Fieller's theorem, Scheffé simultaneous confidence intervals, and ratios of parameters of linear and nonlinear mixed-effects models.

The issue of joint confidence region and simultaneous confidence interval estimation for ratios of the parameters of a nonlinear mixed-effects model is addressed using a Fieller's theorem approach. The method presented is similarly applicable to linear mixed-effects models. In addition, previous work on linear fixed-effects models is demonstrated to be a special case of the present method. The methodology is applied to the ratios of slopes in a study of gestational maturation of placental glucose transfer capacity in sheep.