I'm working on a meta-analysis and have generated a quirky question for which I'm at a bit of a loss. The MA is for a large set of factorial experiments. Calculating the Log Response Ratio (LRR) and variance in said ratio for the experimental data is a cinch, and we're comparing the effects of one type of treatment to the other (and any interactions).
However, my group is curious at examining the effect of HALF the level of one of the treatments (it's a continuous treatment, and we've been looking at the highest versus the lowest level of the treatment). We have fit nonlinear curves for each experiment that describe how the treatment effects the response over a wide range of treatment levels. We've got the coefficient error and residual error for each of these curve fits. And how we want to calculate log(full treatment) - log(half treatment) from the fitted curve for the this half-treatment log response ratio. Easy.
But...how would we then calculate the variance in the half-treatment log response ratio? Would we use the SE estimates for the curve coefficients? The residual error? What would the sample size be for the variance calculation? Or is this unimportant? Thoughts?