How to calculate p value and correlation coefficient for Spearman’s correlation of differential expression data with 40000 permutations?

Question

I have 3 groups,let's call them g1, g2, g3. Each of them is a result of analysis in between groups of conditions, and g1 looks like this

                   geneSymbol      logFC         t      P.Value   adj.P.Val         Beta
EXykpF1BRREdXnv9Xk      MKI67 -0.3115880 -5.521186 5.772137e-07 0.008986062 4.3106665
0Tm7hdRJxd9zoevPlA     CCL3L3  0.1708020  4.162115 9.109798e-05 0.508784638 0.6630544
u_M5UdFdhg3lZ.qe64     UBE2G1 -0.1528149 -4.031466 1.430822e-04 0.508784638 0.3354065
lkkLCXcnzL9NXFXTl4     SEL1L3 -0.2138729 -3.977482 1.720517e-04 0.508784638 0.2015945
0Uu3XrB6Bd14qoNeuc      ZFP36  0.1667330  3.944917 1.921715e-04 0.508784638 0.1213335
3h7Sgq2i3sAUkxL_n8      ITGB5  0.3419488  3.938960 1.960886e-04 0.508784638 0.1066896

g2 and g2 look the same and each has 15568 entries (genes)

How to calculate p value and correlation coefficient for Spearman’s correlation for this data for 40000 permutations?

I joined all 3 groups, g1, g2, g3, and extracted only Beta (B)

I got this data frame, with matching 15568 entries:

                     Beta1       Beta2    Beta3
EXykpF1BRREdXnv9Xk -4.970533 -4.752771 -5.404054
0Tm7hdRJxd9zoevPlA -4.862168 -5.147294 -3.909654
u_M5UdFdhg3lZ.qe64 -5.368846 -5.396183 -5.405330
lkkLCXcnzL9NXFXTl4 -4.367704 -4.847795 -5.148524
0Uu3XrB6Bd14qoNeuc -5.286592 -4.949305 -5.278798
3h7Sgq2i3sAUkxL_n8 -4.579528 -2.403240 -4.710600

To calculate Spearman’s I could use in R:

> cor(d,use="pairwise.complete.obs",method="spearman")
        Beta1          Beta2        Beta3
Beta1 1.000000000  0.234171932  0.002474729
Beta2 0.234171932  1.000000000 -0.005469126
Beta3 0.002474729 -0.005469126  1.000000000

Can someone please tell me what would be the method to use to get correlation coefficient and p value taken in account number of permutations? And am I am correct to use Beta in order to do correlation in between these 3 groups?

Thanks!

Answer 1

A hint to access the correlation coefficient and p-value using the psych package. I'm going to use the mtcars dataset instead of re-typing your dataset as it is not in an easy copy-paste (dput(df)) format.

library(psych)
corr.test.col.1to4 <- corr.test(mtcars[1:4], method = "spearman", use = "complete.obs")
names(corr.test.col.1to4)
#1] "r"      "n"      "t"      "p"      "se"     "sef"    "adjust" "sym"    "ci"     "ci.adj"
# [11] "Call"  

# -------------------------------------------------------------------------
# in your case you probably want to do

#cor.test.beta <- corr.test(d[c("Beta1","Beta2", "Beta3")], method = "spearman", use = "complete.obs")

# -------------------------------------------------------------------------

As you can see from the output of names(corr.test.col.1to4):

r: correlation coefficient

n: number of observation

p: p.value

se: standard error

ci: confidence intervals

So, if you want the correlation coefficient you can pull the values out using

corr.test.col.1to4$r
#             mpg        cyl       disp         hp
# mpg   1.0000000 -0.9108013 -0.9088824 -0.8946646
# cyl  -0.9108013  1.0000000  0.9276516  0.9017909
# disp -0.9088824  0.9276516  1.0000000  0.8510426
# hp   -0.8946646  0.9017909  0.8510426  1.0000000

The p-values

corr.test.col.1to4$p
#               mpg          cyl         disp           hp
# mpg  0.000000e+00 2.345144e-12 2.548135e-12 1.017194e-11
# cyl  4.690287e-13 0.000000e+00 1.365266e-13 5.603057e-12
# disp 6.370336e-13 2.275443e-14 0.000000e+00 6.791338e-10
# hp   5.085969e-12 1.867686e-12 6.791338e-10 0.000000e+00

The standard errors

corr.test.col.1to4$se
#             mpg        cyl       disp         hp
# mpg  0.00000000 0.07537483 0.07614303 0.08156289
# cyl  0.07537483 0.00000000 0.06818175 0.07890355
# disp 0.07614303 0.06818175 0.00000000 0.09586909
# hp   0.08156289 0.07890355 0.09586909 0.00000000

The confidence intervals

corr.test.col.1to4$ci
#               lower          r      upper            p
# mpg-cyl  -0.9559077 -0.9108013 -0.8237102 4.690287e-13
# mpg-disp -0.9549362 -0.9088824 -0.8200941 6.370336e-13
# mpg-hp   -0.9477078 -0.8946646 -0.7935207 5.085969e-12
# cyl-disp  0.8557708  0.9276516  0.9643958 2.275443e-14
# cyl-hp    0.8067919  0.9017909  0.9513377 1.867686e-12
# disp-hp   0.7143279  0.8510426  0.9251848 6.791338e-10

You can save the output on a variable and do further formatting to make the reporting just.

Your second question Am I correct to use Beta in order to do correlation in between these 3 groups? is a valid question which you need to answer/address depending on the question you want to answer as well as report it in such a way that the corr is computed on variable Beta and justify the choice of the variable Beta in your report.

Hope that helps.