Internally, adoptr is built around the joint
distribution of a test statistic and the unknown location parameter of
interest given a sample size, i.e. L[(Xi,θ)|ni] where Xi is the
stage-i test statistic and ni the corresponding sample size. The
distribution class for Xi is
defined by specifying a DataDistribution
object, e.g., a
normal distribution
To completely specify the marginal distribution of Xi, the distribution of θ must also be specified. The classical case where θ is considered fixed, emerges as special case when a single parameter value has probability mass 1.
The simplest supported prior class are discrete
PointMassPrior
priors. To specify a discrete prior, one
simply specifies the vector of pivot points with positive mass and the
vector of corresponding probability masses. E.g., consider an example
where the point δ=0.1 has
probability mass 0.4 and the point
δ=0.25 has mass 1−0.4=0.6.
For details on the provided methods, see
?DiscretePrior
.
adoptr also supports arbitrary continuous priors with support on compact intervals. For instance, we could consider a prior based on a truncated normal via:
cont_prior <- ContinuousPrior(
pdf = function(x) dnorm(x, mean = 0.3, sd = 0.2),
support = c(-2, 3)
)
For details on the provided methods, see
?ContinuousPrior
.
In practice, the most important operation will be conditioning. This is important to implement type one and type two error rate constraints. Consider, e.g., the case of power. Typically, a power constraint is imposed on a single point in the alternative, e.g. using the constraint
If uncertainty about the true response rate should be incorporated in the design, it makes sense to assume a continuous prior on θ. In this case, the prior should be conditioned for the power constraint to avoid integrating over the null hypothesis: