Two-stage designs for gene-disease association studies with sample size constraints

Abstract

Gene-disease association studies based on case-control designs may often be used to identify candidate polymorphisms (markers) conferring disease risk. If a large number of markers are studied, genotyping all markers on all samples is inefficient in resource utilization. Here, we propose an alternative two-stage method to identify disease-susceptibility markers. In the first stage all markers are evaluated on a fraction of the available subjects. The most promising markers are then evaluated on the remaining individuals in Stage 2. This approach can be cost effective since markers unlikely to be associated with the disease can be eliminated in the first stage. Using simulations we show that, when the markers are independent and when they are correlated, the two-stage approach provides a substantial reduction in the total number of marker evaluations for a minimal loss of power. The power of the two-stage approach is evaluated when a single marker is associated with the disease, and in the presence of multiple disease-susceptibility markers. As a general guideline, the simulations over a wide range of parametric configurations indicate that evaluating all the markers on 50% of the individuals in Stage 1 and evaluating the most promising 10% of the markers on the remaining individuals in Stage 2 provides near-optimal power while resulting in a 45% decrease in the total number of marker evaluations.

Figure 1.

Power of a two-stage design for m independent markers as a function of the proportion of markers (i) carried over to Stage 2 for various values of T₂/T₁. There is a single disease locus (D = 1). The signal μ is chosen such that the one-stage design has 80% power to identify the disease locus. The sample size is n = 1000. Dashed lines correspond to m = 100, and solid lines correspond to m = 3000 markers. The pairs of curves (for m = 100 and 3000) given from bottom to top correspond to the following values of T₂/T₁: 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, and 0.60, respectively. The cost fraction corresponding to every pair of curves is indicated in the figure. For example, the top pair of curves gives the power of a two-stage design for m = 100 (dashed line) and 3000 (solid line) when T₂/T₁ = 0.60 for various values of i (shown in the horizontal axis).

Figure 2.

The maximum power of a two-stage design as a function of the proportion of marker evaluations (T₂/T₁) for m = 3000 (solid), 1000 (dot), 500 (dash), 200 (dash-dot), and 100 (long dash) independent markers, for sample size n = 1000. Power is shown for D = 1 single disease locus. The signal μ is such that the corresponding one-stage designs have 80% power to identify the disease locus.