designPrior {BayesRepDesign}

Design prior for effect size

Description

Creates a design prior for the effect size which can then be used for power and sample size calculations of a replication study. The design prior is obtained from updating an initial prior for the effect size by the data from the original study. A normal-normal hierarchical model is assumed, see Pawel et al. (2022) for details.

Usage

designPrior(
  to,
  so,
  mu = 0,
  sp = Inf,
  tau = 0,
  g = sp^2/(tau^2 + so^2),
  h = tau^2/so^2,
  type = c(NA, "conditional", "predictive", "EB")
)

Arguments

to

Effect estimate from original study

so

Standard error of effect estimate from original study

mu

The initial prior mean. Defaults to 0

sp

The initial prior standard deviation. Defaults to Inf (an improper uniform prior)

tau

The initial prior heterogeneity standard deviation. Defaults to 0 (no heterogeneity)

g

The relative initial prior variance g = sp^2/(tau^2 + so^2) (alternative parametrization of prior standard deviation sp)

h

The relative initial prior heterogeneity variance h = tau^2/so^2 (alternative parametrization of prior heterogeneity standard deviation tau)

type

Shortcut for special parameter combinations. The available options are NA, "conditional", "predictive", and "EB" (see details). Defaults to NA

Details

The "conditional" design prior corresponds to a point mass at the original effect estimate, i.e., assuming that the true effect size is equal to the original effect estimate. The "predictive" design prior is obtained from updating a uniform initial prior by the likelihood of the original data. The "EB" design prior is obtained by empirical Bayes estimation of the variance of the normal prior and induces adaptive shrinkage that depends on the p-value of the original effect estimate.

Value

Returns an object of class "designPrior" which is a list containing:

dpMean	The computed mean of the design prior
dpVar	The computed variance of the design prior
to	The specified original effect estimate
so	The specified original standard error
mu	The specified mean of the initial prior
sp	The specified standard deviation of the initial prior
tau	The specified heterogeneity variance

Author(s)

Samuel Pawel

References

Pawel, S., Consonni, G., and Held, L. (2022). Bayesian approaches to designing replication studies. arXiv preprint. doi:10.48550/arXiv.2211.02552

See Also

pors, ssd

Examples

designPrior(to = 1.1, so = 1)