Power and Sample Size Considerations

As mentioned in the previous paragraph, behavioral medicine traits are likely to be influenced by multiple genes and interactions. Therefore, effect sizes of individual genes are expected to be small. Consequently, required sample sizes to detect genetic main effects or gene x environment interactions with sufficient statistical power are expected to be relatively large. Excellent online resources specific to power and sample size calculations for genetic association studies exist (e.g., Quanto (Gauderman and Morrison, 2006) available at http://hydra.usc.edu/gxe or the Genetic Power Calculator (Purcell et al, 2003) at http://statgen.iop.kcl.ac.uk/gpc/).

As examples, we present sample size calculations for genetic main effects and gene x environment interactions for a continuous trait using Quanto (Gauderman and Morrison, 2006). In all models, statistical power is set at 0.80 and we assume additive genetic effects only. Effect sizes are quantified in terms of f, defined as the ratio of the standard deviation between genotype groups to the common standard deviation within genotype groups. Sample sizes for small (f = 0.10), medium (f = 0.25), and large effect sizes (f = 0.40) were calculated (Cohen, 1988). "Gene 1" is modeled after the 5HTTLPR upstream from the serotonin transporter gene (Caspi et al, 2003; Lesch et al, 1996; Risch et al, 2009) with an allele frequency of 0.40 for the risk allele. The outcome is depressive symptoms measured continuously (although binary traits can easily be accommodated) and the environmental risk is modeled after "severe adverse life events" with a prevalence of 30% (Caspi et al, 2003). Sample size requirements for gene main effects (Model A) and gene x environment interactions (Model B) by effect size are presented in Table 29.1.

As can be seen from the table, sample size required varies dramatically with effect size, desired significance level a, and the complexity of the model, as would be expected. A sample size of 500 affords sufficient power to detect a medium effect size for gene main effect models but may pose difficulty in detecting gene x environment interactions of even large effect size. To detect gene x environment interaction of a medium effect, a sample size of about 1500 is required. The required sample size will be even larger if the allele is relatively rare (e.g., 5-10%) or - as shown in Table 29.1 - a large number of markers is typed such as in GWA studies for which the statistical significance criterion is adjusted to 5.0 x 10-8 to take multiple comparisons into account (see Section 4.4). Differing modes of inheritance (additive, dominant, recessive) will also impact effect size and have resulting effects on power and sample size. On the other hand, careful selection and adjustment for environmental covariates may increase the trait heritability and improve power to detect main effects of the gene for a given sample size (Sabatti et al, 2009).

Table 29.1 Sample size calculations for a gene main effect and gene x environmental interaction with 80% power stratified by effect size and a level for additive genetic effects

Model A

Model B

Effect

"Gene" onlya

"Gene x

environment" interaction13

size (f)c

a = 0.05

a = 0.001

a = 5.0 x10-8

a = 0.05

a = 0.001

a = 5.0 x10-8

0.10

1631

3549

8230

7667

16678

38681

0.25

258

561

1300

1200

2611

6055

0.40

98

214

496

453

986

2288

aModel A - main effect of one gene (risk allele frequency of 0.40)

bModel B - interaction effect of one genetic variant with a risk allele frequency of 0.40 and one environmental exposure with a prevalence of 30%, assuming main effect contributions off = 0.10 for the variant and the environmental factor cEffect size in f from Cohen (Cohen, 1988). In this example, f indicates the ratio of the standard deviation between genotype groups to the common standard deviation within genotype groups. Effect size off = 0.10 corresponds to a small effect size, f = 0.25 corresponds to a medium effect size, and f = 0.40 corresponds to a large effect size (Cohen, 1988)

aModel A - main effect of one gene (risk allele frequency of 0.40)

bModel B - interaction effect of one genetic variant with a risk allele frequency of 0.40 and one environmental exposure with a prevalence of 30%, assuming main effect contributions off = 0.10 for the variant and the environmental factor cEffect size in f from Cohen (Cohen, 1988). In this example, f indicates the ratio of the standard deviation between genotype groups to the common standard deviation within genotype groups. Effect size off = 0.10 corresponds to a small effect size, f = 0.25 corresponds to a medium effect size, and f = 0.40 corresponds to a large effect size (Cohen, 1988)

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