Regression Analysis and COVID-19 Testing: A Case Study

Part 1 – Prancing Ponies

It is early 2022, and Prancing Ponies is a household name in the pub industry in England and Wales. Prancing Ponies operates a network of pubs, restaurants, off-licenses and other outlets. After a challenging pandemic period, in which the company’s pubs had to be temporarily closed, the business has strongly rebounded since late 2021, and is now considered one to watch. In an effort to improve the selection of sites for Prancing Ponies pubs in the future, the company has been analysing data from its existing pubs in an attempt to understand the main determinants of cost and revenue.

The Excel file Prancing_Ponies.xlsx contains details of revenues for the past year (Revenue), measured in £millions, for 47 of Prancing Ponies’ pubs. The other variables relate to data currently available at head office. This includes information on management (Management) and staff quality (Staff), both on 9- point scales (with 9 being very good and 1 being very poor); a measure of local per capita annual income (LocalIncome) measured in £000s; and an index of competitor density (Competition) measured in number of pubs within 2 miles of the site.

There is also a dummy variable (ModernType), indicating the type of establishment. A value of 1 for ModernType indicates that the pub has a modern or unusual theme/ambience, and a value of 0 indicates that the pub is of a conventional type. Lastly, there is a variable (Location) that indicates the approximate location of the pub. For this variable, values of 1, 2, 3, 4 and 5 represent the midlands, north, east, south and west, respectively.

(a) Develop a regression model for revenue using the variables available. In your report, make sure to describe your modelling process, and to interpret your final model. (30 marks)

(b) Described below are the details of two sites, which have been offered to Prancing Ponies. Which, if either, would you recommend the company should buy? (10 marks)

A rare opportunity to convert a disused church, St Peter’s, in Leamington Spa. The marketing department is wild about the idea, which has made a number of people sceptical. There are currently 9 restaurants within 2 miles of the site, and market studies have suggested that a couple more could open within the next 12 months.

Proponents of this site have suggested that this level of competition will draw customers to the site. Staffing is not thought to be a problem, except that finding the right manager may be a little more difficult. Recent years have seen a number of tech companies moving into the area, pushing up the per capita income to £32,000 per year. Fixed and running costs, including rent, are thought to be around £1.5m per annum.

Part 2 – COVID Testing (find data from credible sources and make sure to reference)

An old family-owned restaurant near Southwold on the Suffolk coast. The owners have run the place profitably for many years and now wish to retire. The competition density is 2 pubs within 2 miles of the site, the exterior is pleasant but in need of minor repairs and re- thatching. The current members of staff live in the charming village of Clearwater, and are believed to be trustworthy and loyal. An experienced manager at one of the chain’s London locations appears to be interested in relocating there, since it is close to her home town.

However, if a relocation deal cannot be made with this particular manager, it is unclear how difficult it is to hire a quality alternative locally. Average per capita income in the area is £26,000 per annum, which is relatively low due to many of the villagers being agricultural workers. Estimated fixed and running costs, including rent, are about £1.1m.

(a) Obtain the reported sensitivity and specificity for a lateral flow (LF) test and for a polymerase chain reaction (PCR) test for Covid-19. Interpret these values, and discuss the relative importance of the sensitivity and specificity for this test. (10 marks)

(b) Estimate the positive predictive values for the LF and PCR tests. Describe any assumptions you need to make. What information do these values convey? (15 marks)

Consider a hypothetical Region X that has been managing the COVID pandemic effectively, through a package of public health measures (social distancing, vaccination, etc.) and a strict mandatory quarantine for international visitors. As a result, the COVID cases, hospitalisations and death figures have been consistently held below the international average through the previous waves of the pandemic.

However, two years into the pandemic, the trade-dependent economy of Region X has suffered major the negative impact of tight border controls. Economists have estimated that, for each visitor put through mandatory quarantine, the effective monetary and social costs amount to (the local currency equivalent of) £1,000.

Thus, under strong political pressure, the government has decided to remove the mandatory quarantine requirement going forward. Instead, it has commissioned its Public Health Department (PHD) to analyse potential effect of a test-on-arrival strategy.

 
Based on your answers to Part 2 above, the PHD is considering to offer mandatory (LF or PCR) tests to international visitors on arrival, and require only those who test positive to quarantine. If the tests fail to identify a visitor carrying the virus, this may potentially cause a local outbreak.

A combined epidemiological and economic analysis estimates that each such ‘breakthrough’ case would lead to a cost of £20,000 to the public health system and the economy. While the PCR tests are more accurate (from Part 2a), they are also more expensive, costing £100 per visitor, compared with £25 per visitor for the LF tests. However, some officials have also complained about the high costs of these tests and have proposed to lift the quarantine requirements altogether and resume the pre-pandemic policy requiring neither tests nor quarantines.

(a) Develop a decision tree model to identify the optimal testing strategy for Region X. You may reuse the data, calculations and assumptions regarding the tests based on your answer to Part 2, and/or make any further assumptions. (15 marks)

(b) The estimated cost of a ‘breakthrough’ case (i.e., £20,000) is based on a complex model with many assumptions. The epidemiologists and economists have provided a 95% confidence interval of [£8,000, £32,000]. How would the optimal decision depend on the possible inaccuracies in this cost estimate? (10 marks)

(c) How does the optimal decision change with respect to the prevalence rate of COVID in the countries that visitors travel from? (10 marks)