The Approximate Bayes Factor colocalisation analysis described in the
next section essentially works by fine mapping each trait under a single
causal variant assumption and then integrating over those two posterior
distributions to calculate probabilities that those variants are shared.
Of course, this means we can look at each trait on its own quite simply,
and we can do that with the function `finemap.abf`

.

First we load some simulated data. See the data vignette to understand how to format your datasets.

```
library(coloc)
data(coloc_test_data)
attach(coloc_test_data)
```

```
## The following objects are masked from coloc_test_data (pos = 3):
##
## causals, D1, D2, D3, D4
```

Then we analyse the statistics from a single study, asking about the evidence that each SNP in turn is solely causal for any association signal we see. As we might expect, that evidence is maximised at the SNP with the smallest p value

`plot_dataset(D1)`

```
<- finemap.abf(dataset=D1)
my.res 21:30,] my.res[
```

```
## V. z. r. lABF. snp position prior SNP.PP
## 21 0.006158578 3.105184 0.8155100 3.08656163 s21 21 1e-04 1.026731e-11
## 22 0.006047354 3.010816 0.8182363 2.85613791 s22 22 1e-04 8.154269e-12
## 23 0.017869410 1.247449 0.6037164 0.00691776 s23 23 1e-04 4.720461e-13
## 24 0.005427008 3.746694 0.8337827 4.95497248 s24 24 1e-04 6.651159e-11
## 25 0.005699008 3.168342 0.8268940 3.27341820 s25 25 1e-04 1.237678e-11
## 26 0.004712835 5.305229 0.8524283 11.03926980 s26 26 1e-04 2.919269e-08
## 27 0.006988649 2.570785 0.7957235 1.83530152 s27 27 1e-04 2.937930e-12
## 28 0.004730114 5.483924 0.8519673 11.85562507 s28 28 1e-04 6.604085e-08
## 29 0.004929736 4.771115 0.8466779 8.69908643 s29 29 1e-04 2.811547e-09
## 30 0.005566298 3.176653 0.8302407 3.30234473 s30 30 1e-04 1.274002e-11
```

The `SNP.PP`

column shows the posterior probability that
exactly that SNP is causal. Note the last line in this data.frame does
not correspond to a SNP, but to the null model, that no SNP is
causal.

`tail(my.res,3)`

Finally, if you do have full genotype data as here, while this is a
fast method for fine mapping, it can be sensible to consider multiple
causal variant models too. One package that allows you to do this is GUESSFM, described
in^{5}

The idea behind the ABF analysis is that the association of each trait with SNPs in a region may be summarised by a vector of 0s and at most a single 1, with the 1 indicating the causal SNP (so, assuming a single causal SNP for each trait). The posterior probability of each possible configuration can be calculated and so, crucially, can the posterior probabilities that the traits share their configurations. This allows us to estimate the support for the following cases:

- \(H_0\): neither trait has a genetic association in the region
- \(H_1\): only trait 1 has a genetic association in the region
- \(H_2\): only trait 2 has a genetic association in the region
- \(H_3\): both traits are associated, but with different causal variants
- \(H_4\): both traits are associated and share a single causal variant

`coloc.abf`

functionThe function `coloc.abf`

is ideally suited to the case
when only summary data are available.

```
<- coloc.abf(dataset1=D1,
my.res dataset2=D2)
```

```
## PP.H0.abf PP.H1.abf PP.H2.abf PP.H3.abf PP.H4.abf
## 1.38e-18 2.94e-10 8.59e-12 8.34e-04 9.99e-01
## [1] "PP abf for shared variant: 99.9%"
```

`print(my.res) `

`## Coloc analysis of trait 1, trait 2`

```
##
## SNP Priors
```

```
## p1 p2 p12
## 1e-04 1e-04 1e-05
```

```
##
## Hypothesis Priors
```

```
## H0 H1 H2 H3 H4
## 0.892505 0.05 0.05 0.002495 0.005
```

```
##
## Posterior
```

```
## nsnps H0 H1 H2 H3 H4
## 5.000000e+02 1.377000e-18 2.937336e-10 8.593226e-12 8.338917e-04 9.991661e-01
```

Note that if you do find strong evidence for H4, we can extract the
posterior probabilities for each SNP to be causal *conditional on H4
being true*. This is part of the calculation required by coloc, and
contained in the column SNP.PP.H4 in the “results” element of the
returned list. So we can extract the more likely causal variants by

`subset(my.res$results,SNP.PP.H4>0.01)`

```
## snp position V.df1 z.df1 r.df1 lABF.df1 V.df2 z.df2
## 6 s103 103 0.004846592 7.780900 0.8488730 24.75159 0.004102488 7.560002
## 8 s105 105 0.004808487 8.302463 0.8498828 28.34342 0.004100753 7.699676
## r.df2 lABF.df2 internal.sum.lABF SNP.PP.H4
## 6 0.8513388 23.37551 48.1271 0.01098066
## 8 0.8513923 24.28418 52.6276 0.98894507
```

or the 95% credible set by

```
<- order(my.res$results$SNP.PP.H4,decreasing=TRUE)
o <- cumsum(my.res$results$SNP.PP.H4[o])
cs <- which(cs > 0.95)[1]
w $results[o,][1:w,]$snp my.res
```

`## [1] "s105"`