hyper_mtdi_lognormal-class: Hyperprior for lognormal MTDi distributions

In precautionary: Safety Diagnostics for Dose-Escalation Trial Designs

Description

This hyperprior generates lognormal MTDi distributions with their coefficients of variation being drawn from a Rayleigh distribution with mode parameter set to

σ := CV.

Because the standard deviation of this distribution is

sd = σ √(2 - π/2) ~ 0.655 σ,

this conveniently links our uncertainty about CV to its mode, and indeed to other measures of centrality that are proportional to this:

mean = σ √(π/2) ~ 1.25 σ

median = σ √(2 log(2)) ~ 1.18 σ.

The medians of the lognormal distributions generated are themselves drawn from a lognormal distribution with meanlog = log(median_mtd) and sdlog = median_sdlog. Thus, parameter median_sdlog represents a proportional uncertainty in median_mtd.

Slots

CV

Coefficient of variation

median_mtd

Median MTDi

median_sdlog

Proportional uncertainty in median MTDi

precautionary documentation built on Aug. 9, 2021, 9:14 a.m.