# AES Consulting meeting on 3 March 2017

## 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,

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

### Response

- 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.

## Model

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

## Thoughts/Suggestions

- 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.