inhalers.rst

Examples; Inhalers: Ordered Categorical Data

Inhalers: Ordered Categorical Data

An example from OpenBUGS openbugs:2014:ex1 and Ezzet and Whitehead ezzet:1993:REM concerning a two-treatment, two-period crossover trial comparing salbutamol inhalation devices in 286 asthma patients.

Model

Treatment responses are modelled as

$$\begin{aligned} R_{i,t} &= j \quad \text{if}\; Y_{i,t} \in [a_{j-1}, a_j) \quad\quad i=1,\ldots,4; t=1,2; j=1,\ldots,3 \\\ \operatorname{logit}(Q_{i,t,j}) &= -(a_j + \mu_{s_i,t} + b_i) \\\ \mu_{1,1} &= \beta / 2 + \pi / 2 \\\ \mu_{1,2} &= -\beta / 2 - \pi / 2 - \kappa \\\ \mu_{2,1} &= -\beta / 2 + \pi / 2 \\\ \mu_{2,2} &= \beta / 2 - \pi / 2 + \kappa \\\ b_i &\sim \text{Normal}(0, \sigma) \\\ a[1] &\sim \text{Flat}(-1000, a[2]) \\\ a[2] &\sim \text{Flat}(-1000, a[3]) \\\ a[3] &\sim \text{Flat}(-1000, 1000) \\\ \beta &\sim \text{Normal}(0, 1000) \\\ \pi &\sim \text{Normal}(0, 1000) \\\ \kappa &\sim \text{Normal}(0, 1000) \\\ \sigma^2 &\sim \text{InverseGamma}(0.001, 0.001), \end{aligned}$$

where R_i, t is a 4-point ordinal rating of the device used by patient i, and Q_i, t, j is the cumulative probability of the rating in treatment period t being worse than category j.

Analysis Program

inhalers.jl

Results