Results
We calculated the sample size to achieve 80% statistical power according to the genetic models and the heterozygous ORs using a single SNP marker in a case-control study under the assumptions of 5% disease prevalence, 5% MAF, complete LD, 1:1 case-to-control ratio, and 5% type I error rate (α) (Table 1). The dominant model required the smallest sample size to achieve 80% power compared to other genetic models (e.g., 90 cases). In contrast, the effective sample size to test a single SNP under the recessive model was too large to collect with a limited budget, even if the homozygous OR is greater than 4 (e.g., 1,536 cases). It reveals difficulty in detecting a disease allele that follows a recessive mode of inheritance with a moderate sample size.
The sample size and statistical power for the allelic test in a case-control study under the different assumptions of ORhet, MAF, disease prevalence, LD, and case-to-control ratio by allowing a 5% type I error rate are shown in Fig. 1. As shown in Fig. 1A, a lower sample size was required to test allelic association for a single SNP with a larger MAF at the same risk of disease (OR) under the assumptions of 5% disease prevalence, 5% α, complete LD, and 1:1 case-to-control ratio. The minimum number of cases decreased from 1,974 cases for a SNP with a MAF of 5% to 545 cases for a SNP with a MAF of 30% under the same assumption. A high-risk allele showing a high OR requires a smaller sample size to be detected under the same assumption. While an allele with an OR of 1.3 requires 1,974 cases and 1,974 controls to be significantly detected in a case-control study, a SNP with an OR of 2.5 can be detected in a study of 134 cases and 134 controls under the assumption of a MAF of 5%, disease prevalence of 5%, type I error rate of 5%, and D' of 1 (Fig. 1A). The higher prevalence and the higher LD were associated with increased statistical power: for instance, as the LD increased from 0.4 to 0.6, 0.8, and 1, the statistical power obtained from a study of 1,000 cases and 1,000 controls was obviously increased from 26.5% to 49.2%, 72.8%, and 88.4%, respectively, under the assumption of OR 1.3, 5% MAF, 5% prevalence, and 5% α level (Fig. 1B and 1C). In addition, a 1:4 case-to-control ratio, which is the golden standard ratio for the numbers of cases and controls to be collected in a case-control study, showed the most effective sample size to achieve 80% statistical power. In many clinical settings, researchers are able to obtain more data from affected individuals than healthy individuals. On the other hand, there are more healthy participants than participants with a disease in a population-based study. Therefore, the minimum numbers of cases and controls required to achieve 80% statistical power depend on the study design. For a SNP with an allelic OR of 2 and 5% MAF, 127 cases and 508 controls are required in the case of a 1:4 case-control ratio, whereas 248 cases and 248 controls are required in the case of a 1:1 ratio to achieve 80% statistical power under the assumption of 5% prevalence, complete LD, and 5% α level.
In Table 2, we compared the number of cases to the number of case-parent trios to perform a case-control study and a study using case-parent trios by increasing the number of SNPs being analyzed. Genetic association studies with larger numbers of SNP markers require a larger sample size to reduce false positive association due to testing multiple hypotheses. The sample size required in a case-parent study is generally larger than that of a case-control study design. For instance, 248 cases and 248 controls (496 individuals) were required to detect a SNP with an ORhet of 2 and 5% MAF in a case-control study, whereas 282 case-parent trios (846 individuals) were required under the assumption of 5% disease prevalence and complete LD by allowing a 5% α level. However, the sample sizes required in both study designs increase tremendously in a GWAS. Under the same assumptions as shown above, the number of samples increased from 248 cases for a single SNP analysis to 1,206 cases and 1,255 cases for analyses of 500 K SNPs and 1 M SNPs, respectively, based on the threshold of p-value, calculated using a strict Bonferroni correction for multiple hypotheses comparisons. The statistical power to test the same number of subjects was higher for the case-control design than for the case-parent trio design (Fig. 2).