Finding interval with negligible linear trend

Dear list,

I have time course data with many data points per subject over time and 
want to dertermine the interval in which my dependent variable lies 
within given equivalence bounds around a zero (linear) trend.
I thought about using lme4::lmer() (or the like) for fitting a linear 
mixed model with (possibly orthogonal) polynomials in time as fixed 
effects and the corresponding by-subject random intercept and slopes to 
(i) get a (simultaneous) 90% confidence band for the regression function 
and (ii) then determine the interval in which this confindence band lies 
within the equivalence bounds.
But I'm not exactely sure whether this is a reasonable approach and if 
so how I could do this in R.

Any help is highly appreciated.

Best regards,
Maarten