A novel approach to minimize false discovery rate in genome-wide data analysis
- Yuanzhe Bei†^{1} and
- Pengyu Hong^{1}Email author
https://doi.org/10.1186/1752-0509-7-S4-S1
© Bei and Hong; licensee BioMed Central Ltd. 2013
Published: 23 October 2013
Abstract
Background
High-throughput technologies, such as DNA microarray, have significantly advanced biological and biomedical research by enabling researchers to carry out genome-wide screens. One critical task in analyzing genome-wide datasets is to control the false discovery rate (FDR) so that the proportion of false positive features among those called significant is restrained. Recently a number of FDR control methods have been proposed and widely practiced, such as the Benjamini-Hochberg approach, the Storey approach and Significant Analysis of Microarrays (SAM).
Methods
This paper presents a straight-forward yet powerful FDR control method termed miFDR, which aims to minimize FDR when calling a fixed number of significant features. We theoretically proved that the strategy used by miFDR is able to find the optimal number of significant features when the desired FDR is fixed.
Results
We compared miFDR with the BH approach, the Storey approach and SAM on both simulated datasets and public DNA microarray datasets. The results demonstrated that miFDR outperforms others by identifying more significant features under the same FDR cut-offs. Literature search showed that many genes called only by miFDR are indeed relevant to the underlying biology of interest.
Conclusions
FDR has been widely applied to analyzing high-throughput datasets allowed for rapid discoveries. Under the same FDR threshold, miFDR is capable to identify more significant features than its competitors at a compatible level of complexity. Therefore, it can potentially generate great impacts on biological and biomedical research.
Availability
If interested, please contact the authors for getting miFDR.
Keywords
Background
FDR control is a statistical approach to correct multiple comparisons in dealing with multiple hypothesis testing problems. It has now been widely practiced in analyzing genome-wide datasets generated by high-throughput technologies, such as DNA microarray and RNA-Seq, which allows users to simultaneously screen the activities of tens of thousands of genes. These high-throughput datasets require careful analysis to identify a subset of interesting molecular features for follow-up experiments. It is always desired to maximizing findings in data. In the meantime, it should be realized that follow-up experiments can be costly in both time and money. Therefore it is important to control the proportion of wrongly called features among those selected (i.e., FDR).
FDR was first introduced by Benjamini and Hochberg [1] and was later improved by the Storey procedure [2, 3]. As two of the mainstream FDR controlling methods, the BH procedure fixes the error rate and then estimates its corresponding rejection region while the Storey procedure fixes the rejection region and then estimates its corresponding error rate. Efron and his colleagues framed the FDR control problem as a Bayesian problem, and showed that both the BH and Storey approaches are special cases [4–6]. Assuming that the same rejection region is used for each independent test, and the test statistics come from a random mixture of null and alternative distributions, the BH approach, the Storey approach and the Efron's Bayesian approach can be connected with a mixture model of null statistics and alternative statistics weighted by a factor representing the prior probability of getting true nulls. The BH approach simply assumes that the prior probability of true null is equal to 1, which makes it the most conservative one among the three. The Storey approach considers estimating the prior probability of true null. The Efron approach uses empirical Bayesian analysis to further estimate posterior probability of true null based on the prior probability. The BH, Storey and Efron approaches all estimate FDR by taking the p-values of individual features calculated by some sorts of hypothesis tests. The t-test [7] and the Wilcoxon ranksum test [8] (also known as the Mann-Whitney U test, referred as ranksum test in the rest of the paper for conciseness) are two of the most well-known tests for calculating the p-values of individual features.
Significance Analysis of Microarrays (SAM) [9] is another widely applied technique for calling features that behave significantly differently between two conditions. Different from the BH, Storey and Efron approaches, SAM uses a nonparametric method to estimate FDR instead of relying on p-values directly. SAM generates a large number of permutation controls, and the expected number of false positives can be estimated by counting the number of permuted statistics beyond a certain cut-off. Although SAM performed better than the BH and Storey approaches on many datasets in our practices, we found that SAM's results were not optimal in many cases. This is mainly because SAM decides the cut-offs based on the differences between the observed statistics (original statistics) and the expected statistics (averaged statistics from permuted measurements) instead of the estimated FDR, which does not guarantee the lowest FDR.
To address this problem, we developed miFDR - an advanced significance analysis method for optimizing FDR when the number of desired significant features is fixed. A preliminary version of miFDR was published in [10]. In this paper, we provide theoretical explanations and supports for miFDR, and generate more experimental results to demonstrate that miFDR empirically outperforms SAM, the BH approach and the Storey approach. In particular, the simulation test results showed that miFDR was capable of identifying more significant features with its true FDRs consistently bounded by the estimated FDRs. In addition, the true and estimated FDRs of miFDR were lower than those of the other three methods. Furthermore, when applied to real DNA microarray datasets, miFDR was able to identify more biologically relevant genes than other methods.
Methods
FDR under the Bayesian framework
where P (d ∈ Γ) = P (H = 0) P (d ∈ Γ|H = 0) + P (H = 1) P (d ∈ Γ|H = 1).
The term P (p ≤ γ) can be estimated in an empirical way as the proportion of features whose p-values are bounded by the p-value cut-off γ, namely $\widehat{P}\left(p\le \gamma \right)=\#\left\{{p}_{i}\le \gamma \right\}/\#\left\{{p}_{i}\right\}=\#\left\{{p}_{i}\le \gamma \right\}/M$, where #(p_{ i } ≤ γ) denotes the number of p-values bounded by the cut-off γ, and #{p_{ i }} denotes the total amount of p-values which is equivalent to the total number of features M. The BH approach simply assumes that P(H = 0) = 1 while the Storey approach estimates P(H = 0) empirically [2]. SAM adopts the same method to estimate P(H = 0) as the Storey approach [11].
SAM
Different from the BH and Storey approaches, SAM does not assume the distributions of the test statistics. In addition, it introduces corrections to t-statistic and ranksum statistic so that the distribution of the corrected statistics is independent from the levels of feature values. Both t-statistic and ranksum statistic can be represented as a difference score r_{ i } divided by the corresponding standard deviation s_{ i } : r_{ i }/s_{ i }. In particular, let X and Y be two groups of samples with N_{ X } and N_{ Y } samples, respectively. The traditional t-statistic has ${r}_{i}={\overline{X}}_{i}-{\overline{Y}}_{i}$ and ${s}_{i}=\{\left[\sum _{{x}_{im}\in X}{\left({x}_{im}-{\overline{X}}_{i}\right)}^{2}+\sum _{{y}_{in}\in Y}{\left({y}_{in}-{\overline{Y}}_{i}\right)}^{2}\right]\phantom{\rule{2.77695pt}{0ex}}\left(1/{N}_{X}+1/{N}_{Y}\right)/({N}_{X}+{N}_{Y}-2\}{}^{1/2}$; and the traditional ranksum statistic has ${r}_{i}={\overline{R}}_{i}^{X}-{N}_{X}\left({N}_{X}+{N}_{Y}+1\right)/2$ and ${s}_{i}={N}_{X}{N}_{Y}\left({N}_{X}+{N}_{Y}+1\right)/12$, where ${\overline{R}}_{i}^{X}$ is the sum of the ranks of the i-th feature from X (the measurements from X and Y are merged and then ranked from lowest to highest). They share one major drawback: the estimation of the standard deviation s_{ i } is very unstable when the sample size is relatively small, which is very common in studies involving high-throughput technologies. In addition, the distributions of the test statistics vary with respect to the levels of feature values, which makes it difficult to compare features with different value levels. To address these problems, SAM adds a factor s_{0} to the denominator s_{ i } to reduce the variance of the corrected statistic d_{ i } = r_{i}/(s_{ i } + s_{0}) (referred as d-value in the rest of paper for conciseness). In practice, SAM chooses the value of s_{0} from the pool of all {s_{ i }} so that the variance of d_{ i } is minimized. The goal is to make the variance of d_{ i } independent to the expression level [11]. We found the corrected statistics useful in analyzing many datasets in our research.
Since the null distributions of the corrected statistics are unknown, SAM uses permutations of the replicates to estimate FDR. Given a particular rejection region Γ, SAM generates B permutations of the original measurements and estimates P (d ∈ Γ|H = 0) as the median of ${\left\{{P}_{b}\left(\widehat{d}\in \text{\Gamma}\right)\right\}}_{b=1\dots B}$, where $\widehat{d}$ denotes the d-values in the b-th permutation. SAM estimates P (H = 0) in the same way as the Storey approach does [11].
To decide τ^{+} and τ^{-}, SAM introduces a Δ-index which is calculated as follows. First, the features are sorted in ascending order based on their original d-values. Let $\left\{{d}_{i}^{*}\right\}$ denote the d-values of the sorted features. Then the d-values obtained from the permutated replicates are sorted and used to estimate $E\phantom{\rule{2.77695pt}{0ex}}\left[{\widehat{d}}_{i}^{*}\right]$. Finally, the Δ-value of the i-th feature is calculated as ${\text{\Delta}}_{i}={d}_{i}^{*}-E\left[{\widehat{d}}_{i}^{*}\right]$. Given a user-defined threshold Δ_{0}, SAM searches in the ascending order of Δ-values and decides ${\tau}^{+}={d}_{k}^{*}$, where k is the index of the first feature satisfying Δ_{ k } ≥ Δ_{0}. Similarly, SAM searches in the descending order of Δ-value and decides the negative cut-off as ${\tau}^{-}={d}_{l}^{*},$ where l is the index of the first feature satisfying Δ_{ l } ≤ -Δ_{0}.
Minimize FDR - miFDR
Theorem 1: Given a FDR cut-off Ψ ∈ (0,1), miFDR always finds the maximum number of significant features.
Eq. (8) indicates that miFDR always finds the maximum number of features given a specific FDR cut-off.
where ${N}_{{\text{\Delta}}_{0}}^{+}$ and ${N}_{{\text{\Delta}}_{0}}^{-}$ respectively are the numbers of positive and negative features called significant by the positive and negative d-value cut-offs decided by Δ_{0}. It should be noted that users need to manually try several Δ-value cut-offs to find the best Δ_{0}. It is obvious that $\left({N}_{{\text{\Delta}}_{0}}^{+},{N}_{{\text{\Delta}}_{0}}^{-}\right)$ is a special case of $\left({N}^{+},{N}^{-}\right)$ in eq. (8). Hence SAM only explores a subset of options considered by miFDR mainly because SAM does not directly tune d-value cut-offs. Instead, SAM control d-value cut-offs via Δ_{0}. Thus the best result of SAM is bounded by the best result of miFDR.
Algorithm 1: [fdr, feature^{ + }, feature^{ - }] = miFDR$\left(\left\{{d}_{i}\right\},\phantom{\rule{2.77695pt}{0ex}}\left\{{\widehat{d}}_{i,b}\right\},N\right)$
- 1)
Initialize fdr ← ∞, N^{+} ← 0, and N^{-} ← 0.
- 2)
Sort {d_{ i }} in the ascending order to obtain $\left\{{d}_{i}^{*}\right\}.$
- 3)
For (n = 0; n ≤ N; n++)
- a)
Select n positive significant features and N - n negative significant features.
- b)Define the corresponding rejection region$\text{\Gamma}\left({d}_{M-n}^{*},\phantom{\rule{2.77695pt}{0ex}}{d}_{N-n+1}^{*}\right)=\left\{d|d>{d}_{M-n}^{*}\phantom{\rule{2.77695pt}{0ex}}or\phantom{\rule{2.77695pt}{0ex}}d<{d}_{N-n+1}^{*}\right\}$
- c)
Estimate FDR "cFDR" for above rejection region using $\left\{{\widehat{d}}_{i,b}\right\}$.
- d)
If cFDR <fdr, then fdr = cFDR, and update N^{+} ← n and N^{-} ← N - n.
- 4)
Let feature^{+} = the indexes of N^{+} features with the largest d-values; and feature^{ - } as the indexes of N^{-} features with the smallest d-values.
Output: fdr - the estimated FDR; feature^{+} - the indexes of positive significant features; feature^{ - } - the indexes of negative significant features.
Computational complexity of miFDR
Assume that a dataset is composed of W samples, each sample has M features, and the samples are permutated P times to generate the control. It takes O(WMP) for miFDR to compute the permuted statistics (the computation time for one feature in one permutation is proportional to the sample size W), and the computation time for the original statistics can be ignored because $P\gg 1$. Once the original and permuted statistics are computed, miFDR can be applied to achieve two typical goals:
• Minimize FDR when finding N significant features: In this case, miFDR needs to explore N + 1 options. For each option, namely a given (N^{+}, N^{-}) pair, the expected computation time for miFDR to estimate FDR is O(MP) because it has to go through the entire permutation matrix. Thus, the computational complexity for miFDR applied to this goal is O(NMP).
• Find the maximal number of significant features given a FDR cut-off: In this case, miFDR needs to examine up to a certain number M_{ ρ }(0 <M_{ ρ }≤ M) in order to find the best result yielding the required FDR cut-off. In the worst-case scenario, miFDR has to estimate FDRs for all $\frac{1}{2}{{M}_{\rho}}^{2}$ possible (N^{+}, N^{-}) airs that satisfy N^{+} + N^{−} = 1,2, ..., M_{ ρ }. If not well implemented, the worst computational complexity for doing this is $O\left({{M}_{\rho}}^{2}MP\right)$, which is much worse than that of the first goal. However, we noticed that both N^{+} and N^{-} can only be chosen from 0, 1, 2, ...M_{ ρ }. Thus, miFDR can be implemented in a very efficient way as below. We can use the permutated measurements to calculate in advance the one-sided false positives for N^{+} = 0,1,2, ..., M_{ ρ }and N^{−} = 0,1,2, ..., M_{ ρ }in each permutation. This will take O(M_{ ρ }MP) in total. Then, to evaluate a given (N^{+}, N^{-}) pair, all we need to do is simply combine the pre-computed false positives for N^{+} and those for N^{-} in each permutation, and then calculate the median of the combined false positives in O(P). Hence, it will take miFDR $O\left({{M}_{\rho}}^{2}P\right)$to cover all $\frac{1}{2}{{M}_{\rho}}^{2}$options. Since M_{ ρ }≤ M, miFDR has a computational complexity of O(M_{ ρ }MP) to check up to M_{ ρ }features, which is comparable to that of the first goal if the desired number of features N ~ M_{ ρ }. Based on the above idea, we designed Algorithm 2. In practice, the value of M_{ ρ }can be easily tuned by users. By default, we set it to 1000, which worked well in practice so far, and the calculation can be finished in a few minutes. Nevertheless, we theoretically proved that M_{ ρ }can be determined automatically and efficiently (see Theorem S1 in Additional File 1 Appendix C).
Algorithm 2: [N, feature^{ + }, feature^{ - }] = miFDR2 $\left(\left\{{d}_{i}\right\},\phantom{\rule{2.77695pt}{0ex}}\left\{{\widehat{d}}_{i,b}\right\},\text{\Psi},{M}_{\rho}\right)$
- 1)
Initialize fdr ← ∞, N^{+} ← 0, and N^{-} ← 0.
- 2)
Calculate P(H = 0).
- 3)
Sort {d_{ i }} in the ascending order to obtain $\left\{{d}_{i}^{*}\right\}.$
- 4)
For (k = 0; k ≤ M_{ ρ }; k++)
- a)
$T{P}_{k}^{+}=$ the number of the original d-values larger than ${d}_{M-k}^{*}.$
- b)
$T{P}_{k}^{-}=$ the number of the original d-values smaller than ${d}_{k+1}^{*}.$
- c)For (b = 0; k ≤ P; b++)
- i.
$F{P}_{k,b}^{+}=$ the number of the d-values in b-th permutation that are larger than ${d}_{M-k}^{*}.$
- ii.
$F{P}_{k,b}^{-}$ = the number of the d-values in b-th permutation that are smaller than ${d}_{k+1}^{*}.$
- i.
- 5)
For (k =M_{ ρ }; k ≥ 0; k −−)
- a)
Initialize $\hat{cFDR}\leftarrow \infty ,{\hat{N}}^{+}\leftarrow 0,\phantom{\rule{2.77695pt}{0ex}}and\phantom{\rule{2.77695pt}{0ex}}{\hat{N}}^{-}\leftarrow 0$
- b)For (n = 0; n ≤ k; n++)
- i.
The estimated FDR can be obtained efficiently as follows:
- ii.
If $cFDR<\hat{cFDR}$, then $\hat{cFDR}\leftarrow \phantom{\rule{2.77695pt}{0ex}}cFDR$, ${\hat{N}}^{+}\leftarrow n$ and ${\hat{N}}^{-}\leftarrow k-n$.
$cFDR=\frac{\text{median}\left({\left\{F{P}_{n,b}^{+}+F{P}_{k-n,b}^{-}\right\}}_{b=1\dots B}\right)\cdot P\left(H=0\right)}{T{P}_{n}^{+}+T{P}_{k-n}^{-}}$ - i.
- c)
$If\phantom{\rule{2.77695pt}{0ex}}\hat{cFDR}<\text{\Psi}$, then $fdr\leftarrow \hat{cFDR}$, ${N}^{+}\phantom{\rule{2.77695pt}{0ex}}\leftarrow {\hat{N}}^{+},{N}^{-}\leftarrow {\hat{N}}^{-}$, and N ← k. Jump to (6).
- 6)
Let feature^{+} = the indexes of N^{+} features with the largest d-values; and feature^{-} = the indexes of N^{-} features with the smallest d-values.
Output: N - the maximum number of significant features satisfying the FDR cut-off Ψ; feature^{ + } - the indexes of positive significant features; feature^{ - } - the indexes of negative significant features.
Results
We compared the miFDR approach to SAM (v4.0), the BH approach and the Storey approach on both simulation test and real microarray data analysis. We selected two-sided t-test p-values for the BH and Storey approaches (implemented in MATLAB Bioinformatics Toolbox v4.2) because we found two-sided t-test has better performance than one-sided t-test, one-sided ranksum test and two-sided ranksum test. The results showed that miFDR outperformed the other three methods in a wide range of FDR cut-offs.
Simulation test
Null and alternative hypotheses in simulated datasets
Category | # of features | Group 1 | Group 2 |
---|---|---|---|
1 | 5000 | Gaussian with mean = 0 and variance = 1 | Gaussian with mean = 0 and variance = 1 |
2 | 5000 | Uniform in range $\left[-\sqrt{3,}\sqrt{3}\right]$ | Uniform in range $\left[-\sqrt{3,}\sqrt{3}\right]$ |
3 | 50 | Gaussian with mean = 0 and variance = 1 | Gaussian with mean = -2 and variance = 1 |
4 | 150 | Gaussian with mean = 0 and variance = 1 | Gaussian with mean = 1 and variance = 1 |
5 | 150 | Uniform in range $\left[-\sqrt{3,}\sqrt{3}\right]$ | Uniform in range $\left[1-\sqrt{3,}1+\sqrt{3}\right]$ |
6 | 50 | Uniform in range $\left[-\sqrt{3,}\sqrt{3}\right]$ | Uniform in range $\left[1.5-\sqrt{3,}1.5+\sqrt{3}\right]$ |
In each simulation, every approach produced a curve describing the estimated FDR vs. the number of significant features. Those 1000 curves were then averaged with respect to the number of significant features. Since the ground-truth was known, we were able to calculate the true FDR and derive the averaged curve to show true FDR vs. the number of significant features for each approach.
We also ran the simulation test with sample size 6 vs. 6 and 10 vs. 10. The results resonated the above findings (see the Additional File 1 Appendix A & B).
Analyze DNA microarray datasets
Numbers of detected significant genes under FDR cut-off = 0.05
Dataset | miFDR | SAM | BH - t-test | Storey - t-test | BH - ranksum | Storey - ranksum |
---|---|---|---|---|---|---|
GDS1517* | 610 | 546 | 20 | 29 | 0 | 0 |
GDS2154 | 684 | 292 | 150 | 300 | 0 | 0 |
GDS2414 | 322 | 286 | 102 | 115 | 0 | 0 |
GDS2470 | 104 | 58 | 4 | 4 | 0 | 0 |
GDS2552 | 787 | 741 | 245 | 508 | 0 | 0 |
GDS2765 | 177 | 112 | 10 | 20 | 0 | 0 |
GDS2778 | 734 | 701 | 57 | 108 | 0 | 13 |
GDS3087 | 74 | 15 | 2 | 4 | 0 | 0 |
GDS3132 | 453 | 420 | 163 | 205 | 0 | 0 |
GDS3295** | 342 | 267 | 149 | 319 | 0 | 0 |
GDS3395 | 463 | 425 | 98 | 98 | 210 | 56 |
GDS3407*** | 283 | 241 | 1 | 1 | 0 | 0 |
GDS3518 | 450 | 420 | 23 | 43 | 0 | 0 |
GDS3663 | 419 | 235 | 0 | 0 | 0 | 0 |
Two of those datasets happen to be related to hypertension: GDS3661 and GDS3689, which caught our attentions. Hypertension accounts for about 25% of heart failures [13]. If uncontrolled, hypertension can cause various changes in myocardial structure, conduction system and coronary vasculature of the heart, which can further cause the development of left ventricular hypertrophy, atherosclerosis and other complications. It has been proved by both experimental animal and clinical studies that left ventricular hypertrophy could induce myocardial ischemia [3], and eventually result in large-scale programmed cell death and heart failure. We therefore want to see if genes called by miFDR in these datasets are indeed biologically relevant. GDS3661 was generated to investigate the molecular activity underlying the onset hypertensive heart failure, by profiling left ventricular samples from rats with spontaneously hypertension [14]. It used Affymetrix Rat Genome 230 2.0 Array to compare the gene expression levels of 6 heart failure rats (HF-rats) with those of 6 rats without heart failure (Control-rats). Hypertension has been proved by many studies to be highly related to environmental pollution, especially diesel exhaust exposure [15–19]. To discover molecular links between hypertension and diesel exhaust exposure, GDS3689 was generated by profiling samples from rats exposed to diesel exhaust particles [20] using Affymetrix Gene Chip Rat 230A microarray. It compared 4 rats exposed to diesel exhaust particles (DE-rats) with 4 rats without exposure (Control-rats). GDS3689 contains samples of both hypertensive rats and healthy rats. In this paper, we only analyzed the samples of healthy rats.
GDS3661
We set the FDR cut-off as 0.05, and compared the number of probe sets called significant by the BH approach, the Storey approach, SAM, and miFDR. Using either t-test or ranksum test, both the BH approach and the Storey approach failed to identify any significant probe set. At the same FDR cut-off, miFDR identified 210 probe sets versus 129 probe sets identified by SAM.
The probe set lists detected by SAM and miFDR were submitted to DAVID [21, 22] for gene ontology (GO) enrichment analysis. The result showed that miFDR was better than SAM in identifying genes with functions closely related to phenotypic changes from compensated hypertrophy to systolic heart failure. Some typical GO categories are: GO-0007179: transforming growth factor beta receptor signaling pathway (miFDR matched 4 genes vs. SAM matched 3 genes), GO-0010647: positive regulation of cell communication (miFDR 10 genes vs. SAM 5 genes), GO-0012501: programmed cell death (miFDR 9 genes vs. SAM 7 genes), GO-0033554: cellular response to stress (miFDR 10 genes vs. SAM 5 genes), and GO-0040008: regulation of growth (miFDR 9 genes vs. SAM 3 genes).
• Mmp2 (up-regulated in HF-rats by 1.88 folds) may play a critical role in preventing hypertensive heart failure. On the one hand, it was reported that classic preconditioning can inhibit ischemia/reperfusion induced release and therefore offer cardio protection [23] (Figure 4, L1). On the other hand, the suppression of Mmp2 activity by angiotensin-converting enzyme inhibitors can prevent left ventricular remodeling in a rat model of heart failure [24] (Figure 4, L2). Thus, we hypothesize that inhibiting Mmp2 may help prevent heart failure from hypertension.
Rtn4 (up-regulated in HF-rats by 1.59 folds) may have great effects on hypertensive heart failure. Programmed cell death of cardiomyocytes following myocardial ischemia imposes a biomechanical stress on the remaining myocardium, leading to myocardial dysfunction that may cause heart failure or sudden death. It was shown that knocking down Rtn4 inhibits the loss of cardiomyocytes following ischemic/hypoxic injury [25]. It was also reported that Rtn 4 expression was significantly increased in cardiac tissue from patients with dilated cardiomyopathy and from patients who have experienced an ischemic event [26, 27] (Figure 4, L6). These evidences suggest that myocardial ischemia may trigger Rtn4-mediated large scale programmed cell death of cardiomyocytes, which eventually leads to heart failure.
Pdlim5 (up-regulated in HF-rats by 2.96 folds) is a heart and skeletal muscle-specific protein that may perform an essential role in heart development [28]. Pdlim5 are related to hypertensive HF in three ways. Firstly, it was reported that Pdlim5 promoted the expression of hypertrophy markers and increased cell volume when overexpressed in rat neonatal cardiomyocytes [29] (Figure 4, L3). Secondly, Pdlim5 protein was found to preferentially interact with protein kinase C beta (PKCB) which is markedly activated in the cardiac hypertrophic signaling [30] (Figure 4, L4). Finally, it was suggested that the protein of Pdlim5 scaffolded protein kinase D 1 (PKD1), a key enzyme in the response to stress signals in cardiomyocytes, to regulate the cardiac L-type voltage-gated calcium channels [31] (Figure 4, L5). There are several drugs for treating hypertension, myocardial ischemia and cardiac arrhythmias by targeting at this channel.
Besides the three genes (Mmp2, Rtn4 and Pdlim5) mentioned above, we also found several other interesting genes in literature, such as Ptgs 1 (up-regulated in HF-rats with 2.06 folds) and Glrx 2 (up-regulated in HF-rats with 1.35 folds). The human homology of Ptgs 1 regulates the physiological process involving the growth of new blood vessels from pre-existing vessels in endothelial cells. Ptgs 1 can mediate endothelial dysfunction under oxidative stress in chronic heart failure [32]. Therefore, Ptgs 1 may have a strong effect on the onset of hypertensive heart failure.
Mitochondrial Glrx 2 plays a crucial role in cardio-protection [33]. It was shown that Doxorubicin-induced cardiac injury is reduced in transgenic mice expressing the human Glrx 2 when compared to non-transgenic mice [34]. Overexpression of human Glrx 2 in transgenic mice reduces myocardial cell death by preventing both apoptosis and necrosis [33]. We think that the up-regulation of Glrx 2 is most likely due to the auto-adjustment of the heart system to compensate for heart failure. However, the endogenous mechanisms in those heart failure rats were not able to raise Glrx 2 up to a level high enough to prevent the onset from happening.
GDS3689
At FDR < 0.05, the BH and Storey approaches using ranksum p-values failed to identify any significant probe set. If t-test p-values were used, the BH and Storey approaches identified 18 and 249 significant probe sets, respectively. At the same FDR level, miFDR identified 640 probe sets while SAM only identified 388. We submitted the probe set lists identified by miFDR and SAM for GO enrichment analysis. The result showed that miFDR outperformed SAM in identifying genes in those functional categories closely related to the response to diesel exhaust exposure and hypertension, such as GO-0006952: defense response (miFDR identified 17 genes vs. SAM identified 8 genes), GO-0006954: inflammatory response (miFDR 12 genes vs. SAM 6 genes), GO-0009967: positive regulation of signal transduction (miFDR 11 genes vs. SAM 4 genes), GO-0009968: negative regulation of signal transduction (miFDR 8 genes vs. SAM 7 genes), GO-0030198: extracellular matrix organization (miFDR 3 genes vs. SAM 0 genes) and GO-0033554: cellular response to stress (miFDR 21 genes vs. SAM 10 genes).
Literature evidences also suggested that several genes identified only by miFDR can elucidate new molecular connections between diesel exhaust exposure and hypertension, in particular through atherosclerosis. Atherosclerosis is one of the most serious hypertension-related health problems. The arteries of hypertensive animals have greater mass of vascular smooth muscle than normotensive ones, and the alteration in the differentiated state (e.g. increased proliferation, enhanced migration and down-regulation of vascular smooth muscle differentiation marker genes) of vascular smooth muscle cells is known to perform a key function in the development of atherosclerosis. In addition, diesel exhaust particles greatly promote atherosclerosis [35–37]. One study showed that the synergy between diesel exhaust particles and oxidized phospholipids affect the expression profiles of several gene modules corresponding to the pathways relevant to vascular inflammatory processes such as atherosclerosis [38].
• Tgfbr1(up-regulated in DE-rats by 2.05 folds) acts as the upstream of p38 in MAPK signaling pathway (http://www.genome.jp/keggbin/show_pathway?hsa04010). It was shown that diesel exhaust particles activate p 38 to produce interleukin 8 and RANTES by human bronchial epithelial cells [39]. Thus, we suggest that diesel exhaust particles trigger p 38 by activating Tgfbr1 (Figure 5, L1). Tgfbr1 also forms a heteromeric receptor complex with TGF-beta type II receptor that mediates TGF-beta signaling (Entrez Gene summary as of May 30th, 2013: http://www.ncbi.nlm.nih.gov/gene/29591) (Figure 5, L2).
• Zeb 1 (up-regulated in DE-rats by 1.43 folds) mediates TGF-beta signaling in vascular disease and vascular smooth muscle cell differentiation during development [40] (Figure 5, L3), which eventually leads to atherosclerosis.
• Hdac 2 (up-regulated in DE-rats by 1.43 folds) was reported to mediate the suppression of vascular smooth muscle cell differentiation marker genes by POVPC [1-palmitoyl-2-(5-oxovaleroyl)-sn-glycero-3-phosphocholine] [41]. POVPC is concentrated within atherosclerotic lesions and contributes to the pathogenesis of atherosclerosis by inducing profound suppression of vascular smooth muscle cell differentiation marker genes via a transcription factor KLF4 [42] (Figure 5, L5).
• Rab5a(up-regulated in DE-rats by 1.83 folds) was shown to have a strong effect on vascular smooth muscle cell proliferation and migration, which can cause intimal hyperplasia and restenosis. And RNAi-mediated Rab5a suppression can inhibit proliferation and migration of vascular smooth muscle cells [43] (Figure 5, L4).
• Ets 1 (up-regulated in DE-rats with 1.69 folds) may be related to atherosclerosis in two ways. On the one hand, Ets 1 was reported to activate platelet-derived growth factor (PDGF) A-chain [44] and PDGF D-chain [45] (Figure 5, L6). PDGF has been implicated in the pathogenesis of vascular occlusive disorders such as atherosclerosis and restenosis in part due to its regulation of vascular smooth muscle cell phenotype. On the other hand, Ets 1 is also involved in the signaling mechanisms whereby angiotensin II, a potent up-regulator of osteopontin, increases osteopontin expression in vascular smooth muscle cells [46] (Figure 5, L5). Several recent studies have revealed that osteopontin performed multiple roles in the progression of atherosclerotic plaques [47–51].
Conclusions
We presented a new powerful FDR control method - miFDR, which minimizes the estimated FDR when calling a fixed number of significant features. We showed theoretically that the search strategy of miFDR maximizes findings given any certain FDR cut-off. We validated this idea by showing that miFDR outperformed the other three widely accepted FDR control methods (SAM, BH and Storey) in simulation tests and DNA microarray analysis. Literature evidences support that several genes identified only by miFDR are indeed relevant to the underlying biology of interest. Controlling FDR is critical in analyzing genome-wide datasets. Therefore, miFDR is an important innovation that will benefit projects utilizing high-throughput technologies and make a broad impact in the future.
Notes
Declarations
Acknowledgements
Yuanzhe Bei's work is partially supported by the Alexander and Shirley Leaderman President's Scholarship and Fellowship at Brandeis University.
Based on "Significance analysis by minimizing false discovery rate", by Yuanzhe Bei and Pengyu Hong, which appeared in Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on. © 2012 IEEE [10].
Declarations
The publication costs for this article were funded by the corresponding author.
This article has been published as part of BMC Systems Biology Volume 7 Supplement 4, 2013: Selected articles from the IEEE International Conference on Bioinformatics and Biomedicine 2012: Systems Biology. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/7/S4.
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References
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