# A comparison of the power of two cutpoint methods to test for a dose-response relationship: A simulation study

This study compared two methods for categorizing a continuous variable for examining a dose-response trend. The goal was to compare these methods under various conditions likely to occur in epidemiological and other studies addressing the issue of exposure-response relationship. Observed case percentile (OCP) and expected case percentile (ECP) methods were used to categorize a continuous variable into five categories. With regard to a dichotomized outcome variable, linear and exponential underlying response rates in relation to exposure were considered. Normal and lognormal exposure distributions for eight person-year parameter combinations were included. The number of cases occurring followed a Poisson distribution. Exposure and age were the covariates of interest. A Monte Carlo simulation approach was used with the analyses focusing on standardized mortality ratios (SMR) and relative risks (RR). The Poisson trend test statistic and the Wald chi-square statistic for Poisson regression were used to detect trends between risk and the exposure variable; the probability of type I error and the power of these two tests were compared The type I error rates of the Poisson trend test and the Wald chi-square statistic in Poisson modeling of SMRs were approximately 5% for two cutpoint methods for the combinations of the rate functions, exposure and person-years distributions. The type I error rates of the Wald chi-square statistic in Poisson modeling of RRs were around 5% for two cutpoint methods for the combinations of the exponential rate function, exposure and person-year distributions Type I error rates of the Wald chi-square statistic in Poisson modeling of RRs were about 0.1% to 0.5% for the linear rate functions. In the Poisson modeling process of the linear rate function, there were roughly 10% to 40% of the data sets for which the models did not converge. As a result, the type I error rates and power of the test statistics, which were calculated based on the sets for which the model converged, were questionable because of this non-convergence problem The power of these two test statistics was greater for the OCP method than the ECP method when the exposure distribution was lognormal, and either a linear or an exponential rate function in relation to exposure was used. The power of these two statistics was essentially identical for the OCP and ECP methods when exposure was normally distributed. The OCP method is easier to calculate compared to the ECP method for data analysis. Thus, the OCP method is recommended as it was more powerful than the ECP method over a broader range of conditions and was computationally simpler