AESPCA function - Add Non-Parametric p-Value Option

[gabrielodom]

Per the PGDAC meeting with Bing's group, Steven mentioned that we should compare the raw (parametric) $p$-values to the permutation $p$-values to see if there is a clear relationship. Thus we need an option to AESPCA_pVals() to request the raw $p$-value.

[gabrielodom]

See the Identification of DMRs subsection in https://www.nature.com/articles/mp2013114.pdf

[gabrielodom]

We have three components to analyse here:

1. CoxPH Model overall p-values (PermTestSurv())
2. GLM overall p-values (PermTestCateg())
3. LM overall p-values (PermTestReg())

Based on the results in the testing files Test_PermTestSurv_Parametric.R and Test_PermTestCateg_Parametric.R, the Pearson correlation between the raw parametric and raw permutation-based p-values for CoxPH and GLM is very high (0.95 or better, even for 100 replicates). However, the FDRs in the GLM case are not as strongly correlated (0.67 for 100 replicates, 0.85 for 1000). I do not yet have results for the LM case.

[lxw391]

@gabrielodom Please update function using anova(true_mod, test = "LRT")

Also please change AIC to anova function instead to perform LRT test.

[gabrielodom]

Because this is not related to the parametric p-value estimation discussion, I've created a new issue: Issue #57.

[gabrielodom]

For the LM, see Test_PermTestReg_Parametric.R.

Now, all three methods support parametric p-value estimation. To estimate the pathway p-values parametrically, set numReps = 0 in the AESPCA_pVals() function call. Overall, the raw p-values between the parametric and non-parametric options are nearly perfectly correlated (rho > 0.98 even for 100 replicates).

[gabrielodom]

As we see in the attached image, test size does not appear to be a major concern.