### Article

## Adaptive designs in genetic association studies with control of the FDR

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Published: | September 8, 2005 |
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### Outline

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#### Introduction and problem

In the field of genetics rapid technologic advances have sparked great research activity. Nowadays a lot of markers are determined to test for association with a disease in one single genetic study. Control of the familywise error rate (FWER) seems to be too restrictive for this kind of studies that are mostly of explorative nature. Therefore use of false discovery rate (FDR) is also common. Two-stage adaptive designs are attractive to reduce the cost of large-scale genetic studies.

For that reason the combination of control of the FDR with adaptive designs is an appealing question. The procedures used mostly for control of the FDR however are stepwise procedures (such as the explorative Simes procedure proposed for control of the FDR by [Ref. 1]) and at the interim analysis it is not yet known what will be the final bounds in the procedure.

#### Material and Methods

With a new definition of the global p-value in adaptive designs the use of stepwise FDR-controlling procedures can be sensibly realized. Global p-value in this abstract refers to the “final p-value” of a two-stage design and should not be confused with a global p-value in multiple testing. Previous suggestions for the definition of such global p-values comprise [Ref. 2] and [Ref. 3]. The new definition proposed by the authors is much more flexible and respects the definition of worst-case-p-values. Thereby it enables the use of adaptive designs without specified α_{1} which still permit early stopping in favour of the alternative. This definition is based on so-called rejection regions [Ref. 4]. Regions defined by Bauer-Köhne-type [Ref. 5] functions seem to be particularly suited for this definition. The proposed methods can also aid in decision making at the interim analysis.

Especially such Bauer-Köhne-type regions were investigated by the authors in combination with the explorative Simes procedure. Simulations have been performed to assess this combined procedure mainly for the situation of genetic association studies. Markers were considered dichotomous (e.g. dichotomised SNP genotypes). Small case-control association studies (unrelated controls) with about 60 markers (as from preselected candidate regions, therefore a larger proportion of markers was simulated associated) as well as larger scans with 200 markers (with a lower proportion of markers simulated to be associated) were considered. The interim analysis of the adaptive design was performed after approximately half of the maximal sample size. The performance of the new two-stage adaptive design was examined depending on the simulated situation and compared to a one-stage fixed-sample size design. Assessment was done by considering e.g. the number of correctly and falsely rejected hypotheses at the interim and final analysis, the number of markers not to be determined in the second stage because of stopping for reduction and the sample size estimated as necessary for the second stage. Savings were described in terms of costs for patient recruitment and marker determination. As these costs are variable the savings where calculated for different ratios of recruitment to marker determination cost.

#### Results

The proposed two-stage design using the new definition of global p-values for combination of adaptive designs with the control of the FDR can be implemented easily. The results of the performed simulations suggest that there can be great savings from the reduction of the number of markers to be determined in the second stage. This is due to the possibility of stopping for reduction at the interim analysis. However there is the chance that especially rare markers are dropped too early when the sample size in the first stage is too small. But for detection of such rare markers in a one-stage study a huge sample size would be necessary also. The loss of power deriving from using a two-stage design instead of one single stage does not seem to be substantial. The median number of correct rejections after the final analysis using about the same sample size in both designs was equal but there was a trend towards a higher number of rejections in the one-stage design. For an example of detailed results compare table 1 [Tab. 1].

The possibility of sample size adjustment in adaptive designs at the interim analysis seems to be difficult to judge in this kind of studies with multiple endpoints and depends very much on the study situation. In our simulations we did not see important changes in sample size in the adaptive design.

The savings in the candidate gene situation did depend more on the ratio of recruitment cost to marker determination cost as the number of examined markers was smaller and thus the savings that could be achieved by stopping for reduction lower . Exemplary simulation results for different cost ratios are shown in table 2 [Tab. 2].

#### Discussion

A new two-stage procedure for combining control of the FDR with adaptive designs has been proposed. This procedure involves a new definition of global p-values in adaptive designs based on so-called rejection regions. In the practical example situation of genetic association studies simulations have shown that this design offers the chance for savings by marker reduction and other adjustments at the interim analysis.

### References

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- 2.
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- 3.
- Liu, Q, Chi GYH. On sample size and inference for two-stage adaptive designs. Biometrics 2001; 57: 172-177.
- 4.
- Victor, A. Kontrolle der FDR in adaptiven Designs. Dissertation 2005. Fachbereich Medizin der Johannes Gutenberg-Universität Mainz.
- 5.
- Bauer P, Köhne K. Evaluation of experiments with adaptive interim analyses. Biometrics 1994; 50: 1029-1041.