# Combining controls can improve power in two-stage association studies

## TL;DR

This paper introduces a shared-control method for two-stage association studies that enhances statistical power and reduces costs by reusing control samples across discovery and replication phases, with careful error control.

## Contribution

The paper proposes a novel shared-control approach for two-stage studies, improving power and cost-efficiency while discussing its theoretical properties and practical applications.

## Key findings

- Shared-control method increases power in GWAS.
- Type-1 error rates are controlled both analytically and empirically.
- Method is especially useful when control samples are hard to recruit.

## Abstract

High dimensional case control studies are ubiquitous in the biological sciences, particularly genomics. To maximise power while constraining cost and to minimise type-1 error rates, researchers typically seek to replicate findings in a second experiment on independent cohorts before proceeding with further analyses. This paper presents a method in which control (or case) samples from the discovery cohort are re-used in the replication study. The theoretical implications of this method are discussed and simulations used to compare performance against the standard method in a range of circumstances. In several common study designs, a shared-control method allows a substantial improvement in power while retaining type-1 error rate control. An important area of potential application arises when control samples are difficult to recruit or ascertain; for example in inter-disease comparisons, or studies on degenerative diseases. Using similar methods, a procedure is proposed for `partial replication' using a new independent cohort consisting of only controls. This methods can be used to provide some validation of findings when a full replication procedure is not possible. The new method has differing sensitivity to confounding in study cohorts compared to the standard procedure, which must be considered in its application. Type-1 error rates in these scenarios are analytically and empirically derived, and an online tool for comparing power and error rates is provided. Although careful consideration must be made of all necessary assumptions, this method can enable more efficient use of data in genome-wide association studies (GWAS) and other applications.