= + +

Next consider model (17), with random stage effects, Tj, that are assumed to be uncorrelated with dose. It can be shown that

and

So = f30 + 1'1' + € E(St) = (3t

(21) (22)

rij = 1'( Tj - 1') + €* (23) Equations (21) to (23) show that the overall level of the estimated dose response is biased by the average of the stage effects, the slope estimate is not biased, and the stage effects can be detected from the residuals.