Article

# Minimal sizes of cases with a susceptible genotype and minimal odds ratios among susceptible individuals in case-control studies

Department of Preventive Medicine / Biostatistics and Medical Decision Making, Nagoya University Graduate School of Medicine, Nagoya 466-8550, Japan.

Asian Pacific journal of cancer prevention: APJCP (Impact Factor: 2.51). 01/2005; 6(2):165-9. Source: PubMed

**ABSTRACT**

Disease risk elevation due to an environmental factor only for individuals with a susceptible genotype is a typical example of gene-environment interaction. In order to identify risk factors interacting with susceptible genotypes in case-control studies, presumptions on minimal size of cases with the susceptible genotype (S (min)) and odds ratio (OR) among the susceptible individuals (OR(susceptible)) are useful.

Proportion of exposed cases (P(1)) and OR for whole cases (OR(whole)) statistically detectable in a case-control study can be calculated in a conventional method. P(1) was assumed to be a weighted sum of the exposed among cases with the genotype (P(x)) and cases without the genotype (equal to proportion of the exposed among controls, P(0)), i.e., S P(x) + (1 - S) P0, where S is the size (proportion) of cases with the genotype. For each calculated P(1), S became the minimum (S(min)) in case of P(x) = 1. OR(susceptible) was calculated by {P(x) (1 - P(0))} / {(1 - P(x)) P(0)}.

S(min) and OR(susceptible) were listed for the combinations of the above components. For example, a detectable P(1) was 0.638 for P(0)=0.5 in a case-control study with 200 cases (N(1)) and 200 controls (N(0)), when a error of a two-sided test was 0.05 with an 80% of power. In case of P(1)=0.638, OR(whole) was 1.77, producing S(min) = 0.277 for infinite OR(susceptible). It indicates that an environmental factor cannot be detected in case that a high-risk genotype frequency is less than 0.277.

If the size of cases with a susceptible genotype is expected to be less than S(min), case-control studies are unlikely to detect a significant OR of the environmental factor.

Proportion of exposed cases (P(1)) and OR for whole cases (OR(whole)) statistically detectable in a case-control study can be calculated in a conventional method. P(1) was assumed to be a weighted sum of the exposed among cases with the genotype (P(x)) and cases without the genotype (equal to proportion of the exposed among controls, P(0)), i.e., S P(x) + (1 - S) P0, where S is the size (proportion) of cases with the genotype. For each calculated P(1), S became the minimum (S(min)) in case of P(x) = 1. OR(susceptible) was calculated by {P(x) (1 - P(0))} / {(1 - P(x)) P(0)}.

S(min) and OR(susceptible) were listed for the combinations of the above components. For example, a detectable P(1) was 0.638 for P(0)=0.5 in a case-control study with 200 cases (N(1)) and 200 controls (N(0)), when a error of a two-sided test was 0.05 with an 80% of power. In case of P(1)=0.638, OR(whole) was 1.77, producing S(min) = 0.277 for infinite OR(susceptible). It indicates that an environmental factor cannot be detected in case that a high-risk genotype frequency is less than 0.277.

If the size of cases with a susceptible genotype is expected to be less than S(min), case-control studies are unlikely to detect a significant OR of the environmental factor.

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