A cautionary note on using secondary phenotypes in neuroimaging genetic studies.

Almost all genome-wide association studies (GWASs), including Alzheimer's Disease Neuroimaging Initiative (ADNI), are based on the case-control study design, implying that the resulting case-control data are likely a biased, not random, sample of the target population. Although association analysis of the disease (e.g. Alzheimer's disease in the ADNI) can be conducted using a standard logistic regression by ignoring the biased case-control sampling, a standard linear regression analysis on a secondary phenotype (e.g. any neuroimaging phenotype in the ADNI) may in general lead to biased inference, including biased parameter estimates, inflated Type I errors and reduced power for association testing. Despite of this well known result in genetic epidemiology, to our surprise, all the published studies on secondary phenotypes with the ADNI data have ignored this potential problem. Here we aim to answer whether such a standard analysis of a secondary phenotype is valid or problematic with the ADNI data. Through both real data analyses and simulation studies, we found that, strikingly, such an analysis was generally valid (with only small biases or slightly inflated Type I errors) for the ADNI data, though cautions must be taken when analyzing other data. We also illustrate applications and possible problems of two methods specifically developed for valid analysis of secondary phenotypes.