be guaranteed to be equivalent to a corresponding exhaustive search. We present simulation results that show that for simultaneous mapping of three QTL using permutation testing, PruneDIRECT is typically more than 50 times faster than exhaustive search. The speedup is higher for stronger QTL. This could be used to quickly detect strong candidate eQTL networks.