SimReg has a function sim_reg for performing Bayesian Similarity Regression [1]. The aim is to estimate the probability of an association between ontological term sets and a binary variable, and should such an association exist, a characteristic ontological profile such that ontological similarity to the profile increases the probability of the binary variable taking the value TRUE. The procedure has been used in the context of linking an ontologically encoded phenotype (as HPO terms) to a binary genotype (indicating the presence or absence of a rare variant within given genes) [1], so in this guide, we’ll adopt the same theme.

sim_reg is an MCMC routine which accepts many arguments including the response variable y (logical), the ontologically encoded predictor variable x (a list), ones controlling the sampling pattern, ones controlling the tuning of the parameter proposal schemes and others specifying the prior distributions of the parameters.

It returns a list of traces for the sampled parameters as an object of class sim_reg_samples (typically, this requires a lot of memory, and hence it may be preferable to store a summarised version by passing it to summary). Of particular interest is the estimated probability of association - i.e. the posterior mean value of gamma - the model selection indicator. This can be obtained by calling the function P(gamma=1) on the object returned by sim_reg (or on its summarised form). Also, the posterior distribution of the characteristic ontological profile phi may be of interest.

Most of the arguments have default values, so calling of the function can be demonstrated with passing only a few. To set up an environment where we can run a simple example, we need an ontology_index object. The ontologyIndex package contains such an instance - the Human Phenotype Ontology, hpo - so we load the package and the data, and proceed to create an HPO profile template and an enclosing set of terms, terms, from which we’ll generate random term sets upon which to apply the function. In our setting, we’ll interpret this HPO profile template as the typical phenotype of a hypothetical disease. We set template to the set HP:0005537, HP:0000729 and HP:0001873, corresponding to phenotype abnormalities ‘Decreased mean platelet volume’, ‘Autistic behavior’ and ‘Thrombocytopenia’ respectively.

library(ontologyIndex)
library(SimReg)
data(hpo)
set.seed(1)

template <- c("HP:0005537", "HP:0000729", "HP:0001873")
terms <- get_ancestors(hpo, c(template, sample(hpo$id, size=50)))

First, we’ll do an example where there is no association between x and y, and then one where there is an association.

In the example with no association, we’ll fix y, with 10 TRUEs and generate the x randomly, with each set of ontological terms determined by sampling 5 random terms from terms.

y <- c(rep(TRUE, 10), rep(FALSE, 90))
x <- replicate(simplify=FALSE, n=100, expr=minimal_set(hpo, sample(terms, size=5)))

Thus, our input data looks like:

y
##   [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
##  [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [23] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [67] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [78] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [89] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100] FALSE
head(x)
## [[1]]
## [1] "HP:0010337" "HP:0011947" "HP:0003256" "HP:0001155"
## 
## [[2]]
## [1] "HP:0004268" "HP:0011185" "HP:0100393" "HP:0008457" "HP:0002564"
## 
## [[3]]
## [1] "HP:0011304" "HP:0005420" "HP:0040133" "HP:0006563" "HP:0005625"
## 
## [[4]]
## [1] "HP:0004303" "HP:0010337" "HP:0000284" "HP:0012387"
## 
## [[5]]
## [1] "HP:0012823" "HP:0005938" "HP:0006563" "HP:0001991"
## 
## [[6]]
## [1] "HP:0040070" "HP:0012387" "HP:0030266" "HP:0000492" "HP:0009418"

Now we can call the sim_reg function to estimate the probability of an association (note: by default, the probability of an association has a prior of 0.05 and this can be set by passing a gamma_prior_prob argument), and print the mean posterior value of gamma, corresponding to our estimated probability of association.

no_assoc <- sim_reg(ontology=hpo, x=x, y=y)
`P(gamma=1)`(no_assoc)
## [1] 0.0416875

We note that there is a low probability of association. Now, we sample x conditional on y, so that if y[i] == TRUE, then x has 2 out of the 3 terms in template added to its profile.

x_assoc <- lapply(y, function(y_i) minimal_set(hpo, c(
    sample(terms, size=5), if (y_i) sample(template, size=2))))

If we look again at the first few values in x for which y[i] == TRUE, we notice that they contain terms from the template.

head(x_assoc)
## [[1]]
## [1] "HP:0000177" "HP:0001943" "HP:0008450" "HP:0010321" "HP:0001873"
## [6] "HP:0005537"
## 
## [[2]]
## [1] "HP:0002758" "HP:0004379" "HP:0001172" "HP:0000078" "HP:0001873"
## [6] "HP:0005537"
## 
## [[3]]
## [1] "HP:0010460" "HP:0012256" "HP:0000492" "HP:0009832" "HP:0100781"
## [6] "HP:0005537" "HP:0001873"
## 
## [[4]]
## [1] "HP:0010321" "HP:0003130" "HP:0008362" "HP:0005920" "HP:0006500"
## [6] "HP:0005537" "HP:0000729"
## 
## [[5]]
## [1] "HP:0009332" "HP:0001873" "HP:0006498" "HP:0000152" "HP:0005537"
## 
## [[6]]
## [1] "HP:0100523" "HP:0000271" "HP:0009832" "HP:0001873" "HP:0005537"

Now we run the procedure again with the new x and y and print the mean posterior value of gamma.

assoc <- sim_reg(ontology=hpo, x=x_assoc, y=y)
`P(gamma=1)`(assoc)
## [1] 1

We note that we infer a higher probability of association. We can also visualise the estimated characteristic ontological profile, using the function phi_plot, and note that the inferred characteristic phenotype corresponds well to template.

phi_plot(hpo, assoc$phi[assoc$gamma], max_terms=8, fontsize=30)

Note that we must subset the $phi slot by $gamma, as the characteristic ontological profile phi has no effect if gamma == FALSE. A more comprehensive summary of the output can be exported to pdf using the function sim_reg_summary.

summary can also be called print out information about the inference.

print(summary(assoc), ontology=hpo)
## --------------------------------------------------------------------------- 
## P(gamma=1|y) =  1 
## --------------------------------------------------------------------------- 
## Numeric parameters:
##              Parameter  Mean   SD
##                  alpha -6.51 2.02
##               log_beta  3.39 0.66
##           logit_mean_f  0.05 0.60
##  log_alpha_plus_beta_f  2.10 0.95
##           logit_mean_g -1.86 0.93
##  log_alpha_plus_beta_g  1.96 1.02
## --------------------------------------------------------------------------- 
## Phi:
##           t                                                    Name    P
##  HP:0001873                                        Thrombocytopenia 0.70
##  HP:0005537                          Decreased mean platelet volume 0.68
##  HP:0011873                                 Abnormal platelet count 0.30
##  HP:0011876                                Abnormal platelet volume 0.28
##  HP:0000729                                       Autistic behavior 0.24
##  HP:0000708                                  Behavioral abnormality 0.15
##  HP:0000707                       Abnormality of the nervous system 0.14
##  HP:0012638                Abnormality of nervous system physiology 0.12
##  HP:0008362                        Aplasia/Hypoplasia of the hallux 0.05
##  HP:0009343 Small epiphysis of the distal phalanx of the 3rd finger 0.03
## ---------------------------------------------------------------------------

References

  1. D. Greene, NIHR BioResource, S. Richardson, E. Turro, Phenotype similarity regression for identifying the genetic determinants of rare diseases, The American Journal of Human Genetics 98, 1-10, March 3, 2016.