mixstanvar: Mixture distributions as 'brms' priors

In RBesT: R Bayesian Evidence Synthesis Tools

Mixture distributions as brms priors

Description

Adapter function converting mixture distributions for use with brm models via the stanvar facility.

Usage

mixstanvar(..., verbose = FALSE)

Arguments

...	List of mixtures to convert.
verbose	Enables printing of the mixture priors when chains start to sample. Defaults to FALSE.

Details

To declare mixture priors in a brm model requires two steps: First, the mixture densities need to be converted by the adapter function mixstanvar into a stanvars object which is passed to the stanvars argument of the brm function. Doing so extends the Stan code and data generated by brm such that the mixture densities can be used as priors within the brm model. The second step is to assign parameters of the brm model to the mixture density as prior using the set_prior command of brms.

The adapter function translates the mixture distributions as defined in R to the respective mixture distribution in Stan. Within Stan the mixture distributions are named in accordance to the R functions used to create the respective mixture distributions. That is, a mixture density of normals created by mixnorm is referred to as mixnorm_lpdf in Stan such that one can refer to the density as mixnorm within the set_prior functions (the suffix _lpdf is automatically added by brm). The arguments to these mixture distributions depend on the specific distribution type as follows:

Density	Arguments
mixbeta(w, a, b)	w weights, a shapes, b shapes
mixgamma(w, a, b)	w weights, a shapes, b inverse scales
mixnorm(w, m, s)	w weights, m means, s standard deviations
mixmvnorm(w, m, sigma_L)	w weights, m means, sigma_L cholesky factors of covariances

These arguments to the mixture densities refer to the different density parameters and are automatically extracted from the mixtures when converted. Important here are the argument names as these must be used to declare the mixture prior. For each mixture to convert as part of the ... argument to mixstanvar a label is determined using the name given in the list. In case no name is given, then the name of the R object itself is used. To declare a prior for a parameter the mixture distribution must be used with it's arguments following the convention label_argument. Please refer to the examples section for an illustration.

Note: Models created by brm do use by default a data-dependent centering of covariates leading to a shift of the overall intercept. This is commonly not desirable in applications of this functionality. It is therefore strongly recommended to pass the option center=FALSE as argument to the brms formula created with the bf function as demonstrated with the example below.

Value

stanvars object to be used as argument to the stanvars argument of a brm model.

Examples

## Not run: 
# The mixstanvar adapter requires the optional packages brms and glue
stopifnot(require("brms"), require("glue"))

# Assume we prefer a logistic regression MCMC analysis rather than a
# beta-binomial analysis for the responder endpoint of the ankylosing
# spondylitis (AS) example. Reasons to prefer a regression analysis is
# to allow for baseline covariate adjustments, for example.
map_AS_beta <- mixbeta(c(0.62, 19.2, 57.8), c(0.38, 3.5, 9.4))

# First we need to convert the beta mixture to a respective mixture on
# the log odds scale and approximate it with a normal mixture density.
map_AS_samp <- rmix(map_AS_beta, 1E4)
map_AS <- mixfit(logit(map_AS_samp), type="norm", Nc=2)

# Trial results for placebo and secukinumab.
trial <- data.frame(n=c(6, 24),
                    r=c(1, 15),
                    arm=factor(c("placebo", "secukinumab")))

# Define brms model such that the overall intercept corresponds to the
# placebo response rate on the logit scale. NOTE: The use of
# center=FALSE is required here as detailed in the note above.
model <- bf(r | trials(n) ~ 1 + arm, family=binomial, center=FALSE)
# to obtain detailed information on the declared model parameters use
# get_prior(model, data=trial)
# declare model prior with reference to mixture normal map prior...
model_prior <- prior(mixnorm(map_w, map_m, map_s), coef=Intercept) +
    prior(normal(0, 2), class=b)

# ... which must be made available to brms using the mixstanvar adapter.
# Note that the map_AS prior is labeled "map" as referred to in the
# previous prior declaration.
analysis <- brm(model, data=trial, prior=model_prior,
                stanvars=mixstanvar(map=map_AS),
                seed=365634, refresh=0)

# Let's compare the logistic regression estimate for the probability
# of a positive treatment effect (secukinumab response rate exceeding
# the response rate of placebo) to the direct beta-binomial analysis:
hypothesis(analysis, "armsecukinumab > 0")

post_secukinumab <- postmix(mixbeta(c(1, 0.5, 1)), r=15, n=24)
post_placebo     <- postmix(map_AS_beta, r=1, n=6)
pmixdiff(post_secukinumab,  post_placebo, 0, lower.tail=FALSE)
# The posterior probability for a positive treatment effect
# is very close to unity in both cases.

## End(Not run)

RBesT documentation built on May 29, 2024, 10:40 a.m.