Get started with bayesian

Paul-Christian Bürkner & Hamada S. Badr

2021-09-29

library(bayesian)
library(recipes)
library(workflows)

As a simple example, we will model the seizure counts in epileptic patients to investigate whether the treatment (represented by variable Trt) can reduce the seizure counts and whether the effect of the treatment varies with the baseline number of seizures a person had before treatment (variable Base) and with the age of the person (variable Age). As we have multiple observations per person, a group-level intercept is incorporated to account for the resulting dependency in the data. In a first step, we use the recipes package to prepare (a recipe for) the epilepsy data. This data set is shipped with the brms package, which is automatically loaded by bayesian.

epi_recipe <- epilepsy %>%
  recipe() %>%
  update_role(count, new_role = "outcome") %>%
  update_role(Trt, Age, Base, patient, new_role = "predictor") %>%
  add_role(patient, new_role = "group") %>%
  step_normalize(Age, Base)
print(epi_recipe)
## Recipe
## 
## Inputs:
## 
##       role #variables
##      group          1
##    outcome          1
##  predictor          4
## 
##   4 variables with undeclared roles
## 
## Operations:
## 
## Centering and scaling for Age, Base

Above, we not only define the roles of the relevant variables but also normalized the Age and Base predictors to facilitate model fitting later on. In the next step, we use bayesian to set up a basic model structure.

epi_model <- bayesian(
    family = poisson()
  ) %>%
  set_engine("brms") %>%
  set_mode("regression")
print(epi_model)
## Bayesian Model Specification (regression)
## 
## Main Arguments:
##   family = poisson()
## 
## Computational engine: brms

The bayesian function is the main function of the package to initialize a Bayesian model. We can set up a lot of the information directly within the function or update the information later on, via the update method. For example, if we didn't specify the family initially or set it to something else that we now wanted to change, we could use the update method as follows

epi_model <- epi_model %>%
  update(family = poisson())

Next, we define a workflow via the workflows package, by combining the above defined data processing recipe and the model plus the actual model formula to be passed to the brms engine.

epi_workflow <- workflow() %>%
  add_recipe(epi_recipe) %>%
  add_model(
    spec = epi_model,
    formula = count ~ Trt + Base + Age + (1 | patient)
  )
print(epi_workflow)
## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: bayesian()
## 
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 1 Recipe Step
## 
## • step_normalize()
## 
## ── Model ───────────────────────────────────────────────────────────────────────
## Bayesian Model Specification (regression)
## 
## Main Arguments:
##   family = poisson()
## 
## Computational engine: brms

We are now ready to fit the model by calling the fit method with the data set we want to train the model on.

epi_workflow_fit <- epi_workflow %>%
  fit(data = epilepsy)
## Compiling Stan program...
## Start sampling
print(epi_workflow_fit)
## ══ Workflow [trained] ══════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: bayesian()
## 
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 1 Recipe Step
## 
## • step_normalize()
## 
## ── Model ───────────────────────────────────────────────────────────────────────
##  Family: poisson 
##   Links: mu = log 
## Formula: count ~ Trt + Base + Age + (1 | patient) 
##    Data: ~data (Number of observations: 236) 
##   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 4000
## 
## Group-Level Effects: 
## ~patient (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.58      0.07     0.46     0.72 1.00      890     1522
## 
## Population-Level Effects: 
##           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     1.78      0.12     1.55     2.00 1.01      683     1247
## Trt1         -0.27      0.17    -0.60     0.05 1.00      626     1142
## Base          0.73      0.08     0.57     0.89 1.00      809     1323
## Age           0.08      0.08    -0.07     0.24 1.00      755     1475
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

To extract the parsnip model fit from the workflow

epi_fit <- epi_workflow_fit %>%
  extract_fit_parsnip()

The brmsfit object is stored in the fit slot

epi_brmsfit <- epi_fit$fit
class(epi_brmsfit)
## [1] "brmsfit"

We can use the trained workflow, which includes the fitted model, to conveniently predict using new data without having to worry about all the data reprocessing, which is automatically applied using the workflow preprocessor (recipe).

newdata <- epilepsy[1:5, ]
epi_workflow_fit %>%
  predict(
    new_data = newdata,
    type = "conf_int",
    level = 0.95
  )
## # A tibble: 5 × 2
##   .pred_lower .pred_upper
##         <dbl>       <dbl>
## 1           0           8
## 2           0           8
## 3           0           7
## 4           0           8
## 5           6          22

To add the standard errors on the scale of the linear predictors

epi_workflow_fit %>%
  predict(
    new_data = newdata,
    type = "conf_int",
    level = 0.95,
    std_error = TRUE
  )
## # A tibble: 5 × 3
##   .pred_lower .pred_upper .std_error
##         <dbl>       <dbl>      <dbl>
## 1           0           8       2.05
## 2           0           8       2.10
## 3           0           7       1.83
## 4           0           8       2.05
## 5           6          22       4.09