31: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`32: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`33: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 // fLRT`34:[{"id":"303bf35ec85b4ca7aa96cb4e54ded279b9421a9cdc816933938be2211e409fc86bc4c53db28ebbb3756b0d9fc3ce3f8af20717bb7cd8110e2d98b578fc9a1bc9","href":"https://static.observableusercontent.com/files/303bf35ec85b4ca7aa96cb4e54ded279b9421a9cdc816933938be2211e409fc86bc4c53db28ebbb3756b0d9fc3ce3f8af20717bb7cd8110e2d98b578fc9a1bc9","name":"sample1.csv","type":"text/csv","lastModified":1630960922105.189,"size":2228},{"id":"f53547bdacfef49bd0bd606f4d391d0d75929b160a5e7780c45144f150c0826fd2ba1cd1d137d3fcfa177f6d5471d11b8e96be5d699aeeed162e7819a43c2037","href":"https://static.observableusercontent.com/files/f53547bdacfef49bd0bd606f4d391d0d75929b160a5e7780c45144f150c0826fd2ba1cd1d137d3fcfa177f6d5471d11b8e96be5d699aeeed162e7819a43c2037","name":"sample1TableObs.csv","type":"text/csv","lastModified":1631110298966.743,"size":2862},{"id":"dbb74f4f5f2a9be0a7511355fd9074bc1ebdb2d8a9f10621c9ef67a64083e0c6e8a844ce3512ddfd876bacdbcb436b8bdf6aeceb6bb60aae12ac8522a5256899","href":"https://static.observableusercontent.com/files/dbb74f4f5f2a9be0a7511355fd9074bc1ebdb2d8a9f10621c9ef67a64083e0c6e8a844ce3512ddfd876bacdbcb436b8bdf6aeceb6bb60aae12ac8522a5256899","name":"LRTResultSimCSV@1.csv","type":"text/csv","lastModified":1631111776019.465,"size":304163},{"id":"34cc5f31582c1af5738c105b9b10a4bf2d5a9879f6f73987d2e03d95b5a10d93b55f2b1cede04399fd512751c4da853bb84a6ee416c3a0cbfb05bb570744c65d","href":"https://static.observableusercontent.com/files/34cc5f31582c1af5738c105b9b10a4bf2d5a9879f6f73987d2e03d95b5a10d93b55f2b1cede04399fd512751c4da853bb84a6ee416c3a0cbfb05bb570744c65d","name":"LRTResultSimLRCSV.csv","type":"text/csv","lastModified":1631112394367.725,"size":1073266},{"id":"2c120800a1d994bc60dbf60ce9d95a9387d0ae35dd66303d3e8684ea5714db3662c37a184a0b9a989dfb2fcfa633e2f0db5bd6e00ae1397ecbcd2a6707245046","href":"https://static.observableusercontent.com/files/2c120800a1d994bc60dbf60ce9d95a9387d0ae35dd66303d3e8684ea5714db3662c37a184a0b9a989dfb2fcfa633e2f0db5bd6e00ae1397ecbcd2a6707245046","name":"LRTResultFinalCSV.csv","type":"text/csv","lastModified":1631116840679.239,"size":6321},{"id":"5e249e95a04e1987d36310a09135261e93f17637dbd1b9737e84b1f74ef1ea10e2deeb3e5ad3fadbca290ffa150ef7eb0518d165181af48d378c5709e77724cc","href":"https://static.observableusercontent.com/files/5e249e95a04e1987d36310a09135261e93f17637dbd1b9737e84b1f74ef1ea10e2deeb3e5ad3fadbca290ffa150ef7eb0518d165181af48d378c5709e77724cc","name":"AZproducts.csv","type":"text/csv","lastModified":1631155015465.838,"size":1325}] 2f:{"title":"LRT Presentation Components","cells":[{"id":0,"value":"# LRT Presentation Components","pinned":false,"hidden":false,"mode":"md"},{"id":16,"value":"sample1 = await FileAttachment('sample1.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"sample1Summary = SummaryTable(sample1, {label: \"LRT Sample1\"})","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"id":35,"value":"sample1Table = Inputs.table(sample1)","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"id":211,"value":"// JSON.parse(LRTResultObs)","pinned":true,"hidden":false,"mode":"ojs"},{"id":213,"value":"LRTResultObs = await FileAttachment('sample1TableObs.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":91,"value":"sample1TableObs = Inputs.table(LRTResultObs)","pinned":true,"hidden":false,"mode":"ojs"},{"id":96,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":222,"value":"// LRTResultSimCSV = aq.from(LRTResultSim).objects()","pinned":true,"hidden":false,"mode":"ojs"},{"id":232,"value":"LRTResultSimData = await FileAttachment('LRTResultSimCSV@1.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":105,"value":"sample1TableSim = Inputs.table(LRTResultSimData)","pinned":true,"hidden":false,"mode":"ojs"},{"id":110,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":255,"value":"// LRTResultSimLRCSV = aq.from(LRTResultSimLR).objects()","pinned":true,"hidden":false,"mode":"ojs"},{"id":257,"value":"LRTResultSimLRData = await FileAttachment('LRTResultSimLRCSV.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":300,"value":" LRTResultSimMaxLRData = d3.transpose(LRTResultSimLRData.map(n => Object.values(n)))","pinned":true,"hidden":false,"mode":"ojs"},{"id":115,"value":"sample1TableSimLR= Inputs.table(LRTResultSimMaxLRData)","pinned":true,"hidden":false,"mode":"ojs"},{"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(${LRTResultSimLRData})])`","pinned":true,"hidden":false,"mode":"ojs"},{"id":278,"value":"maxlogLRsim = LRTResultSimLRData.map(n => Math.max(...Object.values(n)))","pinned":true,"hidden":false,"mode":"ojs"},{"id":123,"value":"// T_alpha = py`import numpy as np\n// np.quantile(${maxlogLRsim}, 1 - 0.05)\n// `","pinned":true,"hidden":false,"mode":"ojs"},{"id":364,"value":"T_alpha = _math.quantileSeq(maxlogLRsim, 1 - 0.05)","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":185,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":310,"value":"// LRTResultFinalCSV = aq.from(JSON.parse(LRTResult)).objects()","pinned":true,"hidden":false,"mode":"ojs"},{"id":314,"value":"LRTResultFinalData = await FileAttachment('LRTResultFinalCSV.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":323,"value":"products = await FileAttachment('AZproducts.csv').csv({ typed: true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":332,"value":"Array.from(new Set(products.map(n=>n.area)))","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":344,"value":"productsTable = Inputs.table(products.filter(n=>n.area === areaSelector), {\n columns:[\"name\"]\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":6,"value":"# Appendix","pinned":false,"hidden":false,"mode":"md"},{"id":348,"value":"import {select} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":82,"value":"// import { py, pyodide } from '@gnestor/pyodide'","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"import {SummaryTable} from \"@observablehq/summary-table\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":369,"value":"_math = require('https://unpkg.com/mathjs@5.9.0/dist/math.min.js')","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"import { aq, op } from '@uwdata/arquero'","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"import {Plot, d3} from \"@observablehq/plot\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}