Quantile normalization for combining gene-expression datasets

Figures & data

Table 1. Gene expression datasets.

Source	Dataset	N (ER +/−)
Wang et al. [20]	GSE2034	286 (209/77)
Ivshina et al. [21]	GSE4922	245 (211/34)
Desmedt et al. [22]	GSE7390	198 (134/64)
Shi et al. [23]	GSE20194	278 (164/114)
Hatzis et al. [24]	GSE25066	496 (296/200)
Nagalla et al. [25]	GSE45255	137 (89/48)

N: number of samples.

Figure 1. Classification performance in intra-dataset validation (5-fold CV, 100 splits) for simulated datasets.

Table 2. Classification performance in intra-dataset validation (5-fold CV) for simulated datasets.

		Individual datasets			RUV-combined datasets			QN-combined datasets
Classifier	Dataset	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy
SVM	Structure 1^a	80.65 ± 1.06^b	54.10 ± 2.64	75.26 ± 1.29	75.79 ± 1.16(−)^c	51.61 ± 1.99	68.46 ± 1.45(−)	76.37 ± 1.12	52.47 ± 2.01	69.32 ± 1.43
	Test^d	80.76 ± 0.33	54.12 ± 1.13	75.38 ± 0.37	76.23 ± 0.62(−)	52.26 ± 1.07	69.50 ± 0.72(−)	76.39 ± 0.62	52.41 ± 1.06	69.32 ± 0.71
	Structure 2	81.01 ± 1.14	55.69 ± 2.42	75.72 ± 1.34	75.97 ± 1.30(−)	51.97 ± 2.21	68.69 ± 1.64(−)	71.39 ± 1.20(−)^e	43.80 ± 1.97(−)	62.91 ± 1.51(−)
	Test	81.15 ± 0.37	55.98 ± 1.17	75.91 ± 0.37	76.42 ± 0.65(−)	52.69 ± 1.07(−)	69.73 ± 0.74(−)	71.43 ± 0.61(−)	43.76 ± 0.89(−)	62.94 ± 0.66(−)
	Structure 3	99.98 ± 0.03	99.91 ± 0.13	99.97 ± 0.04	100.00	100.00	100.00	100.00	100.00	100.00
	Test	99.979 ± 0.007	99.916 ± 0.036	99.968 ± 0.012	99.998 ± 0.001(+)	99.997 ± 0.002(+)	99.998 ± 0.001(+)	99.998 ± 0.001	99.996 ± 0.003	99.998 ± 0.002
enRS-FLD	Structure 1	81.68 ± 0.95	60.87 ± 2.28	76.92 ± 1.14	76.20 ± 1.19(−)	55.76 ± 1.90(−)	69.79 ± 1.44(−)	77.31 ± 1.07	56.94 ± 1.90	71.17 ± 1.35
	Test	81.77 ± 0.23	60.90 ± 0.70	77.02 ± 0.21	76.67 ± 0.47(−)	56.34 ± 0.69(−)	70.83 ± 0.49(−)	77.34 ± 0.42	56.88 ± 0.68	71.18 ± 0.45
	Structure 2	81.54 ± 1.00	60.52 ± 2.08	76.71 ± 1.17	76.19 ± 1.23(−)	55.65 ± 1.92(−)	69.74 ± 1.48(−)	72.90 ± 1.28	48.93 ± 2.03(−)	65.45 ± 1.58
	Test	81.67 ± 0.29	60.72 ± 0.75	76.87 ± 0.26	76.67 ± 0.49(−)	56.39 ± 0.66(−)	70.83 ± 0.52(−)	72.96 ± 0.53(−)	48.88 ± 0.73(−)	65.49 ± 0.55(−)
	Structure 3	99.99 ± 0.02	99.94 ± 0.08	99.98 ± 0.03	100.00	99.98 ± 0.04	99.99 ± 0.02	100.00	100.00	100.00
	Test	99.985 ± 0.004	99.941 ± 0.019	99.977 ± 0.006	99.997 ± 0.001(+)	99.993 ± 0.002(+)	99.996 ± 0.001(+)	99.998 ± 0.001	99.996 ± 0.002	99.997 ± 0.001

Subscript 1: class 1. Subscript 0: class 0.

^a 100 simulation replicates were generated for each structure. In each replicate, five datasets were generated and randomly split (100 times) for cross-validation (see text).

^b Each value (in percent) is averaged over the 100 replicates, the five datasets, and the 100 splits. A standard error (the number after ±) is estimated from the 100 replicates.

^c The symbol in the brackets indicates if the performance of RUV combination is statistically significantly superior (+) or inferior (−) to that of non-combination with 95% confidence level.

^d For the five datasets, 100 times larger datasets were generated for further testing.

^e The symbol in the brackets indicates if the performance of QN combination is statistically significantly superior (+) or inferior (−) to that of RUV combination with 95% confidence level.

Figure 2. Classification performance in inter-dataset validation (LDOCV) for simulated datasets.

Table 3. Classification performance in inter-dataset validation (LDOCV) for simulated datasets.

		RUV-combined datasets			QN-combined datasets
Classifier	Dataset	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy
SVM	Structure 1	70.82 ± 1.44^a	53.65 ± 2.06	64.67 ± 1.67	75.94 ± 1.32(+)^b	51.46 ± 2.46	68.49 ± 1.71(+)
	Test	70.82 ± 0.86	53.74 ± 0.91	64.73 ± 0.84	76.05 ± 0.60(+)	51.79 ± 1.05(−)	68.66 ± 0.72(+)
	Structure 2	71.01 ± 1.51	54.10 ± 2.25	64.93 ± 1.77	70.94 ± 1.51	43.16 ± 2.34(−)	62.16 ± 1.81
	Test	70.99 ± 0.90	54.06 ± 0.90	64.93 ± 0.87	71.05 ± 0.63	43.21 ± 0.79(−)	62.23 ± 0.66(−)
	Structure 3	99.22 ± 0.19	96.91 ± 0.63	98.75 ± 0.29	100.00(+)	99.99 ± 0.03(+)	100.00(+)
	Test	99.21 ± 0.10	96.90 ± 0.34	98.75 ± 0.15	100.00(+)	100.00(+)	100.00(+)
enRS-FLD	Structure 1	70.18 ± 1.42	56.68 ± 1.79	65.22 ± 1.55	77.22 ± 1.39(+)	56.54 ± 2.37	70.86 ± 1.73(+)
	Test	70.08 ± 0.78	56.58 ± 0.53	65.14 ± 0.68	77.21 ± 0.45(+)	56.61 ± 0.65	70.87 ± 0.48(+)
	Structure 2	70.12 ± 1.46	56.51 ± 1.74	65.12 ± 1.56	72.60 ± 1.49	48.51 ± 2.30(−)	64.96 ± 1.77
	Test	70.12 ± 0.78	56.60 ± 0.51	65.17 ± 0.69	72.76 ± 0.55(+)	48.56 ± 0.72(−)	65.09 ± 0.57
	Structure 3	98.86 ± 0.22	95.83 ± 0.65	98.22 ± 0.33	100.00(+)	100.00(+)	100.00(+)
	Test	98.84 ± 0.12	95.76 ± 0.37	98.19 ± 0.18	100.00(+)	100.00(+)	100.00(+)

^a The standard error is estimated from the 100 simulation replicates.

^b The symbol in the brackets indicates if the performance of QN combination is statistically significantly superior or inferior to that of RUV combination.

Figure 3. Classification performance in intra-dataset validation (5-fold CV, 100 splits) for real datasets.

Table 4. Classification performance in intra-dataset validation (5-fold CV) for real datasets.

		Individual datasets			RUV-combined datasets			QN-combined datasets
Classifier	Dataset	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy
SVM	GSE2034	91.79 ± 0.64^a	77.27 ± 1.79	87.94 ± 0.93	92.40 ± 0.50	80.91 ± 1.22	89.13 ± 0.70	91.62 ± 0.59	78.12 ± 1.58	87.88 ± 0.86
	GSE4922	92.34 ± 0.52	39.28 ± 5.00	86.40 ± 0.93	92.66 ± 0.53	46.69 ± 4.49	87.10 ± 0.93	93.56 ± 0.57	60.76 ± 4.52(+)	88.94 ± 1.00
	GSE7390	91.50 ± 0.62	81.55 ± 1.44	88.35 ± 0.86	90.82 ± 0.71	81.02 ± 1.51	87.63 ± 0.96	90.95 ± 0.69	81.48 ± 1.50	87.84 ± 0.93
	GSE20194	93.14 ± 0.71	90.00 ± 1.11	91.86 ± 0.86	91.77 ± 1.08	88.16 ± 1.59	90.29 ± 1.28	95.44 ± 0.68(+)	93.44 ± 0.99(+)	94.62 ± 0.81(+)
	GSE25066	89.64 ± 0.46	84.71 ± 0.71	87.65 ± 0.56	87.91 ± 1.04	81.71 ± 1.58	85.45 ± 1.24	92.69 ± 0.55(+)	89.51 ± 0.79(+)	91.39 ± 0.64(+)
	GSE45255	87.37 ± 1.16	72.30 ± 2.45	82.66 ± 1.55	87.83 ± 0.85	71.96 ± 2.21	83.03 ± 1.21	86.84 ± 1.17	71.46 ± 2.86	81.99 ± 1.62
	Average	90.96 ± 0.31	74.18 ± 1.05	87.48 ± 0.42	90.57 ± 0.32	75.07 ± 0.89	87.10 ± 0.40	91.85 ± 0.31(+)	79.13 ± 0.98(+)	88.78 ± 0.42(+)
enRS-FLD	GSE2034	91.78 ± 0.48	78.39 ± 1.37	88.09 ± 0.71	93.33 ± 0.29(+)	83.03 ± 0.80(+)	90.42 ± 0.42(+)	92.83 ± 0.24	81.26 ± 0.79	89.63 ± 0.37
	GSE4922	92.65 ± 0.46	52.71 ± 3.34	87.28 ± 0.80	94.15 ± 0.37(+)	66.39 ± 2.63(+)	90.03 ± 0.64(+)	93.99 ± 0.33	65.61 ± 2.36	89.77 ± 0.58
	GSE7390	92.36 ± 0.66	84.19 ± 1.36	89.70 ± 0.88	91.47 ± 0.48	82.34 ± 0.97	88.50 ± 0.64	91.59 ± 0.38	82.61 ± 0.78	88.67 ± 0.50
	GSE20194	92.79 ± 0.70	89.52 ± 1.05	91.46 ± 0.84	95.90 ± 0.73(+)	93.87 ± 1.12(+)	95.08 ± 0.88(+)	96.69 ± 0.63	95.23 ± 0.93	96.09 ± 0.75
	GSE25066	90.40 ± 0.36	86.04 ± 0.58	88.62 ± 0.45	92.82 ± 0.32(+)	89.60 ± 0.48(+)	91.50 ± 0.38(+)	93.08 ± 0.31	90.14 ± 0.46	91.86 ± 0.36
	GSE45255	87.04 ± 1.14	73.31 ± 2.27	82.56 ± 1.48	90.41 ± 0.73(+)	79.29 ± 1.70(+)	86.89 ± 1.01(+)	89.87 ± 0.82	77.62 ± 2.00	86.06 ± 1.16
	Average	91.17 ± 0.29	77.36 ± 0.77	87.95 ± 0.38	93.01 ± 0.23(+)	82.42 ± 0.63(+)	90.41 ± 0.31(+)	93.01 ± 0.23	82.08 ± 0.61	90.35 ± 0.31

Subscript 1: ER+; Subscript 0: ER−.

^a The standard error is estimated from the 100 CV splits.

Figure 4. Classification performance in inter-dataset validation (LDOCV) for real datasets.

Table 5. Classification performance in inter-dataset validation (LDOCV) for real datasets.

		RUV-combined datasets			QN-combined datasets
Classifier	Dataset	F1-measure1	F1-measure0	Accuracy	F1-measure1	F1-measure0	Accuracy
SVM	GSE2034	84.32 ± 2.06^a	71.29 ± 2.83	79.72 ± 2.41	91.40 ± 1.23(+)	78.79 ± 2.82	87.76 ± 1.69(+)
	GSE4922	68.67 ± 2.78	32.26 ± 2.89	57.14 ± 2.94	92.80 ± 1.31(+)	66.67 ± 4.64(+)	88.16 ± 2.04(+)
	GSE7390	86.96 ± 2.52	76.92 ± 3.87	83.33 ± 3.01	90.49 ± 1.95	81.20 ± 3.53	87.37 ± 2.49
	GSE20194	95.76 ± 0.99	93.81 ± 1.45	94.96 ± 1.17	96.07 ± 0.94	94.22 ± 1.43	95.32 ± 1.13
	GSE25066	92.68 ± 1.01	89.95 ± 1.31	91.53 ± 1.14	93.02 ± 1.04	89.88 ± 1.45	91.73 ± 1.21
	GSE45255	85.55 ± 3.15	75.25 ± 5.16	81.75 ± 3.82	86.46 ± 2.25	68.29 ± 5.98	81.02 ± 3.21
	Average	85.66 ± 0.90	73.25 ± 1.37	81.40 ± 1.07	91.71 ± 0.70(+)	79.84 ± 1.62(+)	88.56 ± 0.95(+)
enRS-FLD	GSE2034	91.41 ± 1.44	80.68 ± 2.81	88.11 ± 1.90	92.91 ± 1.33	82.21 ± 2.96	89.86 ± 1.83
	GSE4922	87.07 ± 1.78	55.86 ± 3.67	80.00 ± 2.47	93.63 ± 1.30(+)	68.29 ± 5.45	89.39 ± 2.09(+)
	GSE7390	90.84 ± 1.68	82.09 ± 3.59	87.88 ± 2.27	91.39 ± 1.52	82.17 ± 3.00	88.38 ± 2.00
	GSE20194	95.68 ± 1.26	93.97 ± 2.58	94.96 ± 1.70	96.95 ± 0.97	95.61 ± 1.38	96.40 ± 1.14
	GSE25066	93.50 ± 1.16	91.25 ± 1.83	92.54 ± 1.41	93.98 ± 0.92	91.48 ± 1.25	92.94 ± 1.05
	GSE45255	88.76 ± 2.44	79.17 ± 4.74	85.40 ± 3.17	89.12 ± 1.93	74.07 ± 5.58	84.67 ± 2.86
	Average	91.21 ± 0.73	80.50 ± 1.44	88.15 ± 0.96	93.00 ± 0.56	82.31 ± 1.57	90.28 ± 0.80

^a The standard error is estimated assuming that the numbers of true positive and true negative samples are binomially distributed.

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