Statins are A Major Success Story in Modern Drug Treatment - Statistics Assignment Help

Assignment Task

This assignment covers material in chapters 16–18 of the Unit Notes. All statistical analysis and  graphs must be done using R. Data files are available on the Data Files page on LMS. Relevant R output must be included with your assignment. 
Total marks = 51. 
1. Based on past experience with clinical use of a hypertension drug, a drug company expects that,  if the drug is administered under medical supervision to 4 randomly selected hypertension  patients who were previously untreated, the number whose hypertension is brought under  control will follow this distribution: 
No. brought under control 0 1 2 3 4 
Proportion .004 .047 .211 .422 .316 
The company supplied the drug to 128 doctors who agreed to use it on their next 4 hypertensive  patients. 21 of the doctors were successful with all 4 patients, 63 were successful with 3, 34 succeeded with just 2 patients, and 9 succeeded with only 1 of their next 4 patients. (Here  “succeeded” means “brought the patient’s hypertension under control”.) Are these results  consistent with the distribution of successes expected by the company? Evaluate with a  suitable hypothesis test at 5% significance level, taking care to evaluate and address any  concerns over the assumptions. 
2. Statins are a major success story in modern drug treatment of high LDL cholesterol levels. They  are widely prescribed and their side-effects have been extensively studied.  
One such study advertised online for Australian volunteers aged 25 – 55 years who were either  (a) currently taking statins under medical supervision, or (b) were not taking statins at all. A  small fee was offered to accepted participants, and photographic evidence of identity was  required (e.g., driver’s licence). Volunteers were screened to ensure that none had the same  street address or internet address, or belonged to the same family, and no more than 5 shared  the same postcode. No applications were accepted from internet addresses that lay outside  Australia or appeared to be aliases. After screening, accepted participants were asked to  maintain a daily health journal for a week via an online form that asked about a wide range of  possible side-effects. Confirmation of statin dosage (if any) was obtained from their doctor. 
The table below summarises participants’ journal entries regarding headaches, classified by  statin dose. 
0 mg 10 mg 20 mg 40 mg 80 mg 
Test the hypothesis that, among Australians aged 25 – 55 years, occurrence of headache is  unrelated to statin dose. Include discussion of assumptions and take appropriate action  regarding any problems. If you conclude that there is a relationship, describe it. Use a 5%  significance level. You may assume that the checks on identity and location are adequate.

3. Two deformities of the foot are hallux abducto valgus (HAV) and metatarsus adductus (MA).  HAV is uncommon in youth, but when it occurs it often requires surgery. MA is common but  usually self-correcting. Doctors measured the angles of deformation relevant to both conditions  in 38 young patients who presented for surgery to correct HAV. The data are in the file Feet.csv.  The column headings are – 
HAV The HAV deformation angle in degrees 
MA The MA deformation angle in degrees 
(a) Obtain the following R output, treating HAV as the response variable: 
(i) scatter plot [3] (ii) standardised residual plot [2] (iii) distribution of residuals [3] (iv) regression analysis. [2, total = 10] 
(b) What statistical model is assumed in the regression analysis? [2] (c) As far as possible, assess the extent to which the model is appropriate to the data. [5] 
(d) Use an appropriate hypothesis test to evaluate the evidence that HAV angle is related to  MA angle among young patients presenting for HAV surgery. Use a 5% significance level,  and describe any relationship you find. [5] 
(e) Provide a 90% prediction interval for the HAV angle expected in a young patient whose MA  angle is 21°. [4] 

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