Final Project
STAT 3303: Bayesian Analysis and Statistical Decision Making
Due: Tuesday, April 26, 2022 (submit on Carmen by midnight)
INSTRUCTIONS
This is an exam and should be treated as such. DO NOT discuss any aspect of this exam with anyone other
than your instructor. This includes, but is not limited to, not discussing report structure, coding problems,
instructor expectations, how long the exam took you, whether you finished it, etc. You are responsible for
ensuring that other students do not have access to your exam. Any violation of these instructions constitutes
academic misconduct and will be reported to the university’s Committee on Academic Misconduct.
In response to growing concerns about a new strain of influenza (K9C9) that has been identified in humans
in 10 countries across the world, medical researchers have developed an inexpensive diagnostic test (named
“EZK”). Unfortunately, the EZK diagnostic test is not perfect as it can result in false positives and false
negatives. For this exam, you will analyze data related to this new diagnostic test.
In an effort to quickly assess the diagnostic ability of EZK, the World Health Organization sponsored a
small clinical trial run in each of 10 countries where the K9C9 virus in endemic. Using a highly accurate
(very expensive) diagnostic test, 100 randomly selected subjects in each country were tested for K9C9 – it
can be assumed that the highly accurate and expensive test gives results without error. Each subject was
then administered the EZK test. As expected, not all of the results of the EZK test agreed with the highly
accurate diagnostic results. In the data set flu.txt (available on Carmen), the following variables contain
the results of the clinical trial:
Infected binary indicator of whether the subject is infected (1) or not infected (0) according the highly
accurate diagnostic test
EZK binary indicator of whether the subject’s EZK test was positive (1) or negative (0)
Country country of residence of the subject, where the countries are labeled A-J
Propose a Bayesian hierarchical model for K9C9 status, with Infected as the outcome. After an ap-
propriate transformation, model the probability of a subject having the virus as determined by the highly
accurate test (Infected) as a parametric function (i.e., a function with unknown parameters) of the results
of the EZK test, EZK. Explain how your model can be used to assess the diagnostic ability of the EZK test.
Allow model parameters to vary across country using a hierarchical model structure to account for potential
genetic variation in the virus (i.e., BOTH the virus and accuracy of the tests may be slightly different across
countries). Fit your model and provide appropriate and interesting summaries of your results.
An insurance provider in Country D would like to use your results from to decide whether it is cost effective
to treat patients who test positive for K9C9 using the the EZK test with a drug called Neonicon. (Rolling out
the highly accurate test for use on the general population is known to be cost prohibitive.) The cost to the
insurance company of treating an individual with Neonicon, regardless of whether the individual has K9C9
or not, is $457, and if an infected individual is treated he/she is not expected to generate any additional costs
to the insurance company as a result of complications from the infection. If an infected individual does not
receive Neonicon, the cost to the insurance company is $1,490, which takes into account the potential medi-
cal complications that may arise from not treating the individual. There is no cost to the insurance company
of uninfected individuals not being treated. Using inferences derived from your hierarchical Bayesian model
and a decision theoretic criterion, should the insurance company approve Neonicon presciption for individ-
uals who test positive for K9C9 on the EZK test? Be sure to explain how you come to your conclusion about
what the insurance company should do, assuming the insurance company’s goal is only to minimize costs.
In writing your response be sure to:
1. Define all variables and interpret model parameters in the context of the problem.
2. Specify your model in detail, including conditional independence and prior assumptions (providing
just your code is NOT sufficient).
3. Provide details on model fitting (what were your starting values, how many iterations did your algo-
rithm run, how did you diagnose convergence of the model fitting algorithm).
4. Provide interpretations of the results of your statistical analysis in the context of the problem.
5. Explain your reasoning behind the decision of the insurance company to treat patients with Neonicon.
These are the formatting guidelines:
• Your report should be typed. You may use R Markdown if you wish, but DO NOT include any code
in the main body of your report.
• Carefully proofread and spell check your report. Write in complete sentences and in paragraphs, not
bulleted lists.
• Define all mathematical notation in the text of the report.
• Make sure all figures/tables are straightforward to understand, have captions, and are referenced in
the text.
• Include commented code in an appendix.
• You may assume that the reader is familiar with Bayesian statistics, but not that they are familiar with
the content of STAT 3303. For example, do not refer to specific examples that have been discussed in
lecture or homework.
Your report should be no longer than six pages double-spaced, including figures and tables. (Text, figures,
and tables that are after six pages may not be considered by the instructor.) Your appendix with code does
not count toward the six page limit.
Submit your final exam report as a single PDF file on Carmen before the deadline.
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