Feature Selection for Longitudinal Data by Using Sign Averages to Summarize Gene Expression Values over Time

Table 2

Performance of the proposed method on the traumatic injury application and comparison with other methods.

Method		Size	Rand Index	Test Set
				Error rate	BCM^1	AUPR^2
Proposed methods	Sign Avg. & LASSO/CD^3	32	19.58%	0.351	0.605	0.626
	Sign Avg. & TGDR^4	30	25.21%	0.378	0.590	0.662
Existing methods	limma	47	21.40%	0.432	0.542	0.628
	EDGE	453	13.67%	0.432	0.543	0.622
	glmmLASSO	8	34.99%	0.432	0.519	0.532
	LASSO/CD separately^5	28	13.59%	0.486	0.498	0.508
	TGDR separately^6	133	22.58%	0.378	0.520	0.579
	Mean & LASSO/CD^7	29	17.95%	0.405	0.536	0.560
Using other summary scores	Mean & TGDR^8	36	27.37%	0.405	0.562	0.617
	Median & LASSO/CD^9	22	7.76%	0.351	0.543	0.617
	Median & TGDR^10	43	18.58%	0.405	0.578	0.626
	PC1 & LASSO/CD^11	3	13.59%	0.405	0.504	0.541
	PC1 & TGDR^12	29	32.68%	0.432	0.539	0.548

¹BCM captures the average confidence that a sample belongs to class i when it indeed belongs to that class;
²AUPR is the average of for each class and it captures the ability of correctly ranking the samples known to belong in a given class;
³Sign Avg. & LASSO/CD: pseudo genes were obtained by calculating the sign average of a gene’s expression values across time, and the feature selection method is LASSO in which the optimization method used is coordinate descent;
⁴Sign Avg. & TGDR: pseudo genes were obtained by calculating the sign average of a gene’s expression values across time, and the feature selection/optimization method is threshold gradient descent regularization;
⁵LASSO/CD separately: separate LASSO models were trained at individual time points; the optimization method is CD;
⁶TGDR separately: separate TGDR models were trained at individual time points; the optimization method is TGDR;
⁷Mean & LASSO/CD: pseudo genes were obtained by calculating the average of a gene’s expression values across time, and the optimization method is CD;
⁸Mean & TGDR: pseudo genes were obtained by calculating the average of a gene’s expression values across time, and the optimization method is TGDR;
⁹Median & LASSO/CD: pseudo genes were obtained by calculating the median of a gene’s expression values across time, and the optimization method is CD;
¹⁰Median & TGDR: pseudo genes were obtained by calculating the median of a gene’s expression values across time, and the optimization method is TGDR;
¹¹PC1 & LASSO/CD: pseudo genes obtained by calculating the first principal component of a gene’s expression values across time, and the optimization method is CD;
¹²PC1 & TGDR: pseudo genes were obtained by calculating the first principal component of a gene’s expression values across time, and the optimization method is TGDR.