R语言代写: MAS281 Block 1 Assignment 1

MAS281 Block 1 Assignment 1 Background

You are working for a Contract Research Organisation specialising in health technology ap- praisals. Your organisation has been commissioned by a pharmaceutical company to produce a cost-effectiveness analysis for their new drug for osteoporosis, for submission to NICE. The analysis will present the case for the use of a new drug for (female) patients aged 70 or older. In the following, Drug 1 refers to another drug currently used in the NHS, and Drug 2 is the pharmaceutical company’s new drug, recently licensed, but not currently approved for used in the NHS.

2 The economic model

Following discussion with your clinical advisers, the health economic decision model to be used should have the following structure.

• Costs and QALYs are to be considered over three years of treatment.
• In any given year, a patient is at risk of suffering a bone fracture. The risk is unchanged as long as the patient has no history of bone fractures, but once a fracture has occurred, the risk of subsequent fractures is expected to increase. The risk of fracture will not change a second time following any further fractures. Assume a maximum of one bone fracture per year.
• One year of treatment on Drug 1 costs £5000, and one year of treatment on Drug 2 costs £8000. Patients will get the same drug each year for three years. Assume that all patients will require three years of treatment.
• For each year without a bone fracture, assume the patient accrues 1 QALY. In any year with a bone fracture, the mean QALY accrued is Qf .
• In any year with a bone fracture, a patient will need additional healthcare. The mean cost per patient of this additional healthcare is £Tf .
• A patient on Drug i (with i = 1, 2) has a probability of θi of suffering a bone fracture in any given year, assuming no previous bone fractures.
• A patient on Drug i (with i = 1, 2) has a probability of φi of suffering a bone fracture in any given year, given one or more previous bone fractures.
• Assume all patients at the start of year 1 have not had any prior bone fractures. 1

3 Distributions and data

Assume the following distributions for Qf and Cf
Qf ∼ N (0.6, 0.022 ),

ln Tf ∼ N (8.5, 0.12 ).
In a small trial, patients (aged 70) without a prior fracture were allocated to one of the two

drugs. Numbers of patients suffering a fracture within one year were as follows: Total no. of patients No. of patients having fractures

drug 1 72 drug 2 80

25 10

In an additional trial, patients (aged 70) who already had at least one fracture were allocated to one of the two drugs. Numbers of patients suffering a fracture within one year were as follows:

Total no. of patients No. of patients having fractures

drug 1 55 drug 2 30

25 8

Assume that there is no other information about the effectiveness of the drugs.

4 Tasks

1. Derive formulae for the mean costs and QALYs over the three years, for patients on each drug. Explain carefully how your formulae have been obtained.
2. Calculate the ICER for Drug 2 against Drug 1 (i.e cost per QALY gained if Drug 2 is used for the patient population instead of Drug 1), at the following parameter values:θ1 = 0.35,θ2 = 0.125,φ1 = 0.45,φ2 = 0.27,Qf = 0.6,Tf = 5000.
   If the parameter values were all correct, comment on whether the ICER indicates that

   Drug 2 is cost-effective, compared with Drug 1.

3. Write a function in R that will calculate mean costs and QALYs for the two drugs, as a function of the parameters θ1, θ2, φ1, φ2, Qf , Tf . Use your function to verify that your calculation in (2) is correct.
4. Conduct a Probabilistic Sensitivity Analysis (PSA) to investigate uncertainty in as many parameters as you can, using the distributions and information given in Section 3. Partial credit will be given if you only consider uncertainty in some of the parameters. For any parameter that you are not able to treat as uncertain, use the value specified in Task 2.

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• Include any plots that you think are appropriate.
• After any plot, you must explain clearly what information the plot provides to NICE,

regarding the cost-effectiveness of Drug 2 compared with Drug 1.
5. Comment on whether, in your submission to NICE, you can make the case for a Fast

Track Appraisal for Drug 2.

Plagiarism and collusion

Your submitted project must be entirely your own work. You can ask me for general help with R, or the course material, but you are not allowed to ask anyone else for help with this project, and you should not show your work to anyone else. The University guidelines on plagiarism and collusion are available here.

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Presentation

Present an individual solution to each Task: you do not need to write up your analysis in the style of a report.

Include all R code, and show clearly how you have obtained each result.

For Tasks 2 and 4, you must present and discuss your results separately to any R output: simply presenting the R output will not get full credit.

You are not expected to write a long discussion of any result: keep the discussion short and to the point.

All graphs should be well-presented, with suitable axes labels, captions, font sizes etc. For guidance, see Section 3 in http://www.jeremy-oakley.staff.shef.ac.uk/MAS6005/index.html

5% of the total mark for this assigment will be awarded for preparing your report with RMarkdown.

Please write your registration number only on your project.

7 Deadline

Hand in your project to F10 by 4pm on Monday 26th February. You will need to print off a coversheet first.