Show all working and provide all R functions. ( You will need to use the libraries epiTools, epiR, exact2x2 and DescTools.)

1. intensive treatment for type 1 diabetes: the DCCT study 10 points adapted from Baldi and Moore, exercise 20.44, 3rd edition For a long time, the medical community has been divided about how aggressively to control the blood glucose level of type 1 diabetes. One part of the Diabetes Control and Complications Trial (DCCT) study randomly assigned volunteers with type 1 diabetes with retinopathy (damage to the retina that can lead to blindness) before the study began to either the standard of care treatment or to a more intense treatment aimed at maintaining a blood glucose level as close to normal as possible. The health of both groups was closely monitored for 6 years. For some participants, their retinopathy continued to get worse (progression).

A. Fill in the missing values in the table above. Next, calculate the proportions of patients who progressed in each group

	Progression	No Progression	Total
Conventional Treatment	143		352
Intensive Treatment	77		363

B. Use the conditional probabilities you calculated above to estimate the risk difference and the relative risk, considering the conventional treatment as the "exposure." Show working

C. State the null and alternative hypotheses for the 2 test in terms of the risk difference and in terms of the relative risk.

D. Check that the conditions to use the 2 distribution to find the P value are satisfied.

E. Use R to generate a matrix of the counts . (Use the format that is suited to using the epitab function to find a confidence interval for the relative risk.) Carry out the 2 test. - Paste your R functions and results here

F. Interpret the 2 test: State the P value and the conclusion in the context of this problem, using either the relative risk or the risk difference. (Use = .05 )

G. Find a 95% confidence interval for the relative risk. Paste your R epitab function results here: You should recognize P(progression | conventional tmt) and P(progression | intensive tmt) in the output.