I have paired cobalt concentrations in bird blood and feathers. Blood levels give me an idea of how recent the cobalt exposure was (<30days), feather give the 6 month accumulated total. Previous investigators defined the relationship between blood and feathers by combining populations of birds whose cobalt exposure is low-constant, med-constant, and high-constant (all within bounds of cobalt levels of healthy normal birds). They used OLS blood~feathers to define the "normal" physiological cobalt relationship and then plotted individual blood and feather levels obtained from birds that had recently arrived at a contaminated site. These birds had much higher blood values but much lower feather values than predicted by the OLS (outside the OLS prediction interval). Since there is a difference in the sampling and analytical error for each of these tissues (feather errors are more than 4x the blood errors) I considered using Demming or total least squares RMA regression. In order to identify individual birds whose paired blood and feather values are outside the model I would have liked to rely on the prediction intervals. Would a better, or equally adequate alternative be using quantile regression and use the t 0.75 and t 0.25 lines as an approximation of the prediction interval?
Here's an example using Deming regression in GraphPad Prism:blue dots (constant exposure) are used to generate the regression line, the difference in error measurements between x and y are clear, the red individuals are superimposed for comparison against the constant exposure. I'd like to set a boundary around the regression line that predicts where any future constant exposures will exist (prediction interval) but takes into the consideration the error around X and Y measurements.