Author: Matt Secrest and Isaac Gravestock

# 3. Specifying prior distributions

#### Matt Secrest and Isaac Gravestock

    library(psborrow2)

In this article, you’ll learn how to specify prior distributions in `psborrow2`.

# Specifying prior distributions

Because `psborrow2` creates fully-parametrized Bayesian models, proper prior distributions on all parameters must be specified.

Prior distributions are needed for several parameters, depending on the analysis:

- beta coefficients (e.g. log hazard ratios or log odds ratios) for all coefficients, passed to `add_covariates()`
- ancillary parameters for outcome distributions, such as the shape parameter for the Weibull survival distribution, passed to `outcome_surv_weibull_ph()`
- log effect estimates (e.g. hazard ratios or odds ratios) for the primary contrast between treatments, passed to `treatment_details()`
- baseline outcome rates or odds, passed to outcome functions
- the hyperprior on the commensurability parameter for Bayesian dynamic borrowing (BDB), passed to `borrowing_hierarchical_commensurate()`

See the documentation of these functions for more information.

# Types of prior distributions

The currently supported prior distributions are created with the `prior_` constructors below:

- `prior_bernoulli()`
- `prior_beta()`
- `prior_cauchy()`
- `prior_exponential()`
- `prior_gamma()`
- `prior_half_cauchy()`
- `prior_half_normal()`
- `prior_normal()`
- `prior_poisson()`

For example, we can create an uninformative normal distribution by specifying a normal prior centered around 0 with a very large standard deviation:

    uninformative_normal <- prior_normal(0, 10000)
    uninformative_normal
    # Normal Distribution
    # Parameters:
    #  Stan  R    Value
    #  mu    mean     0
    #  sigma sd   10000

See the documentation for the respective functions above for additional information.

# Visualizing prior distributions

You may sometimes find it useful to visualize prior distributions. In these scenarios, you can call `plot()` on the prior object to visualize the distribution:

    plot(uninformative_normal)

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`plot()` chooses the default axes for you, but you can change these to make differences more obvious. Let’s compare a conservative `gamma(0.001, 0.001)` hyperprior distribution on the commensurability parameter `tau` to an more aggressive `gamma(1, 0.001)` distribution with greater density at higher values of `tau` (which will lead to more borrowing in a BDB analysis):

    conservative_tau <- prior_gamma(0.001, 0.001)
    aggressive_tau <- prior_gamma(1, 0.001)
    plot(aggressive_tau, xlim = c(0, 2000), col = "blue", ylim = c(0, 1e-03))
    plot(conservative_tau, xlim = c(0, 2000), col = "red", add = TRUE)

plot of chunk unnamed-chunk-4