MAT009/MA4609/20 -1- CARDIFF UNIVERSITY EXAMINATION PAPER Academic Year: 2019-2020 Examination Period: Spring Examination Paper Number: MAT009 / MA4609 Examination Paper Title: Healthcare Modelling Duration: THREE hours (from the release of the paper to the submission deadline for solutions) Structure of Examination Paper: There are FIVE pages. There are FOUR questions in total. There are no appendices. The mark obtainable for a question or part of a question is shown in square brackets alongside the question. Instructions to Students: Answer ANY THREE questions. Please note for question 4: if you don’t have graph paper, an approximate plot on plain or lined paper is perfectly acceptable. MAT009/MA4609/20 -2- 1 (i) Provide definitions for the following terms: Immunity Latent period Infectious period Incubation period [15%] (ii) Consider a non-fatal contagious childhood disease, whereby infected children will recover from the illness. A differential equation model to track the dynamics of the spread of such a disease within a population of children is to be developed with the following assumptions: There is a fixed size population of children, n. S denotes the number of susceptible children in the population. I denotes the number of infected children in the population. R denotes the number of recovered children in the population. b is the infection rate (the proportion of SI contacts which lead to a new infection) r denotes the recovery rate per unit time. Clearly stating any assumptions you make, derive (but do not solve) the necessary equations to capture the rate of change of S, I and R. [20%] (iii) State the required conditions for the spread of the contagious childhood disease to become endemic and briefly describe ways in which health officials might try to reduce the chances of an endemic. [15%] (iv) Now assume that the population is not of a fixed size. Let u be the average birth/arrival rate of children into the population per unit time and v be the rate of children leaving the population per unit time. Derive the new equations (but do not solve) for the rate of change of S, I and R. [20%] (v) Further observations suggest that children can in fact repeatedly catch the illness, thus moving between susceptible and infected states. Building on your answer to part (iv) above, derive the new equations (but do not solve) for the rate of change of S and I. [15%] (vi) Suggest and briefly describe an alternative OR method that could be used to more realistically model the spread of a contagious childhood disease. [15%] MAT009/MA4609/20 -3- 2 The following diagram illustrates the progress of patients with Diabetic Neuropathy. Neuropathy is a complication of diabetes that damages the nerves and can lead to ulceration and a condition called Charcot Joint, a severe and debilitating bone complication. Eventually this can lead to the need for amputation. (i) Describe how you might consider the above natural history as a Markov model. Your discussion should include details on data needs and parameter estimation, and the nature of model outputs that could be calculated. [25%] (ii) List the advantages and disadvantages of a Markov approach to modelling Diabetic Neuropathy. [25%] A new drug is available for patients suffering with Charcot Joint that prevents bones from further deterioration and hopefully avoids the need for amputation. NICE (National Institute of Health and Clinical Excellence) is considering whether to provide the drug to patients with Charcot Joint. NICE have requested your assistance. (iii) Outline how you would undertake a cost effectiveness analysis using the Markov model described in (i). Ensure you include definitions of any terms used in your answer. [25%] (iv) Describe how classification tools such as CART could be useful to your analysis and feed into any models you develop for NICE. Your discussion should include a brief explanation of the CART methodology. [25%] Diabetes Neuropathy Ulceration Charcot Joint Amputation MAT009/MA4609/20 -4- 3 System Dynamics (SD) and Discrete Event Simulation (DES) are two well-known simulation techniques used in healthcare modelling. i) Briefly outline the main features of both approaches and describe how you would decide on which approach to use for a particular healthcare issue, listing the criteria that you might use. [30%] Pressure on hospitals is heavy because of limited resources and increasing patient demands. The provision of adequate numbers of beds and appropriate workforce are national concerns. You have been asked by a local hospital to help them develop practical detailed models that provide the necessary information for answering a variety of “What if ..” questions. Examples are the effects of changes in: Number of patients Number of beds for elective and emergency patients Workforce planning ii) Describe in detail how you would work with the hospital to develop such models. Your description should outline the kind of information and data you would require, and the nature and functionality of the models that you would build. [70%] MAT009/MA4609/20 -5x- 4 The following table shows the survival times (in days) for patients diagnosed with end- stage renal disease (ESRD). Group 1 patients received a new drug; Group 2 patients received a placebo. Group 1 n = 10 Group 2 n = 10 60, 60, 60, 60+, 100, 140, 140, 190+, 220, 320+ 10, 10, 20, 40, 60, 80, 80, 80, 100, 120 where + denotes censored data. i) What is meant by the terms: survival time and censored data [10%] ii) For each group (separately) put the data into standard survival time tabular form, calculating S(t), the probability of surviving to time t. [25%] iii) Draw the Kaplain-Meier survival curve for each group on the same graph (if you don’t have graph paper, an approximate plot on plain or lined paper is perfectly acceptable) [25%] iv) Calculate the median survival time for each group. [10%] v) Create a log-rank test table and go on to calculate the log-rank statistic to test the following hypothesis: H0: no difference between survival times for group 1 and group 2 patients. What does this tell you about the effectiveness of the new drug for ESRD (Note that a 2 with 1 df = 3.84 at the 95% level and 6.63 at the 99% level) [30%]
