Two-group comparison of gene signatures: failure of conventional statistical methods and validation of a novel algorithm

doi:10.1038/nprot.2009.106

Method Article

Two-group comparison of gene signatures: failure of conventional statistical methods and validation of a novel algorithm

https://doi.org/10.1038/nprot.2009.106

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Biotechnology

Biochemistry

gene signatures

two-group comparison

nonparametric tests

microarray data

software

Excel add-in

The gene expression profiling could aid the physicians to better understand the cellular morphology, resistance to chemotherapy and overall clinical outcome of disease [1,2]. Such individualized treatment may significantly increase survival due to the optimization of treatment procedure according to clinical pathogenesis. Ein-Dor et al [3] have pointed out that the gene sorted for the same clinical types of patients but different groups differed widely and possessed only few genes in common. An explanation to this lack of overlap between predictive signatures from different studies with the same goal may be due to the presence of more predictive genes than required to design an accurate predictor [4]. However, the microarray technique itself has been shown to be highly reproducible within and across two high volume laboratories [5].

Numerous statistical procedures including t-test [6,7], analysis of variance [8], Pearson correlation [9], Wilcoxon signed-rank test [10,11] and Mann Whitney U test [12,13] have been used for comparison of microarray data. However, the validity of various conventional statistical methods for two-group comparison of gene signatures was never evaluated using carefully selected data sets. A novel algorithm with software support is presented herein for more realistic and comprehensive interpretation of gene signatures.

Computational method and theory of CalcHEPI

The formula used for computation of HEPI score is HEPI=Σ [(Ni(0→t) Sj(0→1)/Nt]x100. Where Ni is the number of genes with Score Sj. The subscript ‘i’ may vary between 0 and total number of genes in the signature and ‘j’ may vary between 0 (minimum score) and 1 (maximum score). Nt is the total number of genes in the signature. First, all the ratios of expression data are categorized according to a logical scale to get the respective Ni and Sj values. The percent contributions of each set of genes (genes with same expression score) are computed and then summed up to get HEPI score. The fold-change strategy used in HEPI scores is robust, accurate and reproducible. Although the concept of fold-change has been described in microarray experiments it has never been utilized for collective interpretation of gene signatures. Technically, the ratio of the color intensity of each spot (probe) measures the relative expression of the corresponding gene under two different experimental conditions. In general, a gene is said to be differentially expressed if the ratio in absolute value of the expression levels between the control and treated group exceeds certain thresholds. The most acceptable expression ratios for up- and down-regulated genes have been suggested as >1.5 and <0.5 respectively [11,17,18]. While adopting the same cut-off values, additional sub-grading has been proposed in this protocol. HEPI scores are simple to interpret, easy to compare and prominent for visual cross checking.

Software design

CalcHEPI software has been developed in Microsoft Excel platform due to Excel’s flexibility, universal availability, and macro-based automation. Moreover, the spreadsheet layout of Excel is perfectly suitable for storing and analyzing microarray data as well as developing microarray analysis software. The data selection is controlled by input box to allow the users to select the paired expression values from any place of the worksheet (Fig. 1). The software then utilizes Excel’s worksheet formula function together with a macro subroutine to compute HEPI scores (Fig. 2). The percent contribution of norm-regulated (green), down-regulated (blue) and up-regulated (red) genes is also shown as a color-coded bar. The output of the software provides a comprehensive understanding of the results in terms of both qualitative (up- or down-regulation) and quantitative (gradation in fold-change) analysis of gene signature with the quick review indicator bar. The clarity and integrity of report format are quite helpful for any cross evaluation. HEPI scores are valid for any size of array signature as they are calculated according to percent (and not number) of differentially expressed genes on a 10 point scale (5 for up regulation and 5 for down regulation).

Software validation

The functional accuracy and reliability of software have been validated using the simulated and real gene signatures data for two-group comparisons. Six pairs of expression data were specifically designed to represent various degrees of similarity/differences (details not shown). Among them, the two groups in pair 4 are not significantly different whereas the groups in pair 6 possess maximum difference. All these 6 pairs were subjected to nonparametric comparisons with Mann-Whitney U test, Kolmogorov-Smirnov test, Kruskal-Wallis test, Wilcoxon signed-rank test, Sign test, Friedman test and Kendall W test using SPSS (Version 10). The real expression data of published signatures including ovarian carcinoma [14], ulcerative colitis [15], leukemia [16] and adenocarcinoma [6] were also analyzed by the above nonparametric tests as well as CalcHEPI. The characteristics of these real signatures have been summarized in our earlier report [10].

A personal computer with Microsoft Excel program.

Installation of CalcHEPI Add-in

Open the Excel program and insert the program CD in drive (if the CalcHEPI software is in a CD). NOTE: Alternatively the software file (115 KB) can be obtained as an e-mail attachment from the author.
In the ‘Tool’ menu of Excel workbook, click on ‘Add-Ins’ and then click on ‘Browse’. Locate your appropriate drive and double click on ‘HEPI’.
The message “Copy HEPI to …” will appear, click ‘Yes’; the appearance of ‘HEPI’ on the menu bar indicates the proper installation of the Add-in.
Remove the software CD (if applicable).
For un-installation, follow all the above steps except selecting ‘HEPI Uninstall’ instead of ‘HEPI’; the removal of ‘HEPI’ from the menu bar will indicate the proper un-installation of the Add-in. Running the program
For computing HEPI score, enter the gene expression data of different groups in separate columns. IMPORTANT: Prior to activating the ‘Input’ window, ensure that the data to be compared reside in adjacent columns.

CAUTION: Since most of the gene signatures are composed of tens to a few hundred specific genes the upper limit of the software has been fixed at 1000 genes to prevent unnecessary system-busy situation due to mistake in data selection. The software will alarm the user if more than 1000 rows are selected in the worksheet.

Once the data entry has been completed, click the ‘HEPI’ button in the menu bar to popup the ‘Input’ window (Fig. 1).
Select the range of data (numbers only) without including the header row (if any) as shown in Fig. 1.
Now clicking the ‘OK’ button executes the software and a comprehensive report is displayed (Fig. 2).

Once the installation of Add-in has been done, the computation of HEPI score is performed instantly after selection of the desired gene expression data.

Please ensure that the data to be compared reside in adjacent columns.
The group against which the other group is to be compared should be on the left column.
The data selection for analysis should only be from TWO ADJACENT columns.
Only numerical data should be selected; any header row with text must not be selected as shown in Fig. 1.
The software accepts only up to 1000 rows data (exceeding this limit will be indicated by a message). However, the users who want to use the software for more number of genes can contact the author to get a modified version with more capacity.

Installation of Add-in for Excel 2007

The instructions for Add-in installation given above are valid for Excel 2003. For installing the Add-in in Excel 2007, follow the following steps:

Click on the Office Button, the big round button in the top left of the Excel window.
Click the Excel Options button at the bottom of this menu to open the dialog box.
Click the Add-Ins item in the list along the left edge of the dialog to see the Add-Ins panel. Make sure the Manage dropdown at the bottom shows Excel Add-Ins
Press the Go button to show the Add-Ins dialog.
Click Browse and use the Browse dialog to locate the add-in file. Troubleshooting

So far, I have not faced any problem with the installation or running this Add-in. However, the users are requested to contact the author in case they encounter any problem associated with this software.

The anticipated results format is shown in Fig. 2. For users' information, the results of software validation using simulated and real signatures clearly demonstrated the incompatibility of conventional statistical methods for comparing gene expression data. Paradoxical outcomes were observed while comparing 6 simulated gene signatures using 7 nonparametric tests (Table 1). Five tests including Mann-Whitney U test, Kruskal-Wallis test, Sign test, Friedman test and Kendall W test resulted same but logically unrealistic P values for all these signature pairs. Surprisingly, these tests showed P=1 for a gene signature with maximum difference (Pair 6, HEPI = 100) and P = 0.001 for a signature with a slight difference (Pair 5, HEPI = 4) (Table 1). The remaining two tests including Kolmogorov-Smirnov test and Wilcoxon signed-rank test also failed to effectively handle these comparisons. For instance, Kolmogorov-Smirnov test resulted P = 0.001 both for similar groups (Pair 4, HEPI = 0) as well as the groups with maximum difference (Pair 6, HEPI = 100). Wilcoxon signed-rank test showed ambiguous results for Pairs 3 and 5 (Table 1). Statistical inconsistency also prevailed while comparing real signatures (Table 1) affixing a question mark on the reliability of nonparametric tests for two-group comparison of gene signatures.

Thus the conventional statistical methods may not be able to handle the peculiar microarray expression data, particularly for two-group comparison of gene signatures. More accurate and unified statistical methods and/or coding systems are therefore needed to ensure routine and uniform clinical application of gene signatures. CalcHEPI is one such effort that may serve as a convenient and robust tool for two-group comparison of gene signatures.

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The author is highly thankful to the research groups of Dr. Kai Wang (Chiroscience R&D, Inc., Bothell, WA, USA); Dr. Thomas P. Dooley (IntegriDerm Inc., Birmingham Alabama, USA); Dr. Todd R. Golub (Massachusetts Institute of Technology, Cambridge, MA, USA) and Dr. Daniel A. Notterman (Princeton University, Princeton, NJ, USA) for using their published data to validate CalcHEPI protocol.

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