2d:null 2e:["$","title",null,{"children":"Therapeutic Tests (Bayes' Theorem) | Dave Brown | Observable"}] 33:T944,data = { let diseaseTotal = Math.round(form.prior * form.count); let healthyTotal = form.count - diseaseTotal; let truePositiveTotal = Math.round(diseaseTotal * form.sensitivity); let trueNegativeTotal = Math.round(healthyTotal * form.specificity); let falseNegativeTotal = Math.round(diseaseTotal * (1 - form.sensitivity)); let falsePositiveTotal = Math.round(healthyTotal * (1 - form.specificity)); const positiveIdsArray = []; const negativeIdsArray = []; const truePositiveIdsArray = []; const trueNegativeIdsArray = []; const falsePositiveIdsArray = []; const falseNegativeIdsArray = []; const disease = new Float64Array(form.count); const positiveTest = new Float64Array(form.count); const random = new Float64Array(form.count); const ids = new Uint32Array(form.count); const pseudoRandom = new MorphCharts.Helpers.PseudoRandom(0); let diseaseCount = 0; let truePositiveCount = 0; let falsePositiveCount = 0; for (let i = 0; i < form.count; i++) { ids[i] = i; random[i] = pseudoRandom.nextFloat(); if (diseaseCount++ < diseaseTotal) { disease[i] = 1; if (truePositiveCount++ < truePositiveTotal) { positiveTest[i] = 1; positiveIdsArray.push(i); truePositiveIdsArray.push(i); } else { negativeIdsArray.push(i); falseNegativeIdsArray.push(i); } } else { if (falsePositiveCount++ < falsePositiveTotal) { positiveTest[i] = 1; positiveIdsArray.push(i); falsePositiveIdsArray.push(i); } else { negativeIdsArray.push(i); trueNegativeIdsArray.push(i); } } } const positiveIds = new Uint32Array(positiveIdsArray); const negativeIds = new Uint32Array(negativeIdsArray); const truePositiveIds = new Set(truePositiveIdsArray); const trueNegativeIds = new Set(trueNegativeIdsArray); const falsePositiveIds = new Set(falsePositiveIdsArray); const falseNegativeIds = new Set(falseNegativeIdsArray); return { ids: ids, diseaseTotal: diseaseTotal, healthyTotal: healthyTotal, positiveIds: positiveIds, negativeIds: negativeIds, truePositiveIds: truePositiveIds, trueNegativeIds: trueNegativeIds, falsePositiveIds: falsePositiveIds, falseNegativeIds: falseNegativeIds, disease: disease, random: random, positiveTest: positiveTest }; }34:T6c1,function layout0() { mutable layout0Calls++; updateFilter(data.ids); // Layout const layoutOptions = { side: side }; sheet.layout(mutable transitionBuffer.currentBuffer, data.ids, layoutOptions); const vertexOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, padding: padding, thickness: thickness // staggerOrder: 0 }; sheet.update(mutable transitionBuffer.currentBuffer, data.ids, vertexOptions); mutable transitionBuffer.currentBuffer.unitType = MorphCharts.UnitType.block; mutable transitionBuffer.currentPalette.colors = null; // Axes const axesOptions = { minBoundsX: sheet.minLayoutBoundsX, maxBoundsX: sheet.maxLayoutBoundsX, minBoundsY: sheet.minLayoutBoundsY, maxBoundsY: sheet.maxLayoutBoundsY, divisionsX: 1, divisionsY: 1, minorGridlinesX: 1, minorGridlinesY: 1, arePickDivisionsVisibleX: false, arePickDivisionsVisibleY: false, titleX: `${form.count} ${form.count == 1 ? "person" : "people"} `, headingX: `${(form.prior * 100).toFixed( 1 )}% have a disease, for which a test is ${Math.round( form.sensitivity * 100 )}% sensitive and ${Math.round(form.specificity * 100)}% specific`, headingSizeX: core.config.axesTextTitleSize }; const axes = MorphCharts.Axes.Cartesian2dAxesHelper.create(core, axesOptions); // Hide zero lines axes.zero[0] = -1; axes.zero[1] = -1; axes.isEdgeVisible[MorphCharts.Edge2D.bottom] = false; axes.isHeadingVisible[MorphCharts.Edge2D.top] = false; axes.setLabels(0, null); axes.setLabels(1, null); core.renderer.currentAxes = [core.renderer.createCartesian2dAxesVisual(axes)]; }35:Tbb2,function layout1() { mutable layout1Calls++; updateFilter(data.ids); // Facet by disease const facets = 2; const binIds = new Uint32Array(data.disease); // #values = #facets, so use values directly without binning const orderedIds = new Uint32Array(form.count); const facetIds = new Uint32Array(form.count); const offsets = new Uint32Array(facets); const counts = new Uint32Array(facets); const facetHelper = new MorphCharts.Helpers.FacetHelper(core); facetHelper.split1d( data.ids, facets, binIds, orderedIds, facetIds, offsets, counts ); // Right-to-left for (let i = 0; i < form.count; i++) { binIds[i] = 1 - binIds[i]; } // Layout per facet for (let facetId = 0; facetId < facets; facetId++) { const layoutOptions = { offset: offsets[facetId], count: counts[facetId], side: side }; sheet.layout( mutable transitionBuffer.currentBuffer, orderedIds, layoutOptions ); } const vertexOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, padding: padding, thickness: thickness, // staggerOrder: 0 // Facets facetCoordsX: binIds, facetsX: 2, facetSpacingX: facetSpacingX }; sheet.update(mutable transitionBuffer.currentBuffer, data.ids, vertexOptions); mutable transitionBuffer.currentBuffer.unitType = MorphCharts.UnitType.block; mutable transitionBuffer.currentPalette.colors = null; const facetScaling = sheet.facetScaling; const axesOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, divisionsX: 1, divisionsY: 1, minorGridlinesX: 1, minorGridlinesY: 1, arePickDivisionsVisibleX: false, arePickDivisionsVisibleY: false, titleSizeX: core.config.axesTextTitleSize * facetScaling, headingSizeX: core.config.axesTextTitleSize * facetScaling, // Facets scaling: facetScaling }; core.renderer.currentAxes = []; for (let i = 0; i < 2; i++) { const axes = MorphCharts.Axes.Cartesian2dAxesHelper.create( core, axesOptions ); axes.setHeading(0, i ? "healthy" : "disease"); axes.setTitle( 0, i ? `${data.healthyTotal} ${ data.healthyTotal == 1 ? "person" : "people" } ` : `${data.diseaseTotal} ${ data.diseaseTotal == 1 ? "person" : "people" } (${form.count} total, ${(form.prior * 100).toFixed( 1 )}% with disease)` ); axes.isHeadingVisible[MorphCharts.Edge2D.top] = false; axes.isEdgeVisible[MorphCharts.Edge2D.bottom] = false; axes.setLabels(0, null); axes.setLabels(1, null); // Hide zero lines axes.zero[0] = -1; axes.zero[1] = -1; // Facet axes.offsetX = sheet.offsetX(i); core.renderer.currentAxes.push( core.renderer.createCartesian2dAxesVisual(axes) ); } }36:T1177,function layout2() { mutable layout2Calls++; updateFilter(data.ids); // Cross-facet by disease and test result const facetsX = 2; const facetsY = 2; const facets = facetsX * facetsY; const binIdsX = new Uint32Array(data.disease); // #values = #facets, so use values directly without binning const binIdsY = new Uint32Array(data.positiveTest); // #values = #facets, so use values directly without binning for (let i = 0; i < form.count; i++) { binIdsX[i] = 1 - binIdsX[i]; // Right-to-left binIdsY[i] = 1 - binIdsY[i]; // Top-to-botton prevents z-fighting transition } const orderedIds = new Uint32Array(form.count); const facetIds = new Uint32Array(form.count); const offsets = new Uint32Array(facets); const counts = new Uint32Array(facets); const facetHelper = new MorphCharts.Helpers.FacetHelper(core); facetHelper.split2d( data.ids, facetsX, facetsY, binIdsX, binIdsY, orderedIds, facetIds, offsets, counts ); // Layout per facet for (let facetId = 0; facetId < facets; facetId++) { const layoutOptions = { offset: offsets[facetId], count: counts[facetId], side: side }; sheet.layout( mutable transitionBuffer.currentBuffer, orderedIds, layoutOptions ); } const vertexOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, colors: data.positiveTest, minColor: 0, maxColor: 1, padding: padding, thickness: thickness, selected: data.truePositiveIds, // staggerOrder: 0 // Facets facetCoordsX: binIdsX, facetCoordsY: binIdsY, facetsX: 2, facetsY: 2, facetSpacingX: facetSpacingX, facetSpacingY: facetSpacingY }; sheet.update(mutable transitionBuffer.currentBuffer, data.ids, vertexOptions); mutable transitionBuffer.currentBuffer.unitType = MorphCharts.UnitType.block; mutable transitionBuffer.currentPalette.colors = palette; const facetScaling = sheet.facetScaling; const axesOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, divisionsX: 1, divisionsY: 1, minorGridlinesX: 1, minorGridlinesY: 1, arePickDivisionsVisibleX: false, arePickDivisionsVisibleY: false, titleSizeX: core.config.axesTextTitleSize * facetScaling, headingSizeX: core.config.axesTextTitleSize * facetScaling, // Facets scaling: facetScaling }; core.renderer.currentAxes = []; for (let i = 0; i < 4; i++) { const axes = MorphCharts.Axes.Cartesian2dAxesHelper.create( core, axesOptions ); switch (i) { case 2: axes.setHeading(0, "disease, positive test"); axes.setTitle( 0, `${data.truePositiveIds.size} true positive${ data.truePositiveIds.size == 1 ? "" : "s" } (${data.diseaseTotal} with disease, ${Math.round( form.sensitivity * 100 )}% sensitive)` ); break; case 3: axes.setHeading(0, "healthy, positive test"); axes.setTitle( 0, `${data.falsePositiveIds.size} false positive${ data.falsePositiveIds.size == 1 ? "" : "s" } ` ); break; case 0: axes.setHeading(0, "disease, negative test"); axes.setTitle( 0, `${data.falseNegativeIds.size} false negative${ data.falseNegativeIds.size == 1 ? "" : "s" } ` ); break; case 1: axes.setHeading(0, "healthy, negative test"); axes.setTitle( 0, `${data.trueNegativeIds.size} true negative${ data.trueNegativeIds.size == 1 ? "" : "s" } (${data.healthyTotal} healthy, ${Math.round( form.specificity * 100 )}% specific)` ); break; } axes.isHeadingVisible[MorphCharts.Edge2D.top] = false; axes.isEdgeVisible[MorphCharts.Edge2D.bottom] = false; axes.setLabels(0, null); axes.setLabels(1, null); // Hide zero lines axes.zero[0] = -1; axes.zero[1] = -1; // Facet const facetX = i % 2; const facetY = 1 - Math.floor(i / 2); // Top to bottom axes.offsetX = sheet.offsetX(facetX); axes.offsetY = sheet.offsetY(facetY); core.renderer.currentAxes.push( core.renderer.createCartesian2dAxesVisual(axes) ); } }37:T984,function layout3() { mutable layout3Calls++; updateFilter(data.positiveIds); const side2 = side; // Math.ceil(Math.sqrt(data.positiveIds.length)); // Layout const layoutOptions = { side: side }; // Grouped layout sheet.layout( mutable transitionBuffer.currentBuffer, data.positiveIds, layoutOptions ); const vertexOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, colors: data.positiveTest, minColor: 0, maxColor: 1, padding: padding, thickness: thickness, selected: data.truePositiveIds // staggerOrder: 0 }; sheet.update( mutable transitionBuffer.currentBuffer, data.positiveIds, vertexOptions ); mutable transitionBuffer.currentBuffer.unitType = MorphCharts.UnitType.block; mutable transitionBuffer.currentPalette.colors = palette; // Axes const axesOptions = { minBoundsX: minBoundsX, maxBoundsX: maxBoundsX, minBoundsY: minBoundsY, maxBoundsY: maxBoundsY, divisionsX: 1, divisionsY: 1, minorGridlinesX: 1, minorGridlinesY: 1, arePickDivisionsVisibleX: false, arePickDivisionsVisibleY: false, titleX: `${ data.truePositiveIds.size + data.falsePositiveIds.size } positive test${ data.truePositiveIds.size + data.falsePositiveIds.size == 1 ? "" : "s" } (${data.truePositiveIds.size} true positive${ data.truePositiveIds.size == 1 ? "" : "s" }, ${data.falsePositiveIds.size} false positive${ data.falsePositiveIds.size == 1 ? "" : "s" })`, headingX: `Probability of disease for positive test is ${ data.truePositiveIds.size }÷${data.truePositiveIds.size + data.falsePositiveIds.size}=${( (100 * data.truePositiveIds.size) / (data.truePositiveIds.size + data.falsePositiveIds.size) ).toFixed(1)}% (~1 in ${Math.round( (data.truePositiveIds.size + data.falsePositiveIds.size) / data.truePositiveIds.size )})`, headingSizeX: core.config.axesTextTitleSize }; const axes = MorphCharts.Axes.Cartesian2dAxesHelper.create(core, axesOptions); axes.isHeadingVisible[MorphCharts.Edge2D.top] = false; axes.isEdgeVisible[MorphCharts.Edge2D.bottom] = false; axes.setLabels(0, null); axes.setLabels(1, null); axes.zero[0] = -1; axes.zero[1] = -1; core.renderer.currentAxes = [core.renderer.createCartesian2dAxesVisual(axes)]; }38:[] 31:{"id":"2648d29ad07b6cec","slug":"therapeutic-tests-bayes-theorem","title":"Therapeutic Tests (Bayes' Theorem)","thumbnail":"00625ab28350623406b07282b18d9c7e41277d135cabf3c57d647b88b6b4c20c","access_level":"public","create_time":"$D2022-07-14T00:56:42.636Z","update_time":"$D2022-10-20T23:42:11.238Z","view_time":null,"first_public_time":"$D2022-09-21T20:05:42.022Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"f95e5b4875be5cbe","login":"drdavidbrown","name":"Dave Brown","avatar_url":"https://avatars-next.observableusercontent.com/88963fdaa5a5da527a27a6607060a72efff09ca642e8347fc61841b6a4689438","tier":"starter_2024"},"version":912,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"23614d94fc931778","login":"drdavidbrown","name":"Dave Brown","avatar_url":"https://avatars-next.observableusercontent.com/88963fdaa5a5da527a27a6607060a72efff09ca642e8347fc61841b6a4689438","tier":null}],"members":[{"type":"individual","id":"23614d94fc931778","login":"drdavidbrown","name":"Dave Brown","avatar_url":"https://avatars-next.observableusercontent.com/88963fdaa5a5da527a27a6607060a72efff09ca642e8347fc61841b6a4689438","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"538dbedaffa7a57e","slug":"morphcharts","title":"MorphCharts","owner":{"id":"f95e5b4875be5cbe","login":"drdavidbrown","name":"Dave Brown"}},"type":"notebook","body":{"title":"Therapeutic Tests (Bayes' Theorem)","cells":[{"id":0,"value":"# Therapeutic Tests (Bayes' Theorem)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":885,"value":"### If a person gets a positive result from a therapeutic test, how likely are they to have the disease?\n\nSee [morphcharts.com](https://morphcharts.com) for more information on the MorphCharts library.\n\nThis notebook shows several views of a synthetic dataset to illustrate sensitivity and specificity in a therapeutic test. The data is generated using values for people count, test specificity & sensitivity, and a prior (occurrence of the disease in the sample population).\n\nUse the Next and Prev buttons to step through the views, and adjust the values to see how it affects the visualizations.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"container = html`

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core.config.transitionStaggering, label: \"Transition Staggering\"})\n transitionStaggering : Inputs.range([0,10000], {value: core.config.transitionStaggering, label: \"Transition Staggering\", step: 100}),\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":552,"value":"viewof buttons = Inputs.button([\n [\n \"Reset\",\n () => {\n core.reset(true);\n }\n ],\n [\n \"Prev\",\n () => {\n let index = mutable layoutIndex;\n if (index == 0) {\n index = 3;\n } else {\n index--;\n }\n mutable layoutIndex = index;\n }\n ],\n [\n \"Next\",\n () => {\n let index = mutable layoutIndex;\n if (index == 3) {\n index = 0;\n } else {\n index++;\n }\n mutable layoutIndex = index;\n }\n ]\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"MorphCharts = import(\"https://cdn.skypack.dev/morphcharts\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"core = {\n const core = new MorphCharts.Core({\n container: container\n });\n core.config.modelDistance = 0.55;\n core.config.selectionColor = [0.9, 0.9, 0];\n core.config.axesGridBackgroundColor = [0.9, 0.9, 0.9];\n core.config.axesGridMajorColor = [0, 0, 0];\n core.reset(false);\n return core;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"renderer = {\n const renderer = new MorphCharts.Renderers.Basic.Main({\n antialias: true,\n });\n core.renderer = renderer;\n return renderer;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"palette = new Uint8Array([\n 0x10, 0xc0, 0xc0, 0xff, // Healthy\n 0xc0, 0x10, 0x10, 0xff // Disease\n]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"sheet = new MorphCharts.Layouts.Sheet(core);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"mutable transitionBuffer = 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useTransition);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"function layout(index, useTransition) {\n mutable layoutPasses++;\n\n if (useTransition) {\n core.renderer.transitionBuffers[0].swap();\n core.renderer.swapAxes();\n }\n switch (index) {\n case 0:\n layout0();\n break;\n case 1:\n layout1();\n break;\n case 2:\n layout2();\n break;\n case 3:\n layout3();\n break;\n }\n if (useTransition) {\n // Begin transition\n core.renderer.transitionTime = 0;\n core.renderer.axesVisibility = MorphCharts.AxesVisibility.none;\n mutable isTransitioning = true;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":736,"value":"mutable filter = null;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":728,"value":"function updateFilter(ids) {\n if (mutable filter != ids) {\n mutable filter = ids;\n const transitionBuffer2 = core.renderer.createTransitionBuffer(ids);\n if (mutable transitionBuffer != null) {\n const previousTransitionBuffer = mutable transitionBuffer;\n transitionBuffer2.previousBuffer.copyFrom(previousTransitionBuffer.previousBuffer);\n transitionBuffer2.previousBuffer.unitType = previousTransitionBuffer.previousBuffer.unitType;\n transitionBuffer2.previousBuffer.update();\n transitionBuffer2.previousPalette.copyFrom(previousTransitionBuffer.previousPalette);\n }\n mutable transitionBuffer = transitionBuffer2;\n core.renderer.transitionBuffers = [mutable transitionBuffer];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":259,"value":"{\n let transitionTime = 0;\n core.config.transitionDuration = parseInt(form.transitionDuration);\n core.config.transitionStaggering = parseInt(form.transitionStaggering);\n const totalTime =\n core.config.transitionDuration + core.config.transitionStaggering;\n while (isTransitioning) {\n transitionTime += 1000 / 60;\n if (transitionTime > totalTime) {\n transitionTime = totalTime;\n mutable isTransitioning = false;\n }\n core.renderer.transitionTime = transitionTime / totalTime;\n yield transitionTime;\n }\n core.renderer.axesVisibility = MorphCharts.AxesVisibility.current;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"side = 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