{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Receiver Operating Characteristic" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": true }, "outputs": [], "source": [ "suppressPackageStartupMessages(library(tidyverse))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logistic regression concept\n", "\n", "In logistic regression, we want to relate some predictor variable (e..g gene expression value) to the **probability** of a binary outcome. We would like a linear model since that is mathematically and computationally tractable, but run into the issue that probabilities are restricted to [0,1]. Logistic regression solves this by transforming the output of a linear model into the [0, 1] range." ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n <- 50\n", "x <- seq(-4, 4, length.out = n)\n", "a = 0\n", "b = 1\n", "\n", "lx <- a + b*x\n", "px <- exp(lx)/(1 + exp(lx))\n", "y <- rbinom(n, 1, px)\n", "\n", "df <- data.frame(y=y, x=x, lx=lx, px=px)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width=4, repr.plot.height=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A linear model cannot be directly interpreted as a probability" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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kLADQJvvRXL/jm2Q8xIJQjj+8knUZzsxswjj6l8Tz+pJCW/+OKsGF83uHprE91z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\nIQIUwPnwofOWiQARIAJEIHgE/g+92E3Vbc1e9AAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(df, aes(x=x, y=lx)) + \n", "geom_point(color='blue') +\n", "labs(x=\"Gene expression value\", \n", " y=\"Linear model relating gene\\nexpression to probability of outcome\")" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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39Mhw4dossuu0zqlJCQYHX2m2++oe+++05OG7rlllvoiiuusN47cuSI1AlT5K68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\nrkx5R11gWiId/vvss4+M+uPSpU6kq4eEpwGl4xt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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(df, aes(x=x, y=y)) + \n", "geom_point() +\n", "geom_line(aes(y=px), color='red') +\n", "labs(x=\"Gene expression value\", y=\"Binary outcome\", \n", " title=\"Probability of outcome given value\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation from logistic model" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sim.binomial <- function(n, b0, b1, b2, b3) { \n", " x1 <- rnorm(n)\n", " x2 <- rnorm(n)\n", " x3 <- rnorm(n)\n", " lx <- b0 + b1 * x1 + b2 * x2 + b3 * x3 \n", " px <- exp(lx)/(1 + exp(lx))\n", " y <- rbinom(n, 1, px)\n", " data.frame(y, px, x1, x2, x3)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LOOCV" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": true }, "outputs": [], "source": [ "set.seed(31219)\n", "data <- sim.binomial(100, 0.1, 0, 1, 0)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
y | px | x1 | x2 | x3 |
---|---|---|---|---|
0 | 0.5830298 | 1.2472628 | 0.23522348 | 1.4787281 |
1 | 0.4546145 | 0.5804904 | -0.28204321 | -0.8217013 |
1 | 0.5417889 | 0.3065363 | 0.06754626 | 1.3946841 |
1 | 0.8080377 | 0.4604304 | 1.33730956 | 0.6502840 |
0 | 0.5436883 | 1.2094387 | 0.07519995 | 0.6585957 |
1 | 0.4011430 | 0.2338796 | -0.50070506 | -0.8225897 |