sagepy/examples/rescoring/rescoring.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fda28e79-c7fb-4ab2-a571-a4f7779107f3",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "# Re-scoring with Sagepy\n",
    "\n",
    "The following notebook contains a basic re-scoring example with `sagepy`. You will:\n",
    "\n",
    "* Read a collection of PSMs from a binary file containing sagepy created PSMs\n",
    "* Calculate FDR with the Sage raw-scores\n",
    "* Have a look at peptide predicted features that can help to improve the number of returned PSMs at a fixed FDR\n",
    "* Use a re-scoring engine, here an [LDA-model](https://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html) from [scikit-learn](https://scikit-learn.org/stable/) to calculate the new score\n",
    "* Compare number of identifications with and without re-scoring\n",
    "\n",
    "This is the follow-up notebook of the \"property_prediction\" notebook. If you haven't read through it, we recommend you start there."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "202e59c1-6100-4725-b7eb-50b6fd2a2423",
   "metadata": {},
   "source": [
    "## Read the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "deca77fe-65b9-4889-a2e0-51148b4dbed2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "from sagepy.utility import psm_collection_to_pandas, decompress_psms\n",
    "from sagepy.qfdr.tdc import target_decoy_competition_pandas\n",
    "\n",
    "# read the binary matches from disk\n",
    "f = open(os.path.join(\"/media/hd01/CCSPred/HELA-GRAD110/imspy/total_psms.bin\"), 'rb')\n",
    "data = f.read()\n",
    "f.close()\n",
    "\n",
    "# convert binary file to PSM objects\n",
    "PSM = decompress_psms(data)\n",
    "\n",
    "# translate the collection of PSMs to pandas table\n",
    "PSM_pandas = psm_collection_to_pandas(PSM)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81eb046b-b7e1-473f-a14e-3cb6ea6f3d09",
   "metadata": {},
   "source": [
    "## Plot the raw scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7d8a68ee-8007-4603-bac1-f2dfae905ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "TARGET = PSM_pandas[PSM_pandas.decoy == False]\n",
    "DECOY = PSM_pandas[PSM_pandas.decoy]\n",
    "\n",
    "plt.title(\"Target vs Decoy Scores for PSMs tryptic HeLa digest timsTOF DDA\")\n",
    "plt.hist(TARGET.hyperscore, density=False, alpha=.8, bins=\"auto\", label=\"Target\")\n",
    "plt.hist(DECOY.hyperscore, density=False, alpha=.8, bins=\"auto\", label=\"Decoy\")\n",
    "plt.xlabel(\"Score\")\n",
    "plt.ylabel(\"Denisty\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5335f362-00a9-4a7b-9389-479fadc04b06",
   "metadata": {},
   "source": [
    "## Generate a collection of initial \"good\" targets using the target-decoy competition with the old score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e4ac8d32-fc6c-4435-b4dc-1a8f8dee34aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sagepy.qfdr.tdc import target_decoy_competition_pandas\n",
    "\n",
    "# target decoy competition, translating raw-scores to q-values\n",
    "TDC_pandas = target_decoy_competition_pandas(\n",
    "    PSM_pandas,\n",
    "    score=\"hyperscore\",\n",
    "    method=\"peptide_psm_peptide\",\n",
    ")\n",
    "\n",
    "TDC_pandas = pd.merge(TDC_pandas.drop(columns=[\"hyperscore\"]), \n",
    "                      PSM_pandas, on=[\"spec_idx\", \"match_idx\", \"decoy\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e31513a2-4176-481d-8e67-3a0156dd6a0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can select target hits with a q-value of 0.01, translating to 1 percent FDR\n",
    "FDR_1_percent = TDC_pandas[(TDC_pandas.q_value <= 0.01) & (TDC_pandas.decoy == False)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc5eb121-639c-44ee-b337-586e82294d62",
   "metadata": {},
   "source": [
    "## Have a look at distributions of good targets and all decoys with respect to predicted features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "96a6cae8-8581-4b69-bec9-66e498ad1b18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2x2 figure layout for delta-rt, delta-ims, median-ppm, and spectral-angle features target good vs decoy all\n",
    "fig, axs = plt.subplots(2, 2, figsize=(12, 10))\n",
    "\n",
    "# Panel 1: delta_rt\n",
    "axs[0, 0].hist(FDR_1_percent['delta_rt'], bins=\"auto\", alpha=.8, density=True, label=\"FDR 1%\")\n",
    "axs[0, 0].hist(DECOY['delta_rt'], bins=\"auto\", alpha=.5, density=True, label=\"Decoy\")\n",
    "axs[0, 0].set_title(\"Distribution of Delta RT\")\n",
    "axs[0, 0].set_xlabel(\"Delta RT\")\n",
    "axs[0, 0].set_ylabel(\"Density\")\n",
    "axs[0, 0].legend()\n",
    "\n",
    "# Panel 2: delta_ims\n",
    "axs[0, 1].hist(FDR_1_percent['delta_ims'], bins=\"auto\", alpha=.8, density=True, label=\"FDR 1%\")\n",
    "axs[0, 1].hist(DECOY['delta_ims'], bins=\"auto\", alpha=.5, density=True, label=\"Decoy\")\n",
    "axs[0, 1].set_title(\"Distribution of Delta IMS\")\n",
    "axs[0, 1].set_xlabel(\"Delta IMS\")\n",
    "axs[0, 1].set_ylabel(\"Density\")\n",
    "axs[0, 1].legend()\n",
    "\n",
    "# Panel 3: median_ppm\n",
    "axs[1, 0].hist(FDR_1_percent['average_ppm'], bins=\"auto\", alpha=.8, density=True, label=\"FDR 1%\")\n",
    "axs[1, 0].hist(DECOY['average_ppm'], bins=\"auto\", alpha=.5, density=True, label=\"Decoy\")\n",
    "axs[1, 0].set_title(\"Distribution of Average PPM\")\n",
    "axs[1, 0].set_xlabel(\"Average PPM\")\n",
    "axs[1, 0].set_ylabel(\"Density\")\n",
    "axs[1, 0].legend()\n",
    "\n",
    "# Panel 4: cosine_similarity converted to spectral angle sim\n",
    "axs[1, 1].hist(FDR_1_percent.spectral_angle_similarity, bins=\"auto\", alpha=.8, density=True, label=\"FDR 1%\")\n",
    "axs[1, 1].hist(DECOY.spectral_angle_similarity, bins=\"auto\", alpha=.5, density=True, label=\"Decoy\")\n",
    "axs[1, 1].set_title(\"Spectral Angle Similarity Distribution\")\n",
    "axs[1, 1].set_xlabel(\"Spectral Angle Similarity\")\n",
    "axs[1, 1].set_ylabel(\"Density\")\n",
    "axs[1, 1].legend()\n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29b010f1-ce97-46ab-a67a-51dfe830865b",
   "metadata": {},
   "source": [
    "## Use LDA as re-scoring engine to transform the available additional peptide features into a better score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "15a350e8-d9ff-44bc-979c-0482584cbd17",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Re-scoring PSMs: 100%|████████████████████████████████████████████████| 5/5 [01:55<00:00, 23.03s/it]\n"
     ]
    }
   ],
   "source": [
    "from sagepy.rescore.lda import rescore_lda\n",
    "\n",
    "# this will run a k-fold cross validation with 5 split (train 4/5, predict 1/5 of the data)\n",
    "PSM_rescored = rescore_lda(\n",
    "    psm_collection=PSM,\n",
    "    num_splits=5,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "57eb05ce-ef78-43ac-a068-632823412ba4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# target-decoy competition is performed again, now using re-score instead of hyper-score\n",
    "TDC_pandas_rescored = target_decoy_competition_pandas(\n",
    "    psm_collection_to_pandas(\n",
    "        PSM_rescored,\n",
    "    ),\n",
    "    method=\"peptide_psm_peptide\",\n",
    "    score=\"re_score\",\n",
    ")\n",
    "\n",
    "TDC_pandas_rescored = pd.merge(TDC_pandas_rescored.drop(columns=[\"re_score\"]), \n",
    "                               PSM_pandas, on=[\"spec_idx\", \"match_idx\", \"decoy\"])\n",
    "\n",
    "# we can select target hits with a q-value of 0.01, translating to 1 percent FDR\n",
    "FDR_1_percent_rescored = TDC_pandas_rescored[(TDC_pandas_rescored.q_value <= 0.01) & (TDC_pandas_rescored.decoy == False)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b18fe3a5-21dc-4ce3-b7c1-13d616febed2",
   "metadata": {},
   "source": [
    "## Inspect distribution of learned re-score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "03851dc5-1c63-4905-b26c-1cb1732b28b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "TARGET = TDC_pandas_rescored[TDC_pandas_rescored.decoy == False]\n",
    "DECOY = TDC_pandas_rescored[TDC_pandas_rescored.decoy]\n",
    "\n",
    "plt.title(\"Target vs Decoy Scores for PSMs tryptic HeLa digest timsTOF DDA\")\n",
    "plt.hist(TARGET.re_score, density=True, alpha=.8, bins=\"auto\", label=\"Target\")\n",
    "plt.hist(DECOY.re_score, density=True, alpha=.8, bins=\"auto\", label=\"Decoy\")\n",
    "plt.xlabel(\"Score\")\n",
    "plt.ylabel(\"Denisty\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3e13797-1602-462f-bf10-abd5978439fa",
   "metadata": {},
   "source": [
    "## Check if re-scoring improved number of identified peptides below a certain FDR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "7c78e8e4-2d9c-4836-b200-e7b187c99eb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib_venn import venn2\n",
    "\n",
    "plt.figure(figsize=(5,5), dpi=120)\n",
    "venn2([set(FDR_1_percent_rescored.sequence), set(FDR_1_percent.sequence)], (\"re-score\", \"hyper-score\"))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}