Local in Time Statistics for detecting weak gene expression signals in blood – illustrated for prediction of metastases in breast cancer in the NOWAC Post-genome Cohort

Figures & data

Table 1 Number of case-control pairs with gene expression data X_g,p in each stratum and year before diagnosis in the screening group

Number of case-control pairs in the screening group
Year before diagnosis	8	7	6	5	4	3	2	1	Sum
stratum With metastases	0	1	6	15	30	24	20	12	108
Without metastases	1	3	10	36	53	59	57	53	272
Sum	1	4	16	51	83	83	77	65	380

Table 2 Number of case-control pairs with gene expression data X_g,p in each stratum and year before diagnosis in the clinical group

Number of case-control pairs in the clinical group
Year before diagnosis	8	7	6	5	4	3	2	1	Sum
stratum With metastases	0	0	1	4	5	2	8	10	30
Without metastases	0	1	3	6	14	8	12	13	57
Sum	0	1	4	10	19	10	20	23	87

Figure 1 Overview of hypothesis tests, prediction methods, variables, and strata.

Notes: Illustration of the association between the data X_g,p, the different hypothesis tests, the prediction methods, the variables used in these tests and methods, and the strata.

Table 3 Association between tumor size and metastases

Group	Metastases	Tumor size (cm)							p-value
		0.05	0.3	0.75	1	1.5	3.5	5	Mean	Independent two sample t-test	Mann-Whitney U-test
Screening	Yes	1	12	56	25	1	3	0	0.86	7.5e-05	7.0e-07
	No	18	79	120	35	1	1	0	0.60
Clinical	Yes	0	2	12	11	0	0	0	0.83	0.32	0.16
	No	1	10	27	11	0	2	2	0.87

Notes: p-values are obtained using an independent two sample t-test (testing if averages are equal) and a Mann-Whitney U-test (testing if it is equally likely that the tumor size of a case with metastases is less than or greater than the tumor size of a case without metastases).

Figure 2 The statistics s_p,(g) and m_p,(g).

Notes: Plots are shown for not standardized data for s_p,(g) and m_p,(g), and also for standardized data for s_p,(g). Curves are shown for the data in the period closest to and furthest from diagnosis. (A) Data from the screening group. (B) Data from the clinical group.
Abbreviations: st.dev., standard deviation; w.r.t, with respect to.

Figure 3 The statistic w_p,_(g) and hypothesis H0-node.

Notes: Plot of statistic (A) and plot of p-values against time (B) for the statistic w_p,_(g) for the screening (left panel) and clinical group (right panel). (A) Plot of the statistic w_p,_(g) where the two periods contain 50 (screening) or 25 (clinical) case-control pairs where the case is without metastases. (B) Plot of p-values against time for the statistic w_p,_(g) (H0-node). In each plot, there is one curve for genes with order 50 (black), 200 (red), 500 (green), 1000 (blue), and 2000 (light blue), respectively. p-value for time point t is equal to the p-value for the time period with middle point closest to t (after the p-values have been smoothed using a median filter with window size 99). The resulting curve is then smoothed using a mean filter with a window size of 1 month. The dotted horizontal line indicates a 0.05 level of significance, while the long vertical lines indicate the years before diagnosis.
Abbreviation: w.r.t, with respect to.

Figure 4 Hypotheses H0-case-ctrl and H0-time.

Notes: Plots of p-values against time for the hypotheses H0-case-ctrl and H0-time where the datasets with cases without metastases are used. (A) Results for data from the screening group. (B) Results for data from the clinical group. In each plot, there is one curve for genes with order 50 (black), 200 (red), 500 (green), 1000 (blue), and 2000 (light blue), respectively. p-value for time point t is equal to the p-value for the time period with middle point closest to t (after the p-values have been smoothed using a median filter with window size 99). The resulting curve is then smoothed using a mean filter with a window size of 1 month. The dotted horizontal line indicates a 0.05 level of significance, while the long vertical lines indicate the years before diagnosis.

Table 4 Number of correctly and wrongly classified cases in the screening group and the clinical group

Group	Years before diagnosis	Number of correctly and wrongly classified cases				p-value (Fisher’s test)	Sensitivity	Specificity	AUC
		Without metastases		With metastases
		FN	TP	FP	TN
Screening	All years	61	47	119	153	0.561	0.44	0.56	0.53
group	Year 1	2	10	26	27	0.030*	0.83	0.51	0.71
Clinical	All years	10	20	26	31	0.049*	0.67	0.54	0.57
group	Year 3–4	2	5	6	16	0.051	0.71	0.73	0.69

Note: *p-value<0.05.

Abbreviation: AUC, area under the curve.

Figure 5 Prediction results.

Notes: (A) Correctly (green) or wrongly (red) classified cases plotted against time to diagnosis for the screening (upper panel) and the clinical group (lower panel). A circle is plotted above every fifth case. Long vertical lines are plotted to indicate the years. Cases with metastases are plotted on the line labeled “With”, while cases without metastases are plotted on the line labeled “Without”. (B) Fraction of correctly classified cases with (red) and without (black) metastases over time for the screening (upper panel) and the clinical group (lower panel). The fraction for each point in time is computed using a moving window of 1 year (clinical) or 100 days (screening). The resulting curve is then smoothed using a median filter with a window size of 1 year (clinical) or 100 days (screening).

Table 5 Top 10 differentially expressed genes in clinically and screening-detected cases when comparing cases with metastases to cases without metastases

Screening-detected cases in the time period centered around 0.5 years before diagnosis
Gene symbol	p-value	Fold change	Breast cancer	Function
RPLP2	1.49E-06	1.19	Overexpressed	Ribosomal phosphoprotein
FKRP	2.18E-05	1.14	No	Protein for posttranslational modification of dystroglycan
ERBB2	4.95E-05	1.18	Overexpressed	Tyrosine-protein kinase receptor
CIB2	4.95E-05	1.13	No	calcium-binding regulatory protein
DDX23	5.16E-05	1.13	No	Member of the DEAD box protein family
RPSI9	5.58E-05	1.16	Overexpressed	Ribosomal protein
LOC401019	5.86E-05	1.19	No	Unknown
PDSS2	6.13E-05	1.23	No	Enzyme involved in coenzyme Q metabolism
DUS3L	8.10E-05	1.12	No	Protein involved in tRNA synthesis
ZNF417	8.58E-05	1.11	No	Protein involved in transcriptional regulation
Clinically detected cases in the time period centered around 2.5 years before diagnosis
CCDC5	1.71E-04	1.16	No	Protein vital to mitotic spindle assembly
MRPL14	2.23E-04	1.23	No	Protein component of the mitochondrial ribosome
NOD1	2.90E-04	1.17	Tumor suppressor	Intracellular pattern-recognition receptor
UTP14A	3.53E-04	1.1	No	Protein involved in ribosome biogenesis
NSMCE1	3.77E-04	1.21	No	Protein involved in repairing of DNA double-strand breaks
SNTA1	1.05E-03	1.1	Overexpressed	Protein involved in organization of the neuromuscular synapse
BAZ1B	1.16E-03	1.16	No	Protein involved in regulation of transcription
IL21R	1.43E-03	1.14	Tumor promoter	cytokine receptor for interleukin 21
POP5	1.45E-03	1.15	No	Protein involved in maturation of tRNA
RARRES3	1.66E-03	1.36	Metastasis suppressor	Protein that inhibits cell growth and proliferation

Note: Genes were sorted by p-value.

Figure 6 ROC curves.

Notes: ROC curves obtained when predicting the metastasis status of the cases. (A) ROC curve for the screening group in year 1 before diagnosis. (B) ROC curve for the clinical group in year 3–4 before diagnosis.
Abbreviation: ROC, receiver operating characteristic.

Figure S1 Boxplots illustrating how the score used in the predictor depends on the number of genes included in the score.

Notes: The score has been normalized by dividing with the number of genes included in the score. The score for the cases with metastases should be positive (lower panel), while the scores for the cases without metastases should be negative (upper panel). (A) Scores for case-control pairs around 6 months from the screening group. (B) Scores for case-control pairs around 2 years and 6 months from the clinical group.