2a:null 2b:["$","title",null,{"children":"LRT Presentation Components | Zhihao Yao | Observable"}] 30:T4b7,// funcLRT_sim = py`import numpy as np // import pandas as pd // def flogLRv(x, fnidot, fndotj, fndotdot): // logLRvr = x * (np.log(x) - np.log(fnidot)) // logLRvr = logLRvr + (fndotj - x) * (np.log(fndotj - x) - np.log(fndotdot - fnidot)) // logLRvr = logLRvr - fndotj * (np.log(fndotj) - np.log(fndotdot)); // logLRvr.fillna(0) // pj = x / fnidot // qj = (fndotj - x) / (fndotdot - fnidot) // logLRvr[ pj < qj ] = 0 // return logLRvr // def fLRT(qnum, number, alpha = 0.05, alphaSpending = 1): // mylist = qnum // mylist["ntrt"] = pd.to_numeric(mylist["ntrt"]) // mylist["nidot"] = pd.to_numeric(mylist["nidot"]) // mylist["ndotj"] = pd.to_numeric(mylist["ndotj"]) // mylist["ndotdot"] = pd.to_numeric(mylist["ndotdot"]) // mylist["logLR"] = flogLRv(mylist["ntrt"], mylist["nidot"], mylist["ndotj"][0], mylist["ndotdot"][0]) // mylist = mylist.sort_values("logLR", ascending=False) // cnstR = number // np.random.seed(123) // mylist["Pvector"] = mylist["nidot"] / mylist["ndotdot"] // mylist["Pobs"] = mylist["ntrt"] / mylist["ndotj"] // sim_cntdata = np.random.multinomial(mylist["ndotj"][0], mylist["Pvector"], size = cnstR) // return sim_cntdata // fLRT`31:T74c,// funcLRT_simLR = py`import numpy as np // import pandas as pd // def flogLRv(x, fnidot, fndotj, fndotdot): // logLRvr = x * (np.log(x) - np.log(fnidot)) // logLRvr = logLRvr + (fndotj - x) * (np.log(fndotj - x) - np.log(fndotdot - fnidot)) // logLRvr = logLRvr - fndotj * (np.log(fndotj) - np.log(fndotdot)); // logLRvr.fillna(0) // pj = x / fnidot // qj = (fndotj - x) / (fndotdot - fnidot) // logLRvr[ pj < qj ] = 0 // return logLRvr // def fLRT(qnum, number, alpha = 0.05, alphaSpending = 1): // mylist = qnum // mylist["ntrt"] = pd.to_numeric(mylist["ntrt"]) // mylist["nidot"] = pd.to_numeric(mylist["nidot"]) // mylist["ndotj"] = pd.to_numeric(mylist["ndotj"]) // mylist["ndotdot"] = pd.to_numeric(mylist["ndotdot"]) // mylist["RR"] = (mylist["ntrt"])*((mylist["ndotdot"]-mylist["nidot"])/(mylist["nidot"]*(mylist["ndotj"]-mylist["ntrt"]))) // mylist["stdRR"] = 1/(mylist["ntrt"]) - 1/mylist["nidot"] + 1/(mylist["ndotj"]-mylist["ntrt"]) - 1/(mylist["ndotdot"]-mylist["nidot"]) // mylist["stdRR"] = np.sqrt(mylist["stdRR"]) // mylist["lowRR"] = np.log(mylist["RR"])- 1.96*(mylist["stdRR"]) // mylist["lowRR"] = np.exp(mylist["lowRR"]) // mylist["uppRR"] = np.log(mylist["RR"])+ 1.96*(mylist["stdRR"]) // mylist["uppRR"] = np.exp(mylist["uppRR"]) // mylist["logLR"] = flogLRv(mylist["ntrt"], mylist["nidot"], mylist["ndotj"][0], mylist["ndotdot"][0]) // mylist = mylist.sort_values("logLR", ascending=False) // cnstR = number // np.random.seed(123) // mylist["Pvector"] = mylist["nidot"] / mylist["ndotdot"] // mylist["Pobs"] = mylist["ntrt"] / mylist["ndotj"] // sim_cntdata = np.random.multinomial(mylist["ndotj"][0], mylist["Pvector"], size = cnstR) // logLRsim = np.array([flogLRv(i, mylist["nidot"], mylist["ndotj"][0], mylist["ndotdot"][0]) for i in sim_cntdata]) // return logLRsim // fLRT`32:T6ca,// funcLRT = py`import numpy as np // import pandas as pd // def flogLRv(x, fnidot, fndotj, fndotdot): // logLRvr = x * (np.log(x) - np.log(fnidot)) // logLRvr = logLRvr + (fndotj - x) * (np.log(fndotj - x) - np.log(fndotdot - fnidot)) // logLRvr = logLRvr - fndotj * (np.log(fndotj) - np.log(fndotdot)); // logLRvr.fillna(0) // pj = x / fnidot // qj = (fndotj - x) / (fndotdot - fnidot) // logLRvr[ pj < qj ] = 0 // return logLRvr // def fLRT(qnum, number, alpha = 0.05, alphaSpending = 1): // mylist = qnum // mylist["ntrt"] = pd.to_numeric(mylist["ntrt"]) // mylist["nidot"] = pd.to_numeric(mylist["nidot"]) // mylist["ndotj"] = pd.to_numeric(mylist["ndotj"]) // mylist["ndotdot"] = pd.to_numeric(mylist["ndotdot"]) // mylist["logLR"] = flogLRv(mylist["ntrt"], mylist["nidot"], mylist["ndotj"][0], mylist["ndotdot"][0]) // mylist = mylist.sort_values("logLR", ascending=False) // cnstR = number // np.random.seed(123) // mylist["Pvector"] = mylist["nidot"] / mylist["ndotdot"] // sim_cntdata = np.random.multinomial(mylist["ndotj"][0], mylist["Pvector"], size = cnstR) // logLRsim = np.array([flogLRv(i, mylist["nidot"], mylist["ndotj"][0], mylist["ndotdot"][0]) for i in sim_cntdata]) // maxlogLRsim = np.array([np.max(i) for i in logLRsim]) // mylist["T_alpha"] = np.quantile(maxlogLRsim, 1 - alpha) // mylist["pvalue"] = np.array([ np.mean(maxlogLRsim > i) for i in mylist["logLR"]]) // if alphaSpending >= 1: // mylist["is_signal"] = (mylist["logLR"] > mylist["T_alpha"]) // else: // mylist["alpha"] = alphaSpending // mylist["is_signal"] = (mylist["pvalue"] < alphaSpending) // mylist = mylist.sort_values("logLR", ascending=False) // return mylist // 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Yao","avatar_url":"https://avatars-next.observableusercontent.com/0bac389abf8df9b4d7c6e09e8f96b464d2c01a64946e8b88cd7e143da5750c0e","tier":null}],"members":[{"type":"individual","id":"01b5d984f2428b1a","login":"howardyao","name":"Zhihao Yao","avatar_url":"https://avatars-next.observableusercontent.com/0bac389abf8df9b4d7c6e09e8f96b464d2c01a64946e8b88cd7e143da5750c0e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"LRT Presentation Components","cells":[{"id":0,"value":"# LRT Presentation Components","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"sample1 = await FileAttachment('sample1.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"sample1Summary = SummaryTable(sample1, {label: \"LRT Sample1\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"varDef = md`\n---\n| Variable Name | Definition | \n|:-----------:|:-------------:|\n| ntrt (${tex`n_{ij}`}) | number of events for the ${tex`ith`} AE and ${tex`jth`} drug |\n| nidot | total number of events for ${tex`ith`} AE (marginal total for ${tex`ith`} row). | \n| ndotj | total number of events for ${tex`jth`} drug (the marginal total for ${tex`jth`} column) | \n| ndotdot | grand total |\n---\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"sample1Table = Inputs.table(sample1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"// funcLRT_obs = py`import numpy as np\n// import pandas as pd\n \n// def flogLRv(x, fnidot, fndotj, fndotdot):\n// logLRvr = x * (np.log(x) - np.log(fnidot))\n// logLRvr = logLRvr + (fndotj - x) * (np.log(fndotj - x) - np.log(fndotdot - fnidot))\n// logLRvr = logLRvr - fndotj * (np.log(fndotj) - np.log(fndotdot));\n// logLRvr.fillna(0)\n// pj = x / fnidot\n// qj = (fndotj - x) / (fndotdot - fnidot)\n// logLRvr[ pj < qj ] = 0\n// return logLRvr\n\n// def fLRT(qnum, alpha = 0.05, alphaSpending = 1):\n// mylist = qnum\n// mylist[\"ntrt\"] = pd.to_numeric(mylist[\"ntrt\"])\n// mylist[\"nidot\"] = pd.to_numeric(mylist[\"nidot\"])\n// mylist[\"ndotj\"] = pd.to_numeric(mylist[\"ndotj\"])\n// mylist[\"ndotdot\"] = pd.to_numeric(mylist[\"ndotdot\"])\n// mylist[\"logLR\"] = flogLRv(mylist[\"ntrt\"], mylist[\"nidot\"], mylist[\"ndotj\"][0], mylist[\"ndotdot\"][0])\n// mylist = mylist.sort_values(\"logLR\", ascending=False)\n// return mylist\n\n// fLRT`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":87,"value":"// LRTResultObs = py`import pandas as pd\n// ${funcLRT_obs}(pd.read_json(${JSON.stringify(sample1)})).to_json(orient=\"records\")`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"// JSON.parse(LRTResultObs)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"LRTResultObs = await FileAttachment('sample1TableObs.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":91,"value":"sample1TableObs = Inputs.table(LRTResultObs)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"$30","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"// LRTResultSim = py`import pandas as pd\n// ${funcLRT_sim}(pd.read_json(${JSON.stringify(sample1)}),1000).transpose()`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":222,"value":"// LRTResultSimCSV = aq.from(LRTResultSim).objects()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":232,"value":"LRTResultSimData = await FileAttachment('LRTResultSimCSV@1.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"sample1TableSim = Inputs.table(LRTResultSimData)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"// LRTResultSimLR = py`import pandas as pd\n// ${funcLRT_simLR}(pd.read_json(${JSON.stringify(sample1)}),1000)`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":255,"value":"// LRTResultSimLRCSV = aq.from(LRTResultSimLR).objects()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":257,"value":"LRTResultSimLRData = await FileAttachment('LRTResultSimLRCSV.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":300,"value":" LRTResultSimMaxLRData = d3.transpose(LRTResultSimLRData.map(n => Object.values(n)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"sample1TableSimLR= Inputs.table(LRTResultSimMaxLRData)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"// maxlogLRsim = py`import numpy as np\n// import pandas as pd\n// np.array([np.max(i) for i in pd.read_json(${LRTResultSimLRData})])`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":278,"value":"maxlogLRsim = LRTResultSimLRData.map(n => Math.max(...Object.values(n)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"// T_alpha = py`import numpy as np\n// np.quantile(${maxlogLRsim}, 1 - 0.05)\n// `","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":364,"value":"T_alpha = _math.quantileSeq(maxlogLRsim, 1 - 0.05)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":143,"value":"LRTResultPlot = Plot.plot({\n height: 200,\n y: {\n grid: true\n },\n x: {\n label: \"Likelihood Ratio →\"\n },\n marks: [\n Plot.rectY(aq.table({maxLogLR:maxlogLRsim}).objects(), \n Plot.binX({y: \"count\"}, \n {x: \"maxLogLR\", \n thresholds: 30,\n fill: \"steelblue\"\n })),\n Plot.ruleY([0]),\n Plot.ruleX([T_alpha], {stroke: \"red\"}),\n Plot.text([[T_alpha, 50]], {text: ['Rejection Region, LLR>'+T_alpha.toFixed(3)], dx: 18, fill:'red'}),\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":185,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":187,"value":"// LRTResult = py`import pandas as pd\n// ${funcLRT}(pd.read_json(${JSON.stringify(sample1)}),1000).to_json(orient=\"records\")`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":310,"value":"// LRTResultFinalCSV = aq.from(JSON.parse(LRTResult)).objects()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":314,"value":"LRTResultFinalData = await FileAttachment('LRTResultFinalCSV.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":193,"value":"sample1TableFinal = Inputs.table(LRTResultFinalData, \n {columns: [\"AEID\", \"ntrt\", \"nidot\", \"ndotj\", \"ndotdot\", \"logLR\", \"T_alpha\", \"pvalue\", \"is_signal\"],\n width: {AE: 250},\n // height: 550,\n align: {\n AEID: \"center\",\n ntrt: \"center\",\n nidot: \"center\",\n ndotj: \"center\",\n ndotdot: \"center\",\n logLR: \"center\",\n T_alpha: \"center\",\n pvalue: \"center\",\n is_signal: \"center\"\n }\n })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":323,"value":"products = await FileAttachment('AZproducts.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"Array.from(new Set(products.map(n=>n.area)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":351,"value":"viewof areaSelector = select({\n title: \"Therapy Area\",\n // description: \"Please pick your favorite stooge.\",\n options: Array.from(new Set(products.map(n=>n.area))),\n value: Array.from(new Set(products.map(n=>n.area)))[1]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":344,"value":"productsTable = Inputs.table(products.filter(n=>n.area === areaSelector), {\n columns:[\"name\"]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"# Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":348,"value":"import {select} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"// import { py, pyodide } from '@gnestor/pyodide'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"import {SummaryTable} from \"@observablehq/summary-table\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":369,"value":"_math = require('https://unpkg.com/mathjs@5.9.0/dist/math.min.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"import { aq, op } from '@uwdata/arquero'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"import {Plot, d3} from \"@observablehq/plot\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1"}} 2f:"$2e:body"