Table 1. Different methods compared in this study.

Name format	Examples	Annotation usage	Explanation
<method>_non	CAVIARBF_non, PAINTOR_non, fgwas_non	No	Fit the intercept using the traditional logistic regression in the EM method. For fgwas_non, no annotation is used
CAVIARBF_glm	CAVIARBF_glm	Yes	Fit all annotations using the traditional logistic regression in the EM method
CAVIARBF_<penalty>_<criterion>	CAVIARBF_L2_CV, CAVIARBF_L1_CV, CAVIARBF_ENET_CV, CAVIARBF_ENET_AIC, CAVIARBF_ENET_BIC	Yes	Use penalized models. L2, $l_2$ penalty; L1, $l_1$ penalty; ENET, elastic net penalty; <criterion> can be AIC, BIC, and CV
CAVIARBF_fb_CV	CAVIARBF_fb_CV	Yes	Assume one causal variant and use the forward-backward annotation selection proposed in fgwas
<method>_top<k>	PAINTOR_top40	Yes	First, annotations are ranked by their individual increase in likelihood compared to the model without any annotation. Then the top k annotations are used
<method>_top<k>t	PAINTOR_top10t, CAVIARBF_top10t	Yes	All annotations are ranked as in top<k>. Then we sequentially select the annotations with additional two thresholds: (1) the absolute correlations between already selected annotations and the annotation to select are less than a threshold, 0.2 in our simulations; (2) the individual P-value of the annotation to select against the null model without any annotation is less than a threshold, 0.05 in our simulations. This method may not be able to select exactly k annotations due to the additional constraints
<method>_step<k>t	PAINTOR_step5t, PAINTOR_step10t	Yes	The difference between step<k>t and top<k>t is that before selecting a new annotation to include, all remaining candidate annotations are ranked based on their individual contributions in likelihood to the model with all current selected annotations. Specifically, let $L_0$ be the log likelihood from the model using the current selected annotations and $L_i$ be the log likelihood from the model using the current selected annotations plus candidate annotation i. Then the difference $L_i-L_0$ is the contribution of adding annotation i. It starts with the candidate annotation with the largest contribution and checks the threshold in the same way as in top<k>t. Once an annotation is selected, all the remaining candidate annotations will be evaluated based on the increase of likelihood for the next selection. This method may not be able to select exactly k annotations due to the additional constraints
fgwas	fgwas	Yes	fgwas with annotation and the forward-backward annotation selection