Assignment of grouped exposure levels for trend estimation in a regression analysis of summarized data

For performing regression analysis of summarized response data containing grouped intervals of exposure, many researchers use pre-assigned doses such as the median values of each interval. However, the trend estimate is considerably sensitive to the choice of the assigned values. In this paper, we propose a method to assign the values to obtain a more accurate regression coefficient applying the likelihood approach. Numerical illustrations and comparisons through simulations showed that the proposed dose assignment can yield better estimates of trend in the regression analysis of two variants than that obtained by the conventional assignment methods such as those that use median values. In particular, for the data of a case-control study, the proposed dose improved the accuracy of the procedures such as that developed by Greenland and Longnecker (1992) compared with the conventional pre-assigned dose.