4. Interpretation of Output

Outputs

Posterior Probabilities

The posterior probabilities for snps to be causal will be output to a .results and will contain the input data with an additional Posterior_Prob column appended.

Example: A results file for a locus of 4 SNPs

CHR POS RSID ZSCORE.P1 ZSCORE.P2 Posterior_Prob
chr1  10 rs1 1.5 3.0 0.013
chr1  15 rs2 -3.2 -1.5 0.130
chr1  20 rs3 4.5 5.5 0.980
chr1  25 rs4 0.8 -0.5 0.002

Gamma Estimates

A file that has the effect size estimates for each of the annotation(s) used. PAINTOR automatically estimates the baseline annotation (A0) and will always output this values as the first line in the file.

Example: Estimates for 1 annotation (+1 baseline) {Baseline, A1}

Baseline A1 
5.2 -1.3

These effect sizes can be converted to probabilities using the expit transformation. For the preceding output the corresponding prior probabilities can be calculated as follows:

The baseline prior probability for any SNP in the fine-mapping dataset to be causal is obtained as:

1/(1 + exp(γ₀)) = 1/(1 + exp(5.2))

= 0.0055

The prior probability for a SNP in A1 is causal is given by:

1/(1 + exp(γ₀ + γ₁)) = 1/(1 + exp(5.2 + (-1.3)))

= 0.01984

Thus, the relative probability for a SNP to be causal given that it is in A1 is simply computed as:

0.01984/0.0055 = 3.6

Final log-bayes factor

This file contains the sum of the log bayes factors. Becasue we do maximum likelihood estimation over the enrichment parameters and the Bayes Factors are proportional to the full likelihood, it follows that we can still construct a likelihood ratio test to assess significance of the annotation effect sizes. To test the marginal significance of a single annotation (A1) one would first fit a PAINTOR model with just the baseline annotation (M0) then fit a joint model with both annotations A0, A1 (M1). The resultant log bayes factors for each model can be used to compute an LRT statistic which will be distributed asymptotically χ² with degrees of freedom = 1 (under the null).

Example: Testing significance of annotation A1

Model 0 sum log bayes factors with only baseline annotation (Baseline)

$> cat OutDirectory/BF.Base

6043.7

Model 1 sum log bayes factors with both annotations(Baseline, A1)

$> cat OutDirectory/BF.A1

6054.2

Now to compute the signfiance of the enrichment simply construct the standard ratio test comparing the null and alternate models.

LRT = -2[logBF(M0)) - (logBF(M1))]

= -2[6043.7 - (6054.2)] = 21

~ χ² (df=1) p-value = 4.59e-06