# Sample size determination for Poisson regression when the exposure variable contains misclassification errors

## Description

Sample size calculation methods for Poisson regression to detect linear trend in logarithm of incidence rates (multiplicative models) and incidence rates (additive models) over ordered exposure groups are developed. These methods are parallel to those of Bull (1993) for logistic regression Moreover, when reliable ancillary misclassification information is available, a slight modification of these calculation methods can be used to determine the required sample size based on the correction of the estimate of the trend parameter in the analysis stage. In which the correction methods is modified from Reade-Christopher and Kupper (1991) We find that, as would be expected, the gradient of incidence rates over these groups and misclassification rate strongly affect the sample size requirements. In a one year study, when exposure variable contains no misclassification, the sample size required varies from 5,054 to 64,534, according to different gradients. Moreover, when a misclassification rate of 30% is assumed, these numbers are multiplied by approximately 1.3 for all gradients The distribution of subjects across exposure groups also affect the sample size requirements. In environmental and occupational studies, subjects may be grouped according to the continuous exposure and the groups chosen are often terciles, quartiles or quintiles, i.e., even distribution over the exposure groups. We find that less sample size is required for this type of distribution Finally, although the use of correction methods reduces the bias of the estimates, there was always greater variance in the estimate than when no correction is used. It would appreciate that when the gradient of incidence rate is small and the misclassification is not severe, then, based on the percentage of the true parameter included in the 95% confidence interval, use of the correction method may not be necessary