21:null 22:["$","title",null,{"children":"Why Librela’s Adverse Reaction Rate is Probably Higher Than 0.18% | d8abased | Observable"}] 27:T524,

Description	Variable	Value
Alleged incidence rate for Librela sADRs (per Zoetis)	${tex`P(\text{L}_{\text{sADR}})`}	0.18%
Total number of dogs affected by a sADR	${tex`N_{\text{dogs\_affected}}`}	Missing
Total number of dogs treated	${tex`N_{\text{dogs\_treated}}`}	Missing
Total number of doses distributed (per Zoetis)	${tex`N_{\text{doses\_distributed}}`}	~${dosesDistributedApril2024.toLocaleString('en-US')} doses
Total number of doses administered	${tex`N_{\text{doses\_administered}}`}	Missing
^*The official global sADR cases received before April 1, 2024, _[d8abased Search and Download](https://librela.d8abased.com/search)_

28:T575,

Description	Variable	Value
Alleged incidence rate for Librela sADRs (per Zoetis)	${tex`P(\text{L}_{\text{sADR}})`}	0.18% (i.e. 1 in 556)
Total number of dogs affected by a sADR (per EVVet)	${tex`N_{\text{dogs\_affected}}`}	${dogsAffectedApril2024.toLocaleString('en-US')}^\*
Total number of dogs treated (calculated)	${tex`N_{\text{dogs\_treated}}`}	${dogsTreatedApril2024}
Total number of doses distributed (per Zoetis)	${tex`N_{\text{doses\_distributed}}`}	~${dosesDistributedApril2024.toLocaleString('en-US')}
Total number of doses administered	${tex`N_{\text{doses\_administered}}`}	Missing
^*The official global sADR cases received before April 1, 2024, _[d8abased Search and Download](https://librela.d8abased.com/search)_

29:T68b,On April 1, 2024 when the incidence rate metrics came to light, Librela had been in the global market for `~${timeInMarketApril2024[1]} months` and in U.S. market for `~7 months`. It is a _monthly_ injection that, according to Zoetis, requires a _minimum_ of 2 doses to demonstrate efficacy. And according to Zoetis, it is a wildly successful and popular product: In Zoetis’ CEO’s own words from their [Q4 2023 earnings call](https://www.fool.com/earnings/call-transcripts/2024/02/13/zoetis-zts-q4-2023-earnings-call-transcript/) ([archive](https://archive.is/VaYY0)): > _We don't just follow trends, we make markets. The launch of Librela and Solensia, the first two injectable monoclonal antibodies for the alleviation of osteoarthritis is fundamentally improving the quality of life for dogs and cats and strengthening the human-animal bond. That's why today, Librela remains the No. 1 selling OA pain product in Europe._ Also, CEO Kristen Peck on the [Q1 2024 earnings](https://www.fool.com/earnings/call-transcripts/2024/05/03/zoetis-zts-q1-2024-earnings-call-transcript/) ([archive](https://archive.is/DP6OI)) call: > _Backed by that commitment, Librela and Solensia are safe and effective. They are anchored in 10 years of science and have been used in Europe for more than three years. In the U.S., 78% of veterinarians who are at the center of care are very satisfied with Librela._ And: > _At Investor Day last May and again at the JPMorgan Healthcare Conference, I shared that our own pain franchise could have peak sales exceeding $1 billion. And we are excited about Librela's performance since its U.S. launch in October, which reaffirms that view. _2a:T688,

Description	Variable	Value
Total number of doses distributed (per Zoetis)	${tex`N_{\text{doses\_distributed}}`}	${dosesDistributedApril2024.toLocaleString('en-US')}^\*
Average doses per dog (simulated)	${tex`N_{\text{doses\_per\_dog}}`}	${(simulator?.doses ?? simulation[9].doses).toLocaleString('en-US')}
Total number of dogs treated with Librela (approx)	${tex`N_{\text{dogs\_treated}}`}	${(simulator?.dogsTreated ?? simulation[9].dogsTreated).toLocaleString('en-US')}
Total number of dogs affected by a sADR (per EVVet)	${tex`N_{\text{dogs\_affected}}`}	${dogsAffectedApril2024.toLocaleString('en-US')}^\*
Incidence rate for Librela sADRs (approx)	${tex`P(\text{L}_{\text{sADR}})`}	${(simulator?.incidenceRateRatio ?? simulation[9].incidenceRateRatio)} (${(simulator?.incidenceRatePercent ?? simulation[9].incidenceRatePercent)}%)
^\*Before April 2024

2b:Te0d,viewof simulator = { const data = simulation; const plot = Plot.plot({ width: width, marginLeft: 0, marginRight: 0, marginBottom: 40, insetTop: 20, height: 600, caption: "Simulation to demonstrate the relationship between average Librela doses per dog and incidence rate for sADRs.", x: { tickSize: 4, label: "Average doses per dog →", labelAnchor: "right" }, y: { label: null }, color: { scheme: "Reds" }, marks: [ Plot.barY( data, { x: "doses", y: "avgDelta", fill: "doses", rx: 6, ry: 6 } ), Plot.barY( data, Plot.pointerX( { x: "doses", y: "avgDelta", fill: "gray", mixBlendMode: "color-dodge", fillOpacity: 0.6, // strokeWidth: 4, // stroke: "black", // strokeOpacity: 0.2, inset: 2, rx: 4, ry: 4 } ) ), Plot.text( data, { x: "doses", y: "avgDelta", text: (d) => d.doses == 2 ? "← Zoetis’ estimate (2)" : d.doses == 10 && dosesDistribution == "Left-skewed" ? "← Mean (10)" : (d.doses == 19 && dosesDistribution == "Gaussian") ? "← Mean (19)" : null, textAnchor: "start", lineAnchor: "middle", dy: 10, fontSize: 11, fontWeight: 600, fill: "red", strokeWidth: 6, stroke: "white", strokeOpacity: 1 } ), Plot.tip( data, Plot.pointerX( { px: "doses", py: "avgDelta", fill: "white", fillOpacity: 0.80, monospace: true, title: (d) => `avg doses/dog: ${d.doses} \n incidence rate: ~${d.incidenceRateRatio} (${d.incidenceRatePercent}%) \n dogs treated: ~${d.dogsTreated.toLocaleString('en-US')}` , pointerSize: 0, fontSize: 12, strokeOpacity: 0.33, frameAnchor: "top-right", } ) ) ] }); // d3.select(plot) // // .selectAll("rect") // .on("pointerleave", function(event, i) { // console.log(event) // plot.value = simulation[9]; // plot.dispatchEvent(new Event("input", {bubbles: true})); // //element.value == null ? console.log("poo") : console.log("whee"); // }) // .on("pointerout", function(event, i) { // console.log(event) // plot.value = simulation[9]; // plot.dispatchEvent(new Event("input", {bubbles: true})); // //element.value == null ? console.log("poo") : console.log("whee"); // }) // .on("pointercanncel", function(event, i) { // console.log(event) // plot.value = simulation[9]; // plot.dispatchEvent(new Event("input", {bubbles: true})); // //element.value == null ? console.log("poo") : console.log("whee"); // }); // element.value = simulation[9]; // element.addEventListener("mousemove", (event) => { // element.value = event.value; // console.log(event.value) // }); // element.addEventListener("mousemove", () => { // // element.value = simulation[9]; // element.dispatchEvent(new Event("input", simulation[9])); // // console.log("Mouse out, default set:", element.value); // }); // element.value = element.value ?? simulation[9] // console.log(element.value); return plot }2c:Te64,Our naive model illustrates the impact our assumptions have on the number of dogs treated, and therefore, the suspected incidence rate. The incidence rate provided by Zoetis makes sense if 7 million dogs were treated with Librela by April 1, 2024. Given that _14 million doses_ were sold by then (according to Zoetis), 7 million dogs could only have been treated if each dog received an average of 2 doses. If every dog who had received Librela by then only received an average of 2 doses, then it brings into question the popularity of Librela over the ${timeInMarketApril2024[1]} months the drug had been in the market at the time; and this in turn has a key bearing on the average doses received by every dog. There are, of course, other ways to get to 7 million dogs treated, and even higher. For instance, a majority of dogs could have dropped off after a single dose because of compliance issues, or worse, serious/unexpected sADRs that could have even led to death. Alternatively, and just as problematic, a large proportion of suspected adverse drug reactions could be missing from the reports altogether. No matter what, the closer you get to the higher number of dogs treated in the simulation (for lower average doses per dog), the more it contradicts Librela’s popularity. For example, the only way that 14 million dogs could have been treated is if those dogs dropped off after a single dose of Librela. This in turn begs many questions, like, _“Why doesn’t Librela work on most dogs?”_ or, _“Are many dogs dropping off Librela due to true lack of efficacy or adverse drug reactions?”_ Of course, it is also possible that 14 million dogs all got their very first dose in March 2024, despite Librela having been on the global market for ${timeInMarketApril2024[1]} months, but that contradicts the alleged popularity of Librela and the allegedly high re-order rates, as established by CEO Kristen Peck on the [Q1 2024 earnings call](https://www.fool.com/earnings/call-transcripts/2024/05/03/zoetis-zts-q1-2024-earnings-call-transcript/) ([archive](https://archive.is/DP6OI)): >_We continue to see good growth in penetration, as well as strong reorder rates, which are approaching 80%, all of which points to positive real-world satisfaction in the clinic and among pet owners._ It also contradicts the sADR reporting trends shown in the above tick chart that follow commercialization in each country so closely—making it abundantly clear when the product respectively launched. Conversely, the lower number of dogs treated in the simulation (for higher average doses per dog), say, in the range of 2-3 million dogs, begs questions on the flip side, like, _“Is Librela really as popular as Zoetis has made it out to be?”_ or, the obvious, _“Doesn’t this mean that the sADR incidence rate is 3-4 times higher?”_ It’s also important to note that the actual distribution of doses per dog is likely more varied than an average number implies. Some dogs may have started treatment as soon as the drug was available in their market, while others may have started more recently. At this point it should be clear that we’re back where we started—an infinite recursive loop with no terminating clause due to the tension between contradictory conditions that can’t be reconciled without clarification from Zoetis. This tension is further exacerbated by uncertainties around the accuracy of the sADR data, the variability in how adverse events are reported, and the high under-reporting rates (>=95% by most estimates). Without independent validation and more transparency from Zoetis, these contradictions will continue to create ambiguity.2d:Td45,We covered a lot of ground in this notebook in service of establishing a mathematical proof for Zoetis' alleged sADR incidence rate for Librela. In short, when paired with the extremely positive qualitative statements the company has made about the drug, the numbers _do not_ add up. As we've demonstrated, the key is to accurately estimate _total dogs treated_, a task whose difficulty is articulated by the United States Food and Drug Administration (FDA) in their April 1, 2024 [response to a FOIA request for records regarding adverse event reports received for Librela](https://www.fda.gov/media/178955/download?attachment) (page 3, emphasis theirs): > _**Accumulated ADE reports should not be used to calculate incidence rates or estimates of drug risk**, because there is no accurate way to determine how many animals were actually given the drug, which is needed as the denominator in calculations of incidence and relative risk._ It seems Zoetis ignored this recommendation from the FDA. And, while we don’t exactly know how Zoetis has determined the number of dogs treated with Librela (i.e. the _denominator_ mentioned in the FDA response), we’ve attempted to reverse-engineer their math and have shown our work in this notebook. Zoetis’ Executive Vice President and Chief Financial Officer, Wetteny N. Joseph, confirmed on the company's [Q2 2024 Earnings Call](https://www.fool.com/earnings/call-transcripts/2024/08/06/zoetis-zts-q2-2024-earnings-call-transcript/) ([archive](https://archive.is/7GU7k)) that they plan to expand their market to dogs with _mild OA_: > _In Europe, shipment is **expanding to moderate and mild OA cases** that were largely untreated, now making up more than 65% of total cases. This is just a glimpse into what we expect in the U.S. over time, as Librela continues to expand the addressable market and gain market share. Despite our early success, we still have significant room for continued expansion._ This is alarming to say the least against the backdrop of our current discussion. --- **We challenge Zoetis to share their mathematics with the public, _before_ they ramp up the expansion of Librela's target market to dogs with milder osteoarthritis**. --- And we hope Zoetis’ disclosure will consider the various factors that should be included in any incidence rate model—from doses in storage to reporting delays that would further exacerbate the numerator in the formula. Not to mention, it will also need to consider the overlooked issue of _suspected drug reaction underreporting_. Scientific literature has consistently found that [over 9 out of 10 sADRs are never reported](https://pubmed.ncbi.nlm.nih.gov/16689555/)—and that’s for _humans_. Expectedly, it’s [significantly worse](https://bvajournals.onlinelibrary.wiley.com/doi/10.1136/vetreco-2017-000224) for veterinary patients as also called out in the [FDA response](https://www.fda.gov/media/178955/download?attachment): > _Underreporting occurs with most adverse event reporting systems. The frequency of reporting for a given drug product varies over time, and may be greater when the drug is newly marketed, or when media publicity occurs._ In the absence of mathematical clarity from Zoetis, we will be forced to independently derive a more realistic model for the Librela sADR incidence rate in future notebooks. 🐾2e:T89b,function simulateMetrics(rangeStart, rangeEnd, distributionType = 'gaussian') { // Define the min and max values for avgDelta const minAvgDelta = 10; const maxAvgDelta = 100; // Calculate the mean of the range for Gaussian const mean = (rangeStart + rangeEnd) / 2; // Standard deviation for Gaussian const stdDev = (rangeEnd - rangeStart) / 6; // Assuming 99.7% of data falls within ±3 standard deviations // Parameters for the shifted Gaussian distribution to create left skew const peak = 10; const skewMean = peak; const skewStdDev = 6; // Adjust this to control the spread // Gaussian function function gaussian(x, mean, stdDev) { return Math.exp(-0.5 * Math.pow((x - mean) / stdDev, 2)); } // Normalize the Gaussian value within the range function normalize(value, min, max) { return min + (max - min) * value; } // Generate the array const metrics = d3.range(rangeStart, rangeEnd).map(d => { let value; if (distributionType === 'gaussian') { // Calculate the Gaussian value value = gaussian(d, mean, stdDev); } else if (distributionType === 'left-skewed') { // Calculate the shifted Gaussian value value = gaussian(d, skewMean, skewStdDev); } else { throw new Error('Invalid distribution type'); } // Map the value to the avgDelta range const avgDelta = normalize(value, minAvgDelta, maxAvgDelta); const dogsTreated = dosesDistributedApril2024 / d; const incidenceRatePercent = (dogsAffectedApril2024 / dogsTreated) * 100 const incidenceRateRatio = ratio(dogsAffectedApril2024 / dogsTreated) return { doses: d, dogsTreated: Math.round(dogsTreated), incidenceRatePercent: d3.format('.2f')(incidenceRatePercent), incidenceRateRatio: incidenceRateRatio, avgDelta: avgDelta, }; }); //${ratio(dogsAffectedApril2024 / (dosesDistributedApril2024 / d.doses))} (${d3.format('.2f')((dogsAffectedApril2024 / (dosesDistributedApril2024 / d.doses)) * 100)}%) return metrics; }2f:T485,function simulationTable(simulation) { const colorScale = d3.scaleLinear().domain([0, simulation.length - 1]).range(["orange", "#d32221"]); const table = html`

${simulation.map((entry, index) => html` `)}

Average doses per dog (simulated ${tex`N_{\text{doses\_per\_dog}}`})	Total number of dogs treated with Librela (~${tex`N_{\text{dogs\_treated}}`})	Incidence rate for Librela sADRs (~${tex`P(\text{L}_{\text{sADR}})`})
${entry.doses}	${entry.dogsTreated.toLocaleString('en-US')}	${entry.incidenceRateRatio} (${entry.incidenceRatePercent}%)
Table values represent simulation results based April 1, 2024 data

`; return table; }30:[{"id":"e8b9220f3138e11a6c68006d63020a0a56d4c613260132a31dd8f81e8efb590f0dbae5462cbbb420ed1129e7c38b67e13e1f097bec3a0a5d1d9623553fe538a2","href":"https://static.observableusercontent.com/files/e8b9220f3138e11a6c68006d63020a0a56d4c613260132a31dd8f81e8efb590f0dbae5462cbbb420ed1129e7c38b67e13e1f097bec3a0a5d1d9623553fe538a2","name":"14-million.jpg","type":"image/jpeg","lastModified":1722228670600.157,"size":351506},{"id":"188cabd91a3fe0e585e2b605b2b9dd63772839b4e6e162c430a5f825c76bdd6d52930d917849b9ea26d73a06f889a6b8e8c732a1552b90f8f36c8df7995ba7cd","href":"https://static.observableusercontent.com/files/188cabd91a3fe0e585e2b605b2b9dd63772839b4e6e162c430a5f825c76bdd6d52930d917849b9ea26d73a06f889a6b8e8c732a1552b90f8f36c8df7995ba7cd","name":"wsj.jpg","type":"image/jpeg","lastModified":1722230406201.143,"size":454783},{"id":"0729bcbf2cc24ba4c375c420db68257663805afb3d834bae2a34ec42b9e2215e16b1de2220a0024083287e29e1b151884049f538268401c6d711ad5ebb0f1dcc","href":"https://static.observableusercontent.com/files/0729bcbf2cc24ba4c375c420db68257663805afb3d834bae2a34ec42b9e2215e16b1de2220a0024083287e29e1b151884049f538268401c6d711ad5ebb0f1dcc","name":"1in556.jpg","type":"image/jpeg","lastModified":1723856381143.246,"size":463837},{"id":"968f4910682ea4caa9b4453a147af8bb9d0d6039abd9e3e21703c81f288243733d046eb1ba1102003911b4238a413c1c888133c3b27abac5a373418adc5daaba","href":"https://static.observableusercontent.com/files/968f4910682ea4caa9b4453a147af8bb9d0d6039abd9e3e21703c81f288243733d046eb1ba1102003911b4238a413c1c888133c3b27abac5a373418adc5daaba","name":"doses@1.jpg","type":"image/jpeg","lastModified":1723857088486.732,"size":722706},{"id":"57d0add87f15d446edde2e562e73d9d79d9c2ea71af64d88507fc9c81ec2dbddbbac62713984bb4082db52e436b6aadb740ee5f1d7b4240a11a68afa4feb1bcf","href":"https://static.observableusercontent.com/files/57d0add87f15d446edde2e562e73d9d79d9c2ea71af64d88507fc9c81ec2dbddbbac62713984bb4082db52e436b6aadb740ee5f1d7b4240a11a68afa4feb1bcf","name":"librela-talking-point.jpg","type":"image/jpeg","lastModified":1723928209632.609,"size":327152},{"id":"9f9b144e8e1302bb5a8b35d76e3c3d7cbc13fe0c3efb9c76716a365d2c301a304795fc660138d8584f3d23134c9f7774c7b455b5228c0aba8cedab306ca1f8e8","href":"https://static.observableusercontent.com/files/9f9b144e8e1302bb5a8b35d76e3c3d7cbc13fe0c3efb9c76716a365d2c301a304795fc660138d8584f3d23134c9f7774c7b455b5228c0aba8cedab306ca1f8e8","name":"wapo.jpg","type":"image/jpeg","lastModified":1722299231168.681,"size":381128}] 25:{"id":"2b6c1685c60b72fc","slug":"incidenceintro","title":"Why Librela’s Adverse Reaction Rate is Probably Higher Than 0.18%","thumbnail":"e1c304ed996979584aa682046e1f16a4e2d9d0a7973b3b49388a796dd8bd433b","access_level":"public","create_time":"$D2024-07-14T05:34:25.959Z","update_time":"$D2024-10-06T18:50:33.474Z","view_time":null,"first_public_time":"$D2024-08-30T19:31:21.597Z","has_unpublished_edits":null,"fork":false,"stars":8,"starred":false,"owner":{"type":"team","id":"387bada7be81c746","login":"d8abased","name":"d8abased","avatar_url":"https://avatars-next.observableusercontent.com/5680b5bdb4c31365df3342e07cb358027698748c24682dbd4476d6e8cc3e9e82","tier":"starter_2024","bio":"Based, in data."},"version":2833,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"ad011ae0dc79cf45","login":"d8abased","name":"the d8a team","avatar_url":"https://avatars-next.observableusercontent.com/70386b934552f1ef82ce5a323c14a14824b8e72ac7d241df9ecb75c85c27608b","tier":null,"bio":""}],"members":[{"type":"team","id":"387bada7be81c746","login":"d8abased","name":"d8abased","avatar_url":"https://avatars-next.observableusercontent.com/5680b5bdb4c31365df3342e07cb358027698748c24682dbd4476d6e8cc3e9e82","tier":"starter_2024","role":"editor"},{"type":"individual","id":"ad011ae0dc79cf45","login":"d8abased","name":"the d8a team","avatar_url":"https://avatars-next.observableusercontent.com/70386b934552f1ef82ce5a323c14a14824b8e72ac7d241df9ecb75c85c27608b","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":{"id":"8e2a9ac146d4c315","slug":"librela","title":"Librela","owner":{"id":"387bada7be81c746","login":"d8abased","name":"d8abased"}},"type":"notebook","body":{"titling":"auto","title":"Why Librela’s Adverse Reaction Rate is Probably Higher Than 0.18%","cells":[{"id":0,"value":"# Why Librela’s Adverse Reaction Rate is _Probably_ Higher Than 0.18%\n## Using Simple Mathematics to Better Estimate Librela’s Risk","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2310,"value":"

The first principle is that you must not fool yourself—and you are the easiest person to fool.
— Richard Feynman

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":21,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2283,"value":"renderMenu()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"We briefly discussed incidence rates for Librela sADRs in our 📘 [`Explore`](https://librela.d8abased.com/explore) notebook. In this notebook, we will dig deeper into this topic, laying groundwork to help us model a more accurate incidence rate in future notebooks. Along the way we’ll investigate how Zoetis may have calculated the incidence rate they shared for Librela sADRs, why it is likely an underestimate, and how a simple but profound tweak can dramatically improve this estimate.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":61,"value":"## What is Incidence Rate and Why Does It Matter?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"embedContent0","database":"$undefined"},{"id":69,"value":"The incidence rate is the probability that a dog administered Librela could be affected by a suspected adverse drug reaction (sADR), as captured by this formula:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"embedContent1","database":"$undefined"},{"id":79,"value":"embedContent2 = sADRFormula()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2118,"value":"Arguably, _incidence rate_ is the most important metric in pharmacovigilance, as it is the key determinant of _risk_ and the key metric considered by regulatory bodies like the FDA and EMA in approving, rejecting, or recalling a new therapeutic. It puts this critical question in our minds:\n\n> _Would you give your dog Librela if the sADR incidence rate was_ `1 in 10,000`? _How about_ `1 in 1,000`, `1 in 100`, `1 in 500`, or `1 in 10`?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"embedContent3","database":"$undefined"},{"id":2752,"value":"While the formula looks simple, the devil here is truly in the details. There are numerous factors that affect the variables that determine the incidence rate.\n\nFor instance, the numerator, ${tex`N_{\\text{dogs\\_affected}}`}, can become artificially low in myriad ways, e.g. Zoetis is only required to report the “serious and unexpected” cases to the FDA within 15 days while the rest can wait for 6 months; standardization issues in VeDDRA terms can end up breaking a single reaction like _ataxia_ into 3-4 reactions; outright failure to report, etc. \n\nConversely, the denominator, ${tex`N_{\\text{dogs\\_treated}}`}, can be rendered artificially high as well, e.g. lack of visibility into how many doses were administered vs. sitting in storage, larger breeds receiving multiple vials as a dose, etc.\n\nThe incidence rate, like any mathematical formula, can be easily gamed even without premeditated malice. And that is why it must be handled with the greatest care.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":187,"value":"## What has Zoetis Shared Publicly?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":648,"value":"On April 12, 2024, _**The Wall Street Journal**_ ran a story about Librela titled, _[“What Killed Their Pets? Owners Blame Meds, but Vets Aren’t Sure”](https://www.wsj.com/health/pharma/dog-cat-arthritis-drugs-bcdddea6)_ ([archive](https://archive.is/5isvx#selection-2609.252-2609.294)): ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":656,"value":"wsj = FileAttachment(\"wsj.jpg\").image({\n style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n width: 650\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":666,"value":"From the story, in reference to Librela and Solensia (Librela’s sister drug for cats; emphasis ours):\n\n> _Zoetis says the medicines are safe, with reports of side effects representing **well less than 1% of the more than 18 million shots of both drugs combined administered** to date in the U.S. and abroad._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":670,"value":"\n\nThe news spread quickly and `NYSE:ZTS` stock was down 8% by the end of the day. In an effort to reassure the public, Zoetis began sharing the alleged incidence rate of Librela adverse drug reactions: `0.18%`.\n\nFor instance, that very day **_Investopedia_** published the incidence rate in their piece titled _[Zoetis Stock Slumps on Report Suggesting Its Arthritis Drugs May Make Pets Sick](https://www.investopedia.com/zoetis-stock-slumps-on-report-suggesting-its-arthritis-drugs-may-make-pets-sick-8630785)_ ([archive](https://archive.is/Uwagg); emphasis ours):\n\n> _In an email to Investopedia, Zoetis said that the drugs are “both safe and effective.” It added that more than 18 million doses have been distributed, and it has \"continued to see **low rates of adverse events with only 0.18% reported for Librela** and 0.3% for Solensia.\"_","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":189,"value":"Then, roughly a week later, on April 20, 2024, _**The Washington Post**_ published _[An arthritis drug helps old dogs, but some owners worry about side effects](https://archive.ph/JmY94)_ ([archive](https://archive.is/5cBNn)).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":758,"value":"wapo = FileAttachment(\"wapo.jpg\").image({\n style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n width: 650\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":765,"value":"This piece carried a corroborating quote from Zoetis’ President of Research and Development, [Robert Polzer](https://www.zoetis.com/our-company/our-story/executive-team/robert-polzer): \n\n> _...a fraction of the dogs using Librela (**less than 0.20 percent**) have experienced “an adverse event,” said Robert Polzer, president of research and development at Zoetis._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":633,"value":"Finally, a couple of weeks later, Zoetis’ CEO, _Kristen Peck_ confirmed the incidence rate on [Zoetis’ Q1 2024 Earnings Call](https://www.fool.com/earnings/call-transcripts/2024/05/03/zoetis-zts-q1-2024-earnings-call-transcript/) ([archive](https://archive.is/DP6OI), emphasis ours):\n\n> _And if you overall look at the rate of reported adverse events, it's about **18% per 10,000 or 0.18%** globally. And I think it's important to keep in mind that no single adverse event is classified under the EMEA guidelines as more than rare, which is more than 1 to 10 out of 10,000. So, we remain very confident in the safety and efficacy of this product. We watch these reported adverse events very carefully._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2388,"value":"Regarding the number of doses administered, Zoetis gave a quote to the [**_Veterinary Information Network (VIN) News Service_**](https://news.vin.com/default.aspx?pid=210&catId=619&Id=12137959) ([archive](https://archive.is/vSuEX)), the media arm of one of the largest online information services devoted to veterinary medicine, with a more granular number than was reported earlier in **_The Wall Street Journal_** (emphasis ours):\n\n> _Zoetis has distributed more than **14 million doses of Librela** and 4 million doses of Solensia since the drugs debuted in 2021, the company told VIN News. It added that the estimated rate of adverse events \"continues to be low with only 0.18% reported for Librela and 0.33% for Solensia\" as of March 2024._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":619,"value":"This was also confirmed in Zoetis’ [own marketing web site](https://www.zoetispetcare.com/products/librela/facts) ([archive](https://web.archive.org/web/20240607233822/https://www.zoetispetcare.com/products/librela/facts)):","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":623,"value":"million = FileAttachment(\"14-million.jpg\").image({\n width: 650,\n style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":695,"value":"You can find other sources as well for the same _incidence rate_ and _doses distributed_ metrics but we have enough for our purposes. So, let’s summarize what we know so far from Zoetis, and then see what we can do with this information.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2113,"value":"$27","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2112,"value":"## Visualizing Incidence Rates","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":83,"value":"As we just established, Librela’s alleged sADR incidence rate on April 1, 2024 was:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":87,"value":"$${tex.block`\nP(\\text{L}_{\\text{sADR}}) = 0.18\\%\n`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":94,"value":"Now, most human brains have trouble picturing what this means, so let’s take a quick sidebar to fix that. \n\nThere is cognitive load in decoding a per_cent_ (i.e. per hundred), especially when the value itself is a fraction. So, our brain usually just short-circuits to, _\"That’s a small number. Nothing to see here!”_, when in fact, `0.18%` can be magnificently large. Context matters a lot, as well as your brain’s ability to break past the optical illusion of percents and reason accurately about what it sees. \n\nLuckily, mathematics gives us an elegant tool for this situation: _ratios_. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":130,"value":"Let’s convert `0.18%` to a ratio and simplify it:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":150,"value":"

\n${tex.block`\n0.18\\% = \\frac{0.18}{100} \\Rightarrow \\frac{18}{10,000} \\Rightarrow \\frac{9}{5000} \\Rightarrow 9 \\text{ in } 5000\n`}\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":143,"value":"In plain English this translates to:\n\n> _For every 5000 dogs treated with Librela, 9 of them will experience an adverse drug reaction._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":145,"value":"We’re willing to bet that your brain can picture this much better. But we can do better and make it more intuitive using some elementary school arithmetic. Let’s divide the numerator and denominator by 9:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":147,"value":"

\n${tex.block`\n\\frac{9}{5000} \\div \\frac{9}{9} = \\frac{9 \\div 9}{5000 \\div 9} = \\frac{1}{556} \\Rightarrow 1 \\text{ in } 556\n`}\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":175,"value":"_Now_ we’re getting somewhere. In plain language, here's what the alleged incidence rate means:\n\n> _For every 556 dogs treated with Librela, 1 of them will experience an adverse drug reaction._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":324,"value":"We bet this is a _lot_ easier to visualize. Now you can set your mind’s eye on one dog in a group of dogs. In fact, if your brain isn’t averse to healthy caution, we bet you pictured _your_ dog among 556 dogs, randomly chosen to experience an ADR.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2421,"value":"

\n ${await \n FileAttachment(\"1in556.jpg\").image({style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n })\n }\n

The percent 0.18 is better expressed as 1 in 556. This image was created with the assistance of DALL·E 2.

\n","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":178,"value":"Expressing percents as ratios is an age-old technique to aid better decision-making when _rates_ are involved. We’ll use this format henceforth and we suggest you do as well, not just in conversations about Librela, but as a way to better understand the world and make choices in your day-to-day lives.\n\nNow we can move on to discussing where this `1 in 556` incidence rate came from.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2098,"value":"## How Zoetis May Have Arrived At This Alleged Incidence Rate, and What Does It Tell Us?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2097,"value":"Let's use this alleged incidence rate to calculate the _**number of dogs**_ who have been treated with Librela, and the _**number of doses**_ these dogs received.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":216,"value":"Recall our incidence rate formula:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1072,"value":"sADRFormula()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2096,"value":"Thanks to the work we already did in [prior notebooks](https://librela.d8abased.com/search), we know that ${tex`N_{\\text{dogs\\_affected}}`} was `${dogsAffectedApril2024.toLocaleString('en-US')}` at the end of March (Q1) 2024.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":341,"value":"Plugging in the values:\n\n${tex.block`\n0.18\\% = \\left( \\frac{${dogsAffectedApril2024.toLocaleString('en-US')}}{N_{\\text{dogs\\_treated}}} \\right)\n`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":234,"value":"And solving for ${tex`N_{\\text{dogs\\_treated}}`}:\n

\n${tex.block`\nN_{\\text{dogs\\_treated}} = \\frac{${dogsAffectedApril2024.toLocaleString('en-US')}}{0.0018} \\approx ${(Math.round(dogsAffectedApril2024 / 0.0018)).toLocaleString('en-US')}\n`}\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":364,"value":"### `Takeaway 1` According to Zoetis, it seems ~${d3.format(\".1s\")((Math.round(dogsAffectedApril2024 / 0.0018)))} dogs had been treated with Librela by April 1, 2024","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2460,"value":"So, the first thing the alleged `1 in 556` incidence rate tells us is, according to Zoetis, approximately `${d3.format(\".1s\")((Math.round(dogsAffectedApril2024 / 0.0018)))} (million)` dogs were treated with Librela at the time of the Zoetis disclosure in April, 2024.\n\nLet's add that to our data table before we move on.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":987,"value":"$28","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":408,"value":"Now, let’s consider the formula to calculate average doses administered per dog:\n\n

\n${tex.block`\nN_{\\text{doses\\_per\\_dog}} = \\left( \\frac{N_{\\text{doses\\_administered}}}{N_{\\text{dogs\\_treated}}} \\right)\n`}\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1153,"value":"When we assume that all distributed doses were administered (which is not the case in reality, but let’s keep things simple for now), our formula to determine _average doses per dog_, works out as follows:\n\n

\n${tex.block`\nN_{\\text{doses\\_per\\_dog}} = \\left( \\frac{N_{\\text{doses\\_administered}}}{N_{\\text{dogs\\_treated}}} \\right) \\approx \\left( \\frac{N_{\\text{doses\\_distributed}}}{N_{\\text{dogs\\_treated}}} \\right) = \\left( \\frac{${dosesDistributedApril2024.toLocaleString('en-US')}}{${dogsTreatedApril2024}} \\right) \\approx ${(Math.round(dosesDistributedApril2024 / (dogsAffectedApril2024 / 0.0018))).toLocaleString('en-US')} \\text{ doses}\n`}\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1146,"value":"Zoetis’ own [marketing materials](https://www.zoetispetcare.com/products/librela/facts) ([archive](https://web.archive.org/web/20240607233822/https://www.zoetispetcare.com/products/librela/facts)) seems to confirm this number (see highlights): ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1139,"value":"doses = FileAttachment(\"doses@1.jpg\").image({\n width: 650,\n style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2467,"value":"### `Takeaway 2` According to Zoetis, it seems dogs treated with Librela before April 2024 had an average of 2 doses","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1176,"value":"The second thing that the alleged `1 in 556` incidence rate tells us is, on average, dogs treated with Librela before April 2024, received `2 doses`. At least, that seems to be the case according to Zoetis.\n\nAnd if this is indeed the case, it has very big implications. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1179,"value":"## Dosis Sola Facit Venenum\n#### _The Dose is the Poison_","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1199,"value":"$29","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1219,"value":"Could such a prolifically marketed, monthly medication that has been on the global market for `~${timeInMarketApril2024[1]} months` as of April 2024—a medication that, by Zoetis’ own admission, _“remains the No. 1 selling OA pain product in Europe”_ and has exceeded sales expectations in the U.S.—have only ever be administered _twice_ on average in every dog that’s ever been treated with it? \n\nWhat if that is incorrect, and the average doses of Librela per dog is actually _higher_? As you'll see below, that would end up _decreasing_ the number of dogs treated, and ultimately _increase_ the incidence rate of a Librela sADR.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1245,"value":"## Improving the Estimate of Average Doses per Dog and Librela sADR Incidence Rate\n#### _A Naive Simulator_","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1189,"value":"The tick chart below of the sADRS reported over Librela’s lifetime shows the true scale of Librela’s time in the global market.\n\nThe implication here is that while some dogs have had only a shot or two of Librela, there are dogs who have likely been receiving Librela for a much longer period (monthly, for years, in fact). The theoretical range for what comprised a Librela treatment on April 1, 2024 was `${timeInMarketApril2024[0]} to ${timeInMarketApril2024[1]} doses`.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1191,"value":"mainTickChart","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1258,"value":"We can simulate a naive left-skewed distribution of average total doses per dog (you can select a normal gaussian distribution for comparison) to visualize the effect of higher average doses per dog on the bigger picture. Given all the factors we’ve discussed so far—time in market, sales insights, etc.—the average dog treated with Librela likely received less than the gaussian mean of `${d3.mean(timeInMarketApril2024)} doses` but almost certainly more than the `2 doses` suggested by Zoetis' marketing materials. It is a monthly injectable, after all, and Zoetis’ own [_Librela Talking Points_](https://www.zoetisus.com/content/pages/Products/Dogs/Librela/Resources/documents/Professional-Resources-Talking-Points-US.pdf) ([archive](https://web.archive.org/web/20240819011925/https://www.zoetisus.com/content/pages/Products/Dogs/Librela/Resources/documents/Pet-Owner-Resources-Print-Brochure-US.pdf)) resource for veterinarians _trains_ them to emphasize this:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2661,"value":"

\n ${await \n FileAttachment(\"librela-talking-point.jpg\").image({\n style: \"border-radius: 0.3rem; border: 1px solid #eeeeee; box-shadow: 0 0px 12px rgba(0, 0, 0, 0.1);\",\n })\n }\n

“Mention that Librela should be given once a month, every month, to ensure the best possible results”, source: Talking With Dog Owners About Librela, downloaded from the Librela ordering page’s Tools & Resources section for veterinarians.

\n","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2658,"value":"Coming back to our simulator, remember, this is a naive model much like the one Zoetis proffered, but it does have one critical improvement: a more _realistic_ measure of the average doses of Librela administered per dog, based on the total time the drug has been in the global market. \n\nAt the risk of overly quoting [George Box](https://en.wikipedia.org/wiki/George_E._P._Box)’s timeless wisdom: \n\n> _“All models are wrong, some are useful.”_\n\nSo, let’s see how our naive simulator can be more useful than Zoetis’ opaque `0.18%` claim.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2080,"value":"Take a second to hover over the red bars below that represent average Librela doses per dog, to see the effect it has on the total number of dogs who received Librela, as well as the incidence rate for a suspected drug reaction (sADR). Use the tick chart above as a guide to estimate how many doses the average dog could have received based on how long Librela has been in different markets.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1450,"value":"viewof dosesDistribution = Inputs.radio([\"Left-skewed\", \"Gaussian\"], {label: \"Distribution\", value: \"Left-skewed\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1480,"value":"$2a","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1299,"value":"$2b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2075,"value":"For those who prefer tables over interactivity, here are the results of the full simulation:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2074,"value":"simulationTable(simulation)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2073,"value":"$2c","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2063,"value":"## Finally & What’s 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