Optimization of Two-Stage Genetic Designs Where Data Are Combined Using an Accurate and Efficient Approximation for Pearson's Statistic

Optimized multi-stage designs controlling the false discovery or the family-wise error rate

When a large number of hypotheses are investigated, we propose multi-stage designs where in each interim analysis promising hypotheses are screened, which are investigated in further stages. Given a fixed overall number of observations, this allows one to spend more observations for promising hypotheses than with single-stage designs, where the observations are equally distributed among all considered hypotheses. We propose multi-stage procedures controlling either the family-wise error rate (FWER) or the false discovery rate (FDR) and derive asymptotically optimal stopping boundaries and sample size allocations (across stages) to maximize the power of the procedure. Optimized two-stage designs lead to a considerable increase in power compared with the classical single-stage design. Going from two to three stages additionally leads to a distinctive increase in power. Adding a fourth stage leads to a further improvement, which is, however, less pronounced. Surprisingly, we found only small differences in power between optimized integrated designs, where the data of all stages are used in the final test statistics, and optimized pilot designs where only the data from the final stage are used for testing. However, the integrated design controlling the FDR appeared to be more robust against misspecifications in the planning phase. Additionally, we found that with increasing number of stages the drop in power when controlling the FWER instead of the FDR becomes negligible. Our investigations show that the crucial point is not the choice of the error rate or the type of design, but the sequential nature of the trial where non-promising hypotheses are dropped in the early phases of the experiment.

Catechol-O-methyltransferase contributes to genetic susceptibility shared among anxiety spectrum phenotypes

BACKGROUND

Catechol-O-methyltransferase (COMT) has been investigated for its possible role in a wide range of psychiatric phenotypes. In particular, several studies support association of this gene with panic disorder and other anxiety-related traits.

METHODS

We examined the COMT gene for association with genetic risk across a range of anxiety spectrum phenotypes. We used multivariate structural equation modeling to select twin pairs scoring at the extremes of a latent genetic risk factor shared by neuroticism, several anxiety disorders, and major depression from a large population-based twin sample. With one member from each of these pairs, the resulting sample of 589 cases and 539 control subjects were entered into a two-stage association study in which genetic markers were screened in stage 1, the positive results of which were tested for replication in stage 2.

RESULTS

The functional val158met polymorphism (rs4680) plus nine other single nucleotide polymorphism markers selected to capture the major allelic variation across the COMT locus were analyzed for differences between cases and control subjects. Although the val (G) allele of rs4680 showed marginally significant association in our combined stage 1 plus stage 2 sample, a high-risk haplotype of this allele with the A allele of rs165599 was significantly over-represented in cases (p = 1.97e-5, odds ratio = 1.95). This haplotype also predicted individual differences in neuroticism and risk for several anxiety disorders and major depression. Consistent with prior studies, our findings are female-specific.

CONCLUSIONS

Variations in the COMT gene contribute to genetic risk shared across a range of anxiety-related phenotypes.

Controlling false discoveries in genetic studies

A false discovery occurs when a researcher concludes that a marker is involved in the etiology of the disease whereas in reality it is not. In genetic studies the risk of false discoveries is very high because only few among the many markers that can be tested will have an effect on the disease. In this article, we argue that it may be best to use methods for controlling false discoveries that would introduce the same ratio of false discoveries divided by all rejected tests into the literature regardless of systematic differences between studies. After a brief discussion of traditional "multiple testing" methods, we show that methods that control the false discovery rate (FDR) may be more suitable to achieve this goal. These FDR methods are therefore discussed in more detail. Instead of merely testing for main effects, it may be important to search for gene-environment/covariate interactions, gene-gene interactions or genetic variants affecting disease subtypes. In the second section, we point out the challenges involved in controlling false discoveries in such searches. The final section discusses the role of replication studies for eliminating false discoveries and the complexities associated with the definition of what constitutes a replication and the design of these studies.

Optimal designs for two-stage genome-wide association studies

Genome-wide association (GWA) studies require genotyping hundreds of thousands of markers on thousands of subjects, and are expensive at current genotyping costs. To conserve resources, many GWA studies are adopting a staged design in which a proportion of the available samples are genotyped on all markers in stage 1, and a proportion of these markers are genotyped on the remaining samples in stage 2. We describe a strategy for designing cost-effective two-stage GWA studies. Our strategy preserves much of the power of the corresponding one-stage design and minimizes the genotyping cost of the study while allowing for differences in per genotyping cost between stages 1 and 2. We show that the ratio of stage 2 to stage 1 per genotype cost can strongly influence both the optimal design and the genotyping cost of the study. Increasing the stage 2 per genotype cost shifts more of the genotyping and study cost to stage 1, and increases the cost of the study. This higher cost can be partially mitigated by adopting a design with reduced power while preserving the false positive rate or by increasing the false positive rate while preserving power. For example, reducing the power preserved in the two-stage design from 99 to 95% that of the one-stage design decreases the two-stage study cost by approximately 15%. Alternatively, the same cost savings can be had by relaxing the false positive rate by 2.5-fold, for example from 1/300,000 to 2.5/300,000, while retaining the same power.

Two-stage designs applying methods differing in costs

MOTIVATION

Two-stage pilot and integrated designs are powerful tools for investigating large numbers of hypotheses. Asymptotically, optimal two-stage designs controlling the familywise error or false discovery rate are considered when costs and effect sizes per measurement differ between stages and total costs are constrained.

RESULTS

Depending on the cost and effect size ratios between the measurements, it is generally more powerful to apply two-stage procedures using one measurement method at both stages. For the practically relevant case that the same method is applied at both stages but designing the second-stage measurements raises extra costs, two-stage designs are more powerful than the single-stage design even for large costs ratios. The power of the optimal pilot and integrated two-stage designs generally are similar, however, the integrated approach is less sensitive even to severe design misspecifications in the planning phase.

AVAILABILITY

R-programs (R, 2005) to calculate asymptotically optimal designs are available on: http://statistics.msi.meduniwien.ac.at/index.php?page=ao2stage