A probability of outcome superiority curve (POSC) shows, for two people who differ by \(\Delta\) on a predictor, the probability that the person with the higher predictor score also has the higher outcome: $$P(\Delta) = P(Y_1 > Y_2 \mid X_1 - X_2 = \Delta).$$
Details
Because the two people are exchangeable, every POSC satisfies
\(P(-\Delta) = 1 - P(\Delta)\): it passes through 0.5 at
\(\Delta = 0\) and is point-symmetric about that point. The curve for
\(\Delta \ge 0\) therefore carries all of the information, and is what
is plotted by default (use plot(x, full = TRUE) to see the full
sigmoid).
Functions
posc_uni(): POSC from a correlation, assuming bivariate normality.posc_multi(): POSC for an optimally weighted composite of several predictors, from a correlation matrix.posc_lm(): POSC for the fitted values of a linear model.posc_emp(): empirical POSC estimated from raw data without assuming normality, with bootstrap confidence bands.posc_comp(): overlay and compare several POSCs.posc_bins(): binned observed proportions for an empirical POSC.
posc_uni(), posc_multi(), posc_lm() and posc_emp() return a
"posc" object with print(),
summary(), plot(), ggplot2::autoplot(),
predict() and as.data.frame()
methods.
Author
Maintainer: Matthew B. Jané matthewbjane@gmail.com
Authors:
Matthew B. Jané matthewbjane@gmail.com