[equiv0]     Equiv: bioequivalence in a
         cross-over trial

The table below shows some data from a two-treatment, two-period crossover trial to compare 2 tablets A and B, as reported by Gelfand et al (1990).


[equiv1]

The response Y ik from the i th subject ( i = 1,...,10) in the k th period ( k = 1,2) is assumed to be of the form

   Y ik ~ Normal(m ik , t 1 )

   m ik = m + (-1) T ik - 1 f / 2 + (-1) k - 1 p / 2 + d i

    d i ~ Normal(0, t 2 )

where T ik = 1,2 denotes the treatment given to subject i in period k , m, f, p are the overall mean, treatment and period effects respectively, and d i represents the random effect for subject i . The graph of this model and its BUGS language description are shown below


Graphical model for equiv example
[equiv2]



BUGS language for equiv example

   model
   {
      for( k in 1 : P ) {
         for( i in 1 : N ) {
            Y[i , k] ~ dnorm(m[i , k], tau1)
            m[i , k] <- mu + sign[T[i , k]] * phi / 2 + sign[k] * pi / 2 + delta[i]
            T[i , k] <- group[i] * (k - 1.5) + 1.5
         }
      }
      for( i in 1 : N ) {
         delta[i] ~ dnorm(0.0, tau2)
      }
      tau1 ~ dgamma(0.001, 0.001) sigma1 <- 1 / sqrt(tau1)
      tau2 ~ dgamma(0.001, 0.001) sigma2 <- 1 / sqrt(tau2)
      mu ~ dnorm(0.0, 1.0E-6)
      phi ~ dnorm(0.0, 1.0E-6)
      pi ~ dnorm(0.0, 1.0E-6)
      theta <- exp(phi)
      equiv <- step(theta - 0.8) - step(theta - 1.2)
   }

Note the use of the step function to indicate whether q = e f lies between 0.8 and 1.2 which traditionally determines bioequivelence.

 Data ( click to open )


 Inits for chain 1        Inits for chain 2    ( click to open )


Results

A 1000 update burn in followed by a further 10000 updates gave the parameteres estimates

[equiv3]