I'm trying to make overlaid ROC curves to represent successive improvements in model performance when particular predictors are added one at a time to the model. I want one ROC curve for each of about 5 nested models (which I will define manually), all overlaid in one plot. For example:

    #outcome var
    y = c(rep(0,50), rep(1, 50))

    #predictors
    x1 = y + rnorm(100, sd = 1)
    x2 = y + rnorm(100, sd = 4)

    #correlations of predictors with outcome
    cor(x1, y)
    cor(x2, y)

    library(Epi)
    ROC(form = y ~ x1, plot = "ROC)
    ROC(form = y ~ x1 + x2, plot = "ROC")


I'd want the two ROC curves on the same plot (and ideally without the distracting model info in the background). Any ggplot/graphics gurus willing to lend a hand?

You should choose "hidden option c", where c is beta regression.  This is a type of regression model that is appropriate when the response variable is distributed as Beta.  You can think of it as analogous to a generalized linear model.  It's exactly what you are looking for.  There is a package in R called betareg which deals with this.  I don't know if you use R, but even if you don't you could read the 'vignettes' anyway, they will give you general information about the topic in addition to how to implement it in R (which you wouldn't need in that case).  



Edit (much later):  Let me make a quick clarification.  I interpret the question as being about the ratio of two, positive, real values.  If so, (and they are distributed as Gammas) that is a Beta distribution.  However, if $a$ is a count of 'successes' out of a known total, $b$, of 'trials', then this would be a count proportion $a/b$, not a continuous proportion, and you should use binomial GLM (e.g., logistic regression). For how to do it in R, see e.g. How to do logistic regression in R when outcome is fractional (a ratio of two counts)?

Another possibility is to use linear regression if the ratios can be transformed so as to meet the assumptions of a standard linear model, although I would not be optimistic about that actually working.  
