Multiple testing correction

[nfancy]

Hi,

Thank you very much for this very useful package. We are using this for comparing the differential cell type proportion in single nuclei RNA sequencing data. A common example can be found here here. I was wondering do we need multiple testing correction for the p-values obtained from each of the cell types? For example see the summary below:

> summary(dirichlet_res)

Call:
DirichletReg::DirichReg(formula = dirichlet_dt ~ diagnosis + brain_region + sex + age + PMI + RIN,
data = sn_ct_prop)

Standardized Residuals:
              Min       1Q   Median       3Q     Max
Astro     -1.8915  -0.5861  -0.0432   0.4115  2.9265
Micro     -1.9210  -0.6087  -0.1745   0.4216  2.1042
Oligo     -3.8777  -1.2850  -0.0789   1.8296  5.8966
OPC       -1.3329  -0.6777  -0.2168   0.1330  4.8122
Vasc      -1.6562  -0.6634  -0.3561   0.2591  2.9518

------------------------------------------------------------------
Beta-Coefficients for variable no. 1: Astro
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)        1.37217    0.30822   4.452 8.51e-06 ***
diagnosisAD       -0.46457    0.18704  -2.484 0.013000 *  
brain_regionmTemp  0.16425    0.18080   0.908 0.363626    
brain_regionSSC    0.49240    0.17622   2.794 0.005202 ** 
sexM               0.81271    0.19663   4.133 3.58e-05 ***
age                0.45041    0.11205   4.020 5.83e-05 ***
PMI                0.04278    0.01148   3.727 0.000194 ***
RIN                0.29228    0.08503   3.437 0.000587 ***
------------------------------------------------------------------
Beta-Coefficients for variable no. 2: Micro
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)        0.40135    0.37210   1.079 0.280766    
diagnosisAD       -0.37726    0.20383  -1.851 0.064187 .  
brain_regionmTemp  0.06662    0.19641   0.339 0.734464    
brain_regionSSC    0.00659    0.19295   0.034 0.972755    
sexM               1.08002    0.23322   4.631 3.64e-06 ***
age                0.58778    0.12377   4.749 2.05e-06 ***
PMI                0.04783    0.01384   3.457 0.000547 ***
RIN                0.49261    0.09790   5.032 4.86e-07 ***
------------------------------------------------------------------
Beta-Coefficients for variable no. 3: Oligo
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)        2.00718    0.33585   5.976 2.28e-09 ***
diagnosisAD       -0.41222    0.19433  -2.121 0.033898 *  
brain_regionmTemp  0.05895    0.17865   0.330 0.741409    
brain_regionSSC    0.30981    0.17623   1.758 0.078757 .  
sexM               0.94630    0.21737   4.353 1.34e-05 ***
age                0.42127    0.11598   3.632 0.000281 ***
PMI                0.02792    0.01170   2.387 0.017000 *  
RIN                0.44467    0.07923   5.613 1.99e-08 ***
------------------------------------------------------------------
Beta-Coefficients for variable no. 4: OPC
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)        0.93467    0.34043   2.746 0.006041 ** 
diagnosisAD       -0.50381    0.19249  -2.617 0.008862 ** 
brain_regionmTemp  0.01828    0.19774   0.092 0.926360    
brain_regionSSC    0.23676    0.19280   1.228 0.219448    
sexM               0.77014    0.21564   3.571 0.000355 ***
age                0.33099    0.12007   2.757 0.005839 ** 
PMI                0.03451    0.01262   2.735 0.006246 ** 
RIN                0.12266    0.09404   1.304 0.192130    
------------------------------------------------------------------
Beta-Coefficients for variable no. 5: Vasc
                  Estimate Std. Error z value Pr(>|z|)   
(Intercept)       -0.08012    0.41009  -0.195  0.84510   
diagnosisAD       -0.31873    0.22023  -1.447  0.14783   
brain_regionmTemp -0.07216    0.24141  -0.299  0.76502   
brain_regionSSC    0.38433    0.23053   1.667  0.09548 . 
sexM               0.75324    0.24958   3.018  0.00254 **
age                0.38217    0.14067   2.717  0.00659 **
PMI                0.03057    0.01519   2.013  0.04412 * 
RIN                0.27600    0.12116   2.278  0.02273 * 
------------------------------------------------------------------
Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log-likelihood: 1564 on 104 df (462 BFGS + 2 NR Iterations)
AIC: -2921, BIC: -2718
Number of Observations: 52
Link: Log
Parametrization: common

So, if I extract the p-values for diagnosisAD for each cell type, do we need to do a multiple-testing correction. Thanks in advance.

Nurun