pvalue2zs function

Transfer p-value of KOs to Z-score

pvalue2zs(
  ko_pvalue,
  mode = c("directed", "mixed")[1],
  p.adjust.method1 = "none"
)

Arguments

• ko_pvalue: data.frame from ko.test, KO_id and p.value columns are required.
• mode: 'mixed' or 'directed' (default, only for two groups differential analysis or multi-groups correlation analysis.), see details in pvalue2zs.
• p.adjust.method1: p.adjust.method for ko.test, see p.adjust

Returns

ko_stat data.frame

Details

'mixed ' mode is the original reporter-score method from Patil, K. R. et al. PNAS 2005. In this mode, the reporter score is undirected , and the larger the reporter score, the more significant the enrichment, but it cannot indicate the up-and-down regulation information of the pathway! (Liu, L. et al. iMeta 2023.)

steps:

1. Use the Wilcoxon rank sum test to obtain the P value of the significance of each KO difference between the two groups (ie $P_{koi}$, i represents a certain KO);

2. Using an inverse normal distribution, convert the P value of each KO into a Z value ($Z_{koi}$), the formula:

$Z_{koi}=\theta ^{-1}(1-P_{koi})$

3. 'Upgrade' KO to pathway: $Z_{koi}$, calculate the Z value of the pathway, the formula:

$Z_{pathway}=\frac{1}{\sqrt{k}}\sum Z_{koi}$

where k means A total of k KOs were annotated to the corresponding pathway;

4. Evaluate the degree of significance: permutation (permutation) 1000 times, get the random distribution of $Z_{pathway}$, the formula:

$Z_{adjustedpathway}=(Z_{pathway}-\mu _k)/\sigma _k$

$\mu _k$ is The mean of the random distribution, $\sigma _k$ is the standard deviation of the random distribution.

Instead, 'directed ' mode is a derived version of 'mixed', referenced from https://github.com/wangpeng407/ReporterScore.

This approach is based on the same assumption of many differential analysis methods: the expression of most genes has no significant change.

steps:

1. Use the Wilcoxon rank sum test to obtain the P value of the significance of each KO difference between the two groups (ie $P_{koi}$, i represents a certain KO), and then divide the P value by 2, that is, the range of (0,1] becomes (0,0.5], $P_{koi}=P_{koi}/2$;

2. Using an inverse normal distribution, convert the P value of each KO into a Z value ($Z_{koi}$), the formula:

$Z_{koi}=\theta ^{-1}(1-P_{koi})$

since the above P value is less than 0.5, all Z values will be greater than 0;

3. Considering whether each KO is up-regulated or down-regulated, calculate $diff\_KO$,

$Z_{koi}=-Z_{koi}\ \ \ \ (diff\_KO<0)$,

so $Z_{koi}$ is greater than 0 Up-regulation, $Z_{koi}$ less than 0 is down-regulation;

4. 'Upgrade' KO to pathway: $Z_{koi}$, calculate the Z value of the pathway, the formula:

$Z_{pathway}=\frac{1}{\sqrt{k}}\sum Z_{koi}$

where k means A total of k KOs were annotated to the corresponding pathway;

5. Evaluate the degree of significance: permutation (permutation) 1000 times, get the random distribution of $Z_{pathway}$, the formula:

$Z_{adjustedpathway}=(Z_{pathway}-\mu _k)/\sigma _k$

$\mu _k$ is The mean of the random distribution, $\sigma _k$ is the standard deviation of the random distribution.

The finally obtained $Z_{adjustedpathway}$ is the Reporter score value enriched for each pathway. In this mode, the Reporter score is directed, and a larger positive value represents a significant up-regulation enrichment, and a smaller negative values represent significant down-regulation enrichment.

However, the disadvantage of this mode is that when a pathway contains about the same number of significantly up-regulates KOs and significantly down-regulates KOs, the final absolute value of Reporter score may approach 0, becoming a pathway that has not been significantly enriched.

Examples

data("KO_abundance_test")
ko_pvalue <- ko.test(KO_abundance, "Group", metadata)
ko_stat <- pvalue2zs(ko_pvalue, mode = "directed")

References

1. Patil, K. R. & Nielsen, J. Uncovering transcriptional regulation of metabolism by using metabolic network topology. Proc Natl Acad Sci U S A 102, 2685–2689 (2005). 2. Liu, L., Zhu, R. & Wu, D. Misuse of reporter score in microbial enrichment analysis. iMeta n/a, e95. 3. https://github.com/wangpeng407/ReporterScore

See Also

Other GRSA: combine_rs_res(), get_reporter_score(), ko.test(), reporter_score()