Region numbers for two endpoints

Shows how the regions used by the decision criteria for two endpoints are numbered (Yamaguchi et al., submitted, Tables 1 and 2).

Usage

qdm_regions(prob = c("posterior", "predictive"), direction = "greater")

Arguments

prob

Either "posterior" (nine regions) or "predictive" (four regions).

direction

"greater" (the default) or "less", as in the criterion: a single value for both endpoints or one value per endpoint.

Value

A character matrix of region labels (printed without quotes), with the conditions on endpoint 1 as column names and those on endpoint 2 as row names.

Details

For posterior probability, the target value (TV) and the minimum acceptable value (MAV) of each endpoint divide the plane of \((\theta_1, \theta_2)\) into nine regions. Columns correspond to endpoint 1 and rows to endpoint 2. For posterior predictive probability, the null values divide the plane into four regions.

For an endpoint on which smaller effects are favorable (direction = "less" in the criterion), the inequalities of that endpoint are reversed, so that region 1 is always the most favorable one: for example, "theta2 < TV2", "TV2 <= theta2 < MAV2" and "theta2 >= MAV2".

References

Yamaguchi, Y., Hu, H., Huang, Y., Han, C., Homma, G. and Wang, A. (submitted). Bivariate Bayesian quantitative decision-making for two endpoints in rare disease drug development.

Examples

qdm_regions("posterior")
#>                      theta1 > TV1 MAV1 < theta1 <= TV1 theta1 <= MAV1
#> theta2 > TV2         R1           R4                   R7            
#> MAV2 < theta2 <= TV2 R2           R5                   R8            
#> theta2 <= MAV2       R3           R6                   R9            
qdm_regions("predictive")
#>                 theta1 > NULL1 theta1 <= NULL1
#> theta2 > NULL2  R1             R3             
#> theta2 <= NULL2 R2             R4             
# Endpoint 2 is a safety endpoint (smaller effects are favorable)
qdm_regions("posterior", direction = c("greater", "less"))
#>                      theta1 > TV1 MAV1 < theta1 <= TV1 theta1 <= MAV1
#> theta2 < TV2         R1           R4                   R7            
#> TV2 <= theta2 < MAV2 R2           R5                   R8            
#> theta2 >= MAV2       R3           R6                   R9