In addition, these two tests can be applied in case–control studies for rare diseases but are not valid for non-rare diseases.In this study, we proposed a method to incorporate the information of disease prevalence to estimate the perils of particular diseases.
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.
With this information and using the method presented in this paper, we calculated the log perils for the four exposure profile (Table 2).
For this example, the log PRISM is 0.121 with a 95% confidence intervals of We proposed a method to incorporate information regarding disease prevalence to estimate disease perils, and then adopted a PRISM test to assess the sufficient-cause interaction in a case–control study.
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.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.In our method, only the disease prevalence of the population at large is required () and not the detailed sex, age, or exposure profile-specific prevalence; the overall prevalence is readily available from vital statistics or previously published studies.For non-rare diseases, we showed that the odds-scale RERI test and the odds-scale PRISM test (where risks and log perils are approximated by odds directly) tend to become too liberal.Moreover, we adopted the PRISM test to assess the sufficient-cause interaction in case–control studies for non-rare diseases.The Monte Carlo simulation showed that our proposed method can maintain reasonably accurate type I error rates in all situations.As for the odds-scale RERI test, its type I error rates are small at low disease prevalence values but can become inflated when the disease prevalence is greater than 0.4.Figure 2 shows the simulation results of the powers.With a larger sample size, the type I error rates for the odds-scale PRISM test are inflated even at low disease prevalence values.By contrast, the risk-scale RERI test is a very conservative test with extremely small type I error rates.