Pearson's Test, Trend Test, and MAX Are All Trend Tests with Different Types of Scores

Pearson's test is one of the most commonly used statistics for testing genetic association of case-control data. The trend test is another one which assumes a dose-response model between the risk of the disease and genotypes. To apply the trend test, a set of ordered scores is assigned a priori based on the underlying genetic model. Pearson's test is model-free and robust, but is less powerful for common genetic models. MAX is another robust test statistic, which takes the maximum of the trend tests over a family of scientifically plausible genetic models. We show that the three test statistics are all trend tests but with different types of scores; whether the scores are prespecified or data-driven, or whether the scores are ordered (restricted) or not ordered (unrestricted). We then provide insights into power performance of the three tests when the underlying genetic model is unknown and discuss which test to use for the analyses of case-control genetic association studies.