Zinc absorption

  • 4 steer
  • 3 periods (diets) /steer
  • 2 washes (order of buffers)/periods

In each period, the difference is in the diet.

In each wash,

  1. Insert a random buffer (9 ppm zinc vs 0 ppm zinc) into rumen
  2. measure zinc at times 0, 5, 20, 35, 50, and 65 minutes
  3. wash out period
  4. Insert the other buffer
  5. measure zinc


  • zinc measurement or
  • proportion zinc remaining relative to amount measured at 5 minutes

Zinc generally appears to have an exponential decay pattern across time. So responses for the purpose of modeling include parameters from an estimated curve with formula $B+(X0-B)e^{kt}$ where $X0$ is the measurement at time 5 and $B$ and $k$ are the estimated parameters.


The model will be according to the multiple cross-over design.


  • Using the proportion is very sensitive to the amount measured at 5 minutes which could cause a positive correlation amongst the other measurements. One suggestion is to model the actual measurement (rather than the proportion remaining) and use the 5 minute measurement as an offset.
  • Consider monotone function estimation to estimate the means at time 5 through 65. Then use the ratio of the estimated mean at time 5 minus the estimated mean at time 15 divided by the estimated mean at time 5 minus the estimated mean at time 65.
  • Try to plot the data all on one page with faceting for buffer, wash, diet and period with one line per steer.