Case Control Study Statistics Definition

Table 1 summarized the comparative results of four methods.The proposed method also reveals the desirable statistical properties in further simulation with unbalanced sample sizes between the case and control groups and unequal prevalence between two exposures.

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A RERI test is based on risk additivity, and a PRISM test is based on log peril additivity, where peril is defined to be the inverse of a survival.

Risks and perils should be estimated in a cohort study; therefore, both tests are to be used in such a study.

We used Tong et al.’s case–control data on essential hypertension to demonstrate our method.

The case–control study assessed the effects of A1166C site of AT1R gene polymorphism (AC CC versus AA genotypes) and noise exposure ( that the hypertension prevalence is 25.2% with a population size of 100,000.

We considered different sample sizes and assumed that a case–control study recruited 500 cases and 500 controls (Panel A in Fig. The powers under the alternative hypothesis, respectively, when the disease prevalence is 0.02 (upper panel) and when it is 0.2 (lower panel): 500 cases and 500 controls (A, D), 1000 cases and 1000 controls (B, E), and 5000 cases and 5000 controls (C, F).

from vital statistics to the case–control study to estimate the disease risks necessary for calculating RERI, similar to what we did to estimate the disease perils necessary for calculating PRISM (more details in S4 Exhibit).At present, neither RERI nor PRISM tests can be valid for sufficient-cause interaction in case–control studies for non-rare diseases.In this study, we proposed a method to incorporate the information of disease prevalence to estimate disease perils.Then, we adopted a PRISM test to assess the sufficient-cause interaction in a case–control study for non-rare diseases is in the rejection region (for the null hypothesis of no sufficient-cause interaction).R code (S2 Exhibit) and SAS code (S3 Exhibit) are provided for all computations. We checked the type I error rate under the null hypothesis of no sufficient-cause interaction () when the disease prevalence was 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, and 0.5, respectively.The powers of the proposed method reached more than 80% in all scenarios.The powers of the odds-scale PRISM test are comparable to (when the disease prevalence is 0.02) and greater than (when the disease prevalence is greater than 0.2) those of the proposed method.Both the odds-scale RERI test and the odds-scale PRISM test are the approximation mentioned in the previous studies level for all scenarios.For the odds-scale PRISM test, type I error rates are stable at 0.05 at low disease prevalence but are inflated when the disease prevalence is greater than 0.2.Sufficient-cause interaction (also called mechanistic interaction or causal co-action) has received considerable attention recently.Two statistical tests, the ‘relative excess risk due to interaction’ (RERI) test and the ‘peril ratio index of synergy based on multiplicativity’ (PRISM) test, were developed specifically to test such an interaction in cohort studies.


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