MAST90072 – Assignment 3 Instructions: Please complete the Plagiarism Declaration. (If you haven’t done that already.) Your solutions to the assignment should be left in the MAST90072 assignment boxes, located on the ground floor in the Richard Berry Building (north entrance). Don’t forget to staple your solutio
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MAST90072 – Assignment 3 Instructions: Please complete the Plagiarism Declaration. (If you haven’t done that already.) Your solutions to the assignment should be left in the MAST90072 assignment boxes, located on the ground floor in the Richard Berry Building (north entrance). Don’t forget to staple your solutions and to print your name, student ID, the subject name and code and your tutorial session. The submission deadline is 11:59 pm, Monday, 21st of May. (Remember, the building closes at 6 pm.) Many questions have short answers. Where interpreting data analyses, give careful and concise explanations. Clarity, neatness and style count. 1. In a survival analysis experiment, what three types of censoring are you likely to encounter. 2. Why is the logistic function P(x) = exp(x)/(1+exp(x)) employed to model probabilities as a function of x? Why not use a linear model? If P(x) is the probability of an event of interest as a function of x, give expressions for the odds of this event and the log-odds of the event as functions of x. 3. Your company has received complaints about the purity of a protein you have been producing. To study the problem the following alternatives were proposed: (a) Measure the purity of the first four batches produced each day. (b) Measure the purity of four batches sampled at random times during each day. (c) Measure the purity of four batches arising from taking a sample every two hours for each 8 hour working day. (d) Measure the purity of every batch produced. What are the benefits and potential problems associated with each of the method? Which would you recommend? 4. The SAS data set plasma from Exercise 7.1 Der & Deveritt was collected to relate erythrocoyte sedimentation rate (ESR) to two plasma proteins fibrinogen and γ-globulin. The value ESR= 0 represents a healthy individual and ESR=1 an unhealthy individual. Fit one logistic regression model to examine the relationship between ESR and the two proteins. Give a brief summary of your conclusions based on only this model. 5. The (artificial) data in the file loglin.dbf is the number of ecoli bacteria that grew in a media. The explanatory variables x.1 and x.2 represent the chemical composition of the media and x.3 relates to the amount of light. Fit one log linear Poisson regression model with all terms as main effects to these data. Give a brief summary of your conclusions based on only this model. 6. The SAS data set prostate (Exercise 8.2 of Der & Everitt) arose from a randomized trial to compare two treatments for prostate cancer. Treatment value 0 is the placebo, Status; 1=dead, 0=censored, Time is survival time in months, Age is age at trial entry, Haem is Serum haemoglobin level, size is the tumor size (cm squared) and Gleason is an index combining tumor stage and grade. Fit a proportional hazards model to determine the most important variables related to survival. Give a brief summary of your conclusions.
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