Analysis of ordered categorical data with score averaging: with applications to case-control genetic associations

The trend test is often used for the analysis of 2×<italic>K</italic> ordered categorical data, in which <italic>K</italic> pre-specified increasing scores are used. There have been discussions on how to assign these scores and the impact of the outcomes on different scores. The scores are often assigned based on the data-generating model. When this model is unknown, using the trend test is not robust. We discuss the weighted average of a trend test over all scientifically plausible choices of scores or models. This approach is more computationally efficient than a commonly used robust test MAX when <italic>K</italic> is large. Our discussion is for any ordered 2×<italic>K</italic> table, but simulation and applications to real data are focused on case-control genetic association studies. Although there is no single test optimal for all choices of scores, our numerical results show that some score averaging tests can achieve the performance of MAX.