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If the company is denied the financial support for the project B, then it will continue to produce the existing types of medications with a guaranteed profit of $ .. However, the cost of preparing the proposal for Hirschmann Scientific Foundation would still be $1 million. If funding is received for drug B, then, outcomes for drug B research can be a success and a profit of $ ... or a failure and loss of $ On other words, Success A support Failure Hint 4: We have to develop each decision alternative. If we select "Exciting Medications" alternative, then it means that the company prefers not to apply for financial support. The company will continue to produce the existing types of medications with a guaranteed profit of $ . Note that in this case the cost of preparing the proposal for Hirschmann Scientific Foundation is not applicable. Project A Project B O Existing MedicationsSTAT 2112 Assignment 1 In today's world, there is a growing need for new and innovative drugs, vaccines, biologicals, diagnostics and gene therapeutics, particularly now that people are getting older and more and more microorganisms are becoming resistant to drugs. J ean-J acques Berthoud Pharmaceutical Company (Berthoud C ompagnie Pharmaceutique or Berthoud for short) began operations in a small lab at McGill University in 1998, primarily focusing on meeting the chemical needs of local researchers. The company became known for its strong chemistry expertise and expanded both its operational lab footprint as well as its customer base. By 2010, Berthoud had outgrown its operational space and moved to its current 100,000 square foot facility in Montreal. The company provides drug discovery, development and manufacturing services to the pharmaceutical and biotechnology industries in Canada. The company is currently about to make an important strategic decision. It is becoming increasingly clear that in addition to surgery, chemotherapy, and radiation, cancer immunotherapy has grown into a new and very promising method of cancer treatment. Unlike other methods, immunotherapy focuses on using your body's own immune system to fight cancer. One factor is becoming more and more important over the last months. Recent statistics showed that the morbidity and mortality of COVID- 19 is higher in elderly and male patients. Specically in cancer patients, those who are elderly andlor who have lung cancer, hematologic malignancy, advanced-stage disease, active solid tumor, or a diagnosis of solid tumor in the past 5 years, or who had oncological surgery performed in the last 30 days, are at highest risk of an unfavorable outcome. However, statistical analysis also showed that namely in such cases immunotherapeutic drugs proved extremely efcient and can be literally life-saving. There are challenges, however. First, most of the immunotherapeutic drugs are very new and their side effects are not yet properly studied. Secondly, these medications are usually very expensive and so far are mostly not covered by OHIP and similar insurance plans. Revised Decision Tree Hint 1: The company is considering hiring the Edinburgh Medical Research Company (EMRC) from UK to estimate their chances with the development and financial success of drug B. Or, in other words, the company needs to choose wisely whether to hire or not the Edinburgh Medical Research Company (EMRC) specialists. That is what the construction of the revised decision tree should start with. 6 HIRE O HIRE Do Not HIRE Simple Do Not Decision HIRE Tree Hint 2: If the company hires the Edinburgh Medical Research Company (EMRC) specialists, then they will provide either favourable report predicting a success of the drug B research, or unfavourable report predicting that the research for drug B will most likely end up in failure. At this step, the posterior probabilities should be calculated. For that, it is better to summarize all given probability information. Originally, the probability of Health Canada approval of the created medication B (success for drug B) is 0.25 or 25%, and there is 0.75 or 75% of failure in research of drug B. It is known that there is a 90% chance that EMRC provides a favourable report given the positive outcome. There is also an 80% chance that EMRC provides an unfavourable repot given the negative outcome. P(Failure) = 0.75 P(Unfavourable|Success) = P(Unfavourable| Failure) = 0.80 P(Success) = 0.25 P(Favourable|Success) = 0.90 P(Favourable|Failure) =Berthoud has a very strong research branch - the Lavoisier Medical Research Institute or Lavoisier Institut de Recherche Medicale (LIRM), where renowned scientists, including one Nobel Prize winner, work side by side with young and enthusiastic recent university graduates. The scientists from the LIRM came up with two revolutionary ideas responding to the challenges of immunotherapy. They started developing a medication (let us call it drug A as the true chemical name is very long) that is supposed to be at least as efficient as existing types of immunotherapeutic medications, but much less expensive and therefore available to most patients. Meanwhile, another group at the LIRM are working on drug B (let us call it this), which will be expensive still, but is based on new principles and is expected to be extremely efficient with minimum side effects. Both research directions need a lot of funding, but they could generate a huge profit for Berthoud. Drug B would potentially become more profitable for the company than drug A, but drug A research has a higher likelihood of being completed within 1-2 years. At this point, the company has some financial difficulties and cannot fully support these LIRM projects. Therefore, the company's research teams are going to apply to the famous Hirschmann Scientific Foundation, known to be very generous when it comes to anticancer research. According to the rules, however, the foundation will consider only one project, so the company is facing a dilemma: to go ahead with project A or project B if they want to apply for funding. Each project has an estimated cost of $60 million, and the foundation can cover half of it. The rest will be invested by the company. At this point the management think that they have an 80% chance to get support from Hirschmann Scientific Foundation if they submit the project A proposal and a 70% chance to get support from Hirschmann Scientific Foundation if they submit the project B proposal. If the company's proposal is rejected or not submitted for whatever reason, then Berthoud will continue to produce existing immunotherapeutic medications instead of developing new ones. Not necessarily, every promising idea ends up in success. If funding is received for drug A, then, realistically speaking, the detailed forecast would look like this: Outcomes for drug A research Probability Profit/Loss (S millions) Great success 0.20 500 Moderate success 0.10 200 Some success 0.30 50 No success 0.40 - 100 If funding is received for drug B, then the detailed forecast would not be readily available as the research will be based on the methods that have never been used before. Then the forecast would look like this: Outcomes for drug B research Probability Profit/Loss ($ millions) Success 0.25 1000 Failure 0.75 - 250 If the company is denied financial support or prefers not to apply, then it will continue to produce the existing types of medications with a guaranteed profit of $50 million. Profits/losses listed above do not incorporate the supposed $30 million investment by the company in the research. The cost of preparing the proposal for Hirschmann Scientific Foundation is $1 million.Hint 3: In the next step, we have to calculate the posterior probabilities. To do that we can ll out the following tables: Probability Revisions Given a Favourable Report State of Prior Conditional Probability Joint Posterior Probability Nature Probability P(Fav.|State of Nature) Probability P(State of NatureIFav.) Probability Revisions Given UuFavoIrable Report State of Conditional Probability Joint Posterior Probability Nature Probability P(Fav.lState of Nature) Probability P(State of NatureIFav.) WM.- --_l Hint 4: After receiving favourable or unfavourable report from EMRC specialists, the comapny still has to make a decision. Note, that information from experts cannot change probabilities related to the project A and Existing Medication, so EMVs of Project A and Existing Medication remain invariant, practically the same as in the simple tree (except for specialists' fee that eventually will be subtracted). Only Project B is affected, as altered probabilities would alter the EMV. Therefore, However, some in the management think that the development and production of drug B entails too much risk and uncertainty, and it would be better to focus on drug A only. The company is considering hiring the Edinburgh Medical Research Company (EMRC) from UK to estimate their chances with the development and nancial success of drug B. EMRC experts will provide a favourable report (success is the most likely outcome of the drug B research) or an unfavourable report (the research for drug B will most likely end up in failure). Success means that the medication with expected properties is created and approved by Health Canada. It is known that there is a 90% chance that EMRC provides a favourable report given the positive outcome. There is also an 80% chance that EMRC provides an unfavourable repot given the negative outcome- EMRC specialists need six months to complete their analysis and request $10 million as they have to use expensive equipment and hire additional staff. Of course, the company would like to get a report from EMRC before they make a decision and submit their proposal to Hirschmann Scientic Foundation. The company needs a qualied second opinion, as at the moment opinions among management itself are sharply divided and votes are split. ; ;r'* .Q 1": 4 - Please perform an analysis of the problem facing the Jean-Jacques Berthoud Pharmaceutical Company (Berthoud), and prepare a report that summarizes your ndings and recommendations. Include the following items in your report: 1. A (simple) decision tree that shows the logical sequence of the decision problem given the EMRC research information is not available. 2. A recommendation regarding what Berthoud should do if the EMRC information is not available. 3. A decision strategy that Berthoud should follow if the research is conducted based on the posterior probabilities and a revised decision tree. 4. A recommendation as to whether Berthoud should employ EMRC, along with the detailed decision policy, the value of the information provided by the research rm and the efciency of this information. Use Excel TreePlan to construct both decision trees. Include the details of your analysis as well as the Treele output as an appendix to your report. Great success PROFIT support success Some success Project A No success do not support Success support Failure Project B do not support Existing ledication O Favourable Great success PROFIT Moderate support success some success HIRE Project A No success Unfavourable do not support Success Simple support Do Not Decision HIRE Failure Tree Project B do not support Existing dicationsAssignment 1 (HINTS) STAT 2112 Simple Decision Tree Hint 1: We should identify the decision alternatives and start drawing a sketch of the simple decision tree. The company can apply for project A funding or for project B funding. In both cases, the financial support can be granted or denied. Also, the company might prefer not to apply and continue to produce the existing types of medications. Thus, we get the decision alternatives: Project A, or Project B, or Existing Medications. Project A Project B Existing Medications Hint 2: We have to develop each decision alternative. Say, for the project A, we have two main scenarios: the project A is supported (and we have to continue developing the scenario); the project A is not supported. support Project A O do not supportIf the company is denied the financial support for the project A, then it will continue to produce the existing types of medications with a guaranteed profit of $ .However, the cost of preparing the proposal for Hirschmann Scientific Foundation would still be $1 million. If funding is received for drug A, then, outcomes for drug A research can be: a great success and a profit of $ 1... or; a moderate success and a profit of $ XX ... ... or ; some success and a profit of . or; no success and loss of $ . On other words, Great success PROFIT Moderate support success O Some success No success Hint 3: We have to develop each decision alternative. Say, for the project B, we have two main scenarios: the project B is supported (and we have to continue developing the scenario); the project B is not supported. support Project B do not support